Research ArticleImpact of Heterogeneity on Opinion DynamicsHeterogeneous Interaction Model

Xi Chen Zhan Wu Hongwei Wang and Wei Li

School of Automation Huazhong University of Science and Technology Key Laboratory of Ministry of Education forImage Processing and Intelligent Control Wuhan 430074 China

Correspondence should be addressed to Wei Li liwei0828mailhusteducn

Received 19 December 2016 Accepted 22 March 2017 Published 24 April 2017

Academic Editor Alicia Cordero

Copyright copy 2017 Xi Chen et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Considering the impact that physical distance and other properties have on the change of opinions this paper introduces anintensionmodel of theHegselmann-Krause (KH)modelmdashheterogeneous interaction (HI)model Based on the classical KHmodelHI model designs new interaction rules and the interactive radius considering the impact of heterogeneous attributes such asphysical distance individual conformity and authority The experiment results show that the opinion evolution of the HI modelwill be similar to the classic KH model when the interactive radius is above the particular threshold value (120590 gt 600) Unlike theKH model which leads to the polarization phenomenon most agents reach a consensus in HI model when the confidence radiusequals 02 and the interactive radius remains within regulatory limits (150 lt 120590 lt 520) The conclusions show that interactiveradius affects public opinion evolution HI model can explain more conscious opinion evolution in real life and has significancethat effectively guides public opinion

1 Introduction

As a social phenomenon in the social system public opin-ion has attracted considerable interest from researchers indifferent scientific fields A news article may spread globallyin just a few seconds and further becomes a macroscopicnetwork for public opinion [1] Such rapid transmissioncan adversely affect peoplersquos normal and orderly lives astate which may have considerable effect on the order ofour society If the propagation law of public opinion incommunications media and new media is allowed to playout it will result in negative consequences for social stabilityin certain locales and situations Public opinion evolutionis a highly complex process [2] and it is influenced byindividual and environmental factors with dynamics [3] Theevolutionary model of public opinion is becoming a focalpoint for research in the study of public opinion

At present the most frequently used opinion dynamicsmodels include the Deffuant model [4] Hegselmann-Krausemodel [5] and Sznajd model [6] The KH model is thetypical model At each discrete time every individual setsthe average value of the neighborrsquos opinion which is less

than a confidence threshold as the next moment individualrsquosopinion in the KH model With the change in size of theconfidence threshold the overall evolution of public opinionis divided into discrete polarization and consensus [7 8]which is similar to real life situations In real life however theupdate of an individualrsquos opinion will be affected by a varietyof aspects such as psychological factors and social influenceThe evolutionary process will be more complex

In a recent study considering the different environmentsand conditions in the evolution process many improved KHmodels were put forward When public opinion evolutionoccurred on the Internet considering that the individual isunable to obtain all individualsrsquo opinions Chen et al [9]proposed a high-effect priority bounded confidence modelbased on confidence threshold and social influence and itcontains a dual mechanism In real life all individuals arenot the same and their confidence thresholds are differentLorenz [10] proposed an improved KH model whereinthe confidence threshold is heterogeneous and divided theagents into open-minded and closed-minded agents Con-sidering the influence of authority control on the publicopinion Chen et al [11] proposed a network model of

HindawiComplexityVolume 2017 Article ID 5802182 10 pageshttpsdoiorg10115520175802182

2 Complexity

pinning control Considering the opinion exchange betweenindividuals is not decided by unilateral decision the modelconsiders the interplay between individual ability factorsLiang et al [12] put forward an opinion dynamics modelbased on heterogeneous confidence parameters and socialpower but this model only considers the heterogeneity ofindividual confidence threshold without fully consideringindividual heterogeneity In 2013 Jalili [13] put forwardan opinion evolution model based on the difference inindividuals and imported social influence on a small numberof individuals and then used this small group to guide attitudechange This model defines social influence that is basedon the difference of the network topology and ignores theindividualrsquos heterogeneity on the role of social influenceAlthough the above models consider many factors duringevolution they still lack consideration of some aspects suchas individual heterogeneity and interactive radius

Previous studies have explained the public opinion phe-nomenon in a real society but rarely consider the impact ofspatial constraints on opinion exchange They assume thatindividuals are homogenous and failed to consider differentindividual attributes In fact full contact of any person to allthe other individuals is impossible As personal resources arefinite there is a limit on communication space assumed asspatial constraints Through long-term survey psychologistsfound that with closer geographical location individualshave more communication and interaction Li and Zhangintroduced an eyeshot mechanism similar to spatial con-straints and investigated the effect of eyeshot on opiniondynamics However the model is set on square lattices andindividual property heterogeneity is not considered [14] Ifall other conditions remain the same adjacent people havemore opportunity to meet with each other and know moreabout each other and thus are more likely to form a trustrelationship Individuals who live in different localities formsocial groups with different languages cultural backgroundreligious belief and national tradition owing to the naturalgeological barriers The same social groups of people have ahigher recognition and trust level and the communicationbetween each other is more easily and more likely to havea similar attitude because of factors such as language andculture Communication between individuals of two differentsocial groups may produce the opposite results owing tobackground difference In general language cultural back-ground religious beliefs traditional factors and so forth havethe characteristics of geographical location convergence

In this thesis we introduce spatial constraints into mod-eling the evolution process of public opinion Local commu-nication is formed under the limitation of physical distancebetween two individuals Combined with the researches inpsychology and sociology new factors including individualattributes personality characteristics and public authorityare expressed quantitatively Using the agent-based methodan evolutionary model of public opinion based on physicaldistance is developed Through comparisons with two clas-sical bounded confidence models our results are in goodagreement with the new features in the expansion of humancommunication and provide a comprehensive explanationfor the evolution of public opinion in real social systems

2 Heterogeneous Interaction Model

In this section we construct an evolution modelmdashHeter-ogeneous Interaction Model (HI) Firstly we provide adetailed illustration about some related definitions whichplay a vital role during the evolution process Based on thesepreliminaries we provide a description of some assumptionsabout the model Subsequently we present the algorithm ofHI model

21 Attributes of Individuals In previous studies of opinionmodeling the heterogeneity of individuals has been unrep-resented and individuals in social networks were assumedto be identical It is evident that different social individualsmanifest various social attributes and have different waysof forming their opinions In our model several importantinfluence factors are abstracted and quantified to representthe heterogeneity among individuals

(1) Character Trait It can be concluded that opinion for-mation is greatly affected by character trait of a personIn the real world the degree of belief in rumors dependson the individual itself A conformity parameter is definedto measure the different degree of opinion variation 120582119894 isassigned to agent 119894 to denote the individual conformity [15]of agent 119894 Extremists are introduced on behalf of the type ofpeople who refuse to change their attitude or wholly followothers in the evolution process In general extremists onlytake a small portion Conformity parameter assignment isbased on the principle of 8020The Italian economist Paretoproposed the 8020 rule He believes that for many eventsthe most important part which plays a decisive role is onlyapproximately 20 and the remaining 80 is secondary andnonconclusive After long-term exploration many imbalancephenomena in life have been discovered that can be explainedby the 8020 rule which has beenwidely used in fields such associology and businessmanagement In ourmodel about 20of people are considered as extremists and 80 of individualsare ordinary individuals The values are taken into accountaccording to the following criteria (Figure 1)

(a) 10 of individuals are the dogmatic people with 120582119894 =01

(b) 10 of individuals are the copycats with 120582119894 = 09(c) 80of individuals are the easy-going people with120582119894 =

05

(2) Geographic Position Spatial constraints are quantifiedthrough the physical distance between two individualsHence geographic position is introduced to compute thephysical distance between two individuals Geographicalposition determines the community a person belongs toThephysical distance between two individuals determines localcommunication with others in the system which is a betterway to describe information exchange in a so-called realisticsociety The reference collection one can communicate withis decided by geographic position which is the core conditionfor modeling opinion dynamics We use two-dimensionalcoordinates to represent geographic positions of individuals

Complexity 3

0

100

200

300

400

500

600

700

800

900

1000

Individual conformity

Freq

uenc

y

0 01 02 03 04 05 06 07 08 09 1

Figure 1 Individual conformity distribution

(119883119894 119884119895) is assigned to agent 119894 to denote the geographicposition of agent 119894 The maximum value of both 119883119894 and 119884119894is 119889max The physical distance between agent 119894 and agent 119895 isquantified as

119889 (119894 119895) = radic(119883119894 minus 119883119895)2 + (119884119894 minus 119884119895)2 (1)

An interactive radius parametermdash120575 is assigned to agent119894 on behalf of the communication ability 120575 determines thereference collection one has access to

(3) Public Authority Generally speaking individuals of highprestige or great social power would be more widespread andhave greater acceptance among common people To repre-sent the diversity of attributes among individuals a publicauthority parameter is assigned to each agent regarding socialinfluence on neighbors in opinion exchange which is relatedto the individual attributes

To quantify the individual public authority [16] we referto the fifth population census data of China and consider ageeconomic level and educational attainment as the three mostimportant factors in determining public authority Otherissues are considered as a random factorThe public authorityof the individual 119894 is computed as

PA119894 = [1199081 1199082 1199083 1199084] sdot [119878age 119878economy 119878edu 119878other]119879 (2)

where 1199081 + 1199082 + 1199083 + 1199084 = 1 and 119878age 119878economy 119878edu 119878otherrespectively denote the age economic level educationalattainment and a random factorThe values of public author-ity are a real number between [0 1] distributed as Figure 2A public authority is entirely different from social power [13]The definition of social power is SP119894 = (119896119894)120572 where 119896 isthe degree of the individual 119894 Social power only considersthe heterogeneity impact of network topology without taking

0

100

200

300

400

500

600

700

800

900

1000

Individual public authority

Freq

uenc

y

0 01 02 03 04 05 06 07 08 09 1

Figure 2 Individual public authority distribution

into account individual attributes Public authority proposedin our model is only related to individual attributes

22Model Assumptions Beforewemodel the evolution proc-ess we give a description of some assumptions about themodel

(a) Opinion evolution follows the principle of boundedconfidence which means that only people with simi-lar opinions talk to each other

(b) As individual resources are finite it is impossiblefor any individual to get in touch with all the otherpersons and there is a limit on the communicationspace assumed as spatial constraints

(c) Different social individuals manifest various socialattributes and social power

(d) Public media is ignored during the process of opinionevolution

23 Algorithm Description By the above hypothesis we nowpresent the HI model according to the behavior characteris-tics of individual interaction Consider a system consistingof 119873 agents Assume that agent 119894 keeps a real number repre-senting hisher initial opinion 119909119894(119905) randomly distributed inthe range of 0sim1 where 0 stands for extreme agreement and1 stands for extreme disagreement All of the agents have thesame confidences radius 120576 and the same interactive radius 120590At each discrete time 119905 opinion update process is performedonce including the reference collection calculation exchangecollection calculation and opinion update in turn

(1) Reference Collection Calculation Under the condition ofspatial constraints only individuals within a certain range ofspace would be considered when the individual 119894 interacts

4 Complexity

in perspective Moreover the collection constituted by theseindividuals is called a reference collection of the individual119894 For a given time 119905 the physical distance radius 119889119894 ofthe individual 119894 defines the size of the reference collectionThe reference collection Distance(119894) of individual 119894 can becalculated as follows

Distance (119894) 119895 | 0 lt 119889 (119894 119895) lt 120575 1 le 119895 le 119873 119895 = 119894 (3)

In the above equation the physical distance radius 120575 is afixed constant

(2) Exchange Collection Calculation According to the size oftheir trust in the neighborhood an individual with a certainscope of opinion difference would be chosen The collectionconstituted by these individuals is called exchange collectionof the individual 119894 For a given time 119905 the exchange collectionNeighbor(119894) of node 119894 is decided by the radius of trust 120576119894and reference collection Distance(119894) Its can be calculated asfollows

Neighbor (119894) 119895 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 lt 120576119894 119895 isin Distance (119894) 119895 = 119894 (4)

As can be seen from the equation the individual isexcluded from the exchange collection by the filtration ofreference collection in HI model However the individualhimself must be included in the exchange collection of classi-cal limited trust model Therefore the exchange collection ofHI model may be empty

(3) Opinion Update When the exchange collection is deter-mined the system begins to exchange opinions In the nextmoment the individual 119894maintains his current opinion withprobability 1 minus 120582119894 and is affected by his trusted friend withprobability 120582119894 the influence of individual 119895 on individual 119894is proportional to the public authority PA119895 of the individual119895 When the exchange collection of individual 119894 is empty theopinion of the individual 119894 remains unchanged The opinionof individual 119894 at 119905 + 1 time is expressed as

119909119894 (119905 + 1)

= (1 minus 120582119894) 119909119894 (119905) + 120582119894sum

119895isin119873119894

PA119895sum119895 PA119895 times 119909119895 (119905) Neighbor (119894) = 120601

119909119894 (119905) Neighbor (119894) = 120601(5)

Opinion updating formula shows that the new opinion ofthe individual in the next moment is formed under the jointaction of the individualrsquos current opinion his personalitycharacteristics the opinion and public authority of trustedfriends

An algorithm flowchart of our proposed model is shownin Figure 3 Our model operates as follows

Step 1 (parameter initialization) Set appropriate parametersincluding the number of individuals physical distance radiusconfidence radius and evolution time

Beginning

Parameter initialization

Essential data generation

Calculate the exchangecollection

Opinion update

End

End of time or meetexternal terminationconditions

Evolution result output

Figure 3 HI model algorithm flowchart

Step 2 (essential data generation) According to statisticalproportion essential data is generated to initialize the basicattributes of each agent

Step 3 Calculate the exchange collection and the currentagent change opinion with according to (3) and (4)

Step 4 (opinion update is completed) If the exchange col-lection is not empty then the current individual updateshis opinion according to (5) at next step or his opinionwill remain unchanged Loop Steps 3 and 4 until all of theopinions achieve stable states Then the evolution is ended

Step 5 (evolution result output) Output the time evolutionresult of the individual opinions initial opinion distributioncurve and terminal opinion distribution curve

3 The Opinion Research ofHI Model in Full-Connected Networkand Scale-Free Network

According to the fifth population census data of China [17]this paper utilizes the statistical data of age proportionpopulation proportion in different geographical positionsand education level proportion respectively in juvenileyouth middle age and old age We obtained the economiccondition in the various regions Geographical distributionproportion age proportion and education proportion arepresented in Table 1

Complexity 5

Table 1 The statistical data of the fifth population consensus

Geographical distribution proportion ()East South West North Middle Southeast Northeast Southwest Northwest2286 1104 023 1177 2046 274 842 2095 153

Gender () Age ()Male Female Infants Child Juvenile Youth Middle-aged Elderly5163 4837 317 508 1467 3761 2976 971

Proportion of education among the juvenile () Proportion of education among the youth ()Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior268 7579 2153 0 204 2163 7035 598Proportion of education among the middle-aged () Proportion of education among the elderly ()

Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior888 3826 49 386 4755 3682 1358 205

The simulation environment is designed as follows

(1) Essential data of 1000 nodal attributes is generatedaccording to the statistical proportion of the fifthnational census

(2) The platform for essential data generation is devel-oped in C The simulation environment is Matlab2010b and the database is SQLServer 2008

(3) According to the fifth census data we can obtainthe individualrsquos physical location (119889max = 1000) Thephysical distance between agent 119894 and agent 119895 iscalculated from formula (4) The physical distancedistribution is shown in Figure 4

31The Comparison of HIModel and KHModel To comparethe differences between HI model and classical KH modelthis paper compares the opinion evolution of the two modelsin all connected networks and scale-free networks underthe same individual attributes (confidence radius physicaldistance and initial opinion) distribution Selections ofconfidence radius are 005 02 and 03 The initial opinionis random distribution between (0 1) Individual authorityand conformity are according to the distribution of Figures1 and 2 respectively As shown in Figure 4 80 of thephysical distance between two individuals is more than 600Therefore the interactive radius is set at 600

The evolution result in the full-connected network isshown in Figure 5The Figure indicates that the opinion evo-lution will be from discrete to polarization finally reaching aconsensus in bothHImodel andKHmodel with the increaseof confidence radius The evolutions of public opinion oftwo models are similar and the stable opinions are thesame However the convergence time is very different Theconvergence time of HImodel is longer than the convergencetime of KH mode As the limitation of the interactive radiusin HI model the evolution process tends to be slow

The evolution result in scale-free networks is shown inFigure 6 The opinion evolution will be from discrete topolarization finally reaching a consensus in both HI modeland KH model with the increase of confidence radiusHowever in a scale-free network no matter what kind of

0 100 200 300 400 500 600 700 800 900 1000 1100Distance

Distance

Fequ

ency

0

02

04

06

08

1

12

14

16

18

2

times105

Figure 4 The physical distance distribution

model the convergence time is longer than that in the full-connected network in the same situation This is because thenumber of individual joint nodes is reduced and it cannotreach a steady state in a short time which leads to an increasein the convergence time

From the above experimental result it shows that theevolution time will be longer when interactive radius limitsthe HI model In KH model without the limitation ofinteractive radius individuals can have more easy access toall other individual opinions in the system and update theiropinion in a relatively short time The global opinion couldreach a steady state quickly Also KH model ignores theinterpersonal influence and individual cognitive differencesand just puts the average value of the neighborrsquos opinionwhich is less than a confidence threshold with an ownopinion as for the next moment opinion However theinfluence of different neighbors on him is not the same whenindividual takes part in opinion interaction process in thereal world It makes the individual exchange opinion under

6 Complexity

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

Time

0

01

02

03

04

05

06

07

08

09

1

(a) 120576 = 005

10 20 30 40 50 60 70 80Time

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(b) 120576 = 02Time

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

Time10 20 30 40 50 60 70 80

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(c) 120576 = 03

Figure 5 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in full-connected network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(a) 120576 = 005

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(b) 120576 = 02

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 500Time

0010203040506070809

1

Opi

nion

(HI m

odel

)

(c) 120576 = 03

Figure 6 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in the scale-free network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

Complexity 3

0

100

200

300

400

500

600

700

800

900

1000

Individual conformity

Freq

uenc

y

0 01 02 03 04 05 06 07 08 09 1

Figure 1 Individual conformity distribution

(119883119894 119884119895) is assigned to agent 119894 to denote the geographicposition of agent 119894 The maximum value of both 119883119894 and 119884119894is 119889max The physical distance between agent 119894 and agent 119895 isquantified as

119889 (119894 119895) = radic(119883119894 minus 119883119895)2 + (119884119894 minus 119884119895)2 (1)

An interactive radius parametermdash120575 is assigned to agent119894 on behalf of the communication ability 120575 determines thereference collection one has access to

(3) Public Authority Generally speaking individuals of highprestige or great social power would be more widespread andhave greater acceptance among common people To repre-sent the diversity of attributes among individuals a publicauthority parameter is assigned to each agent regarding socialinfluence on neighbors in opinion exchange which is relatedto the individual attributes

To quantify the individual public authority [16] we referto the fifth population census data of China and consider ageeconomic level and educational attainment as the three mostimportant factors in determining public authority Otherissues are considered as a random factorThe public authorityof the individual 119894 is computed as

PA119894 = [1199081 1199082 1199083 1199084] sdot [119878age 119878economy 119878edu 119878other]119879 (2)

where 1199081 + 1199082 + 1199083 + 1199084 = 1 and 119878age 119878economy 119878edu 119878otherrespectively denote the age economic level educationalattainment and a random factorThe values of public author-ity are a real number between [0 1] distributed as Figure 2A public authority is entirely different from social power [13]The definition of social power is SP119894 = (119896119894)120572 where 119896 isthe degree of the individual 119894 Social power only considersthe heterogeneity impact of network topology without taking

0

100

200

300

400

500

600

700

800

900

1000

Individual public authority

Freq

uenc

y

0 01 02 03 04 05 06 07 08 09 1

Figure 2 Individual public authority distribution

into account individual attributes Public authority proposedin our model is only related to individual attributes

22Model Assumptions Beforewemodel the evolution proc-ess we give a description of some assumptions about themodel

(a) Opinion evolution follows the principle of boundedconfidence which means that only people with simi-lar opinions talk to each other

(b) As individual resources are finite it is impossiblefor any individual to get in touch with all the otherpersons and there is a limit on the communicationspace assumed as spatial constraints

(c) Different social individuals manifest various socialattributes and social power

(d) Public media is ignored during the process of opinionevolution

23 Algorithm Description By the above hypothesis we nowpresent the HI model according to the behavior characteris-tics of individual interaction Consider a system consistingof 119873 agents Assume that agent 119894 keeps a real number repre-senting hisher initial opinion 119909119894(119905) randomly distributed inthe range of 0sim1 where 0 stands for extreme agreement and1 stands for extreme disagreement All of the agents have thesame confidences radius 120576 and the same interactive radius 120590At each discrete time 119905 opinion update process is performedonce including the reference collection calculation exchangecollection calculation and opinion update in turn

(1) Reference Collection Calculation Under the condition ofspatial constraints only individuals within a certain range ofspace would be considered when the individual 119894 interacts

4 Complexity

in perspective Moreover the collection constituted by theseindividuals is called a reference collection of the individual119894 For a given time 119905 the physical distance radius 119889119894 ofthe individual 119894 defines the size of the reference collectionThe reference collection Distance(119894) of individual 119894 can becalculated as follows

Distance (119894) 119895 | 0 lt 119889 (119894 119895) lt 120575 1 le 119895 le 119873 119895 = 119894 (3)

In the above equation the physical distance radius 120575 is afixed constant

(2) Exchange Collection Calculation According to the size oftheir trust in the neighborhood an individual with a certainscope of opinion difference would be chosen The collectionconstituted by these individuals is called exchange collectionof the individual 119894 For a given time 119905 the exchange collectionNeighbor(119894) of node 119894 is decided by the radius of trust 120576119894and reference collection Distance(119894) Its can be calculated asfollows

Neighbor (119894) 119895 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 lt 120576119894 119895 isin Distance (119894) 119895 = 119894 (4)

As can be seen from the equation the individual isexcluded from the exchange collection by the filtration ofreference collection in HI model However the individualhimself must be included in the exchange collection of classi-cal limited trust model Therefore the exchange collection ofHI model may be empty

(3) Opinion Update When the exchange collection is deter-mined the system begins to exchange opinions In the nextmoment the individual 119894maintains his current opinion withprobability 1 minus 120582119894 and is affected by his trusted friend withprobability 120582119894 the influence of individual 119895 on individual 119894is proportional to the public authority PA119895 of the individual119895 When the exchange collection of individual 119894 is empty theopinion of the individual 119894 remains unchanged The opinionof individual 119894 at 119905 + 1 time is expressed as

119909119894 (119905 + 1)

= (1 minus 120582119894) 119909119894 (119905) + 120582119894sum

119895isin119873119894

PA119895sum119895 PA119895 times 119909119895 (119905) Neighbor (119894) = 120601

119909119894 (119905) Neighbor (119894) = 120601(5)

Opinion updating formula shows that the new opinion ofthe individual in the next moment is formed under the jointaction of the individualrsquos current opinion his personalitycharacteristics the opinion and public authority of trustedfriends

An algorithm flowchart of our proposed model is shownin Figure 3 Our model operates as follows

Step 1 (parameter initialization) Set appropriate parametersincluding the number of individuals physical distance radiusconfidence radius and evolution time

Beginning

Parameter initialization

Essential data generation

Calculate the exchangecollection

Opinion update

End

End of time or meetexternal terminationconditions

Evolution result output

Figure 3 HI model algorithm flowchart

Step 2 (essential data generation) According to statisticalproportion essential data is generated to initialize the basicattributes of each agent

Step 3 Calculate the exchange collection and the currentagent change opinion with according to (3) and (4)

Step 4 (opinion update is completed) If the exchange col-lection is not empty then the current individual updateshis opinion according to (5) at next step or his opinionwill remain unchanged Loop Steps 3 and 4 until all of theopinions achieve stable states Then the evolution is ended

Step 5 (evolution result output) Output the time evolutionresult of the individual opinions initial opinion distributioncurve and terminal opinion distribution curve

3 The Opinion Research ofHI Model in Full-Connected Networkand Scale-Free Network

According to the fifth population census data of China [17]this paper utilizes the statistical data of age proportionpopulation proportion in different geographical positionsand education level proportion respectively in juvenileyouth middle age and old age We obtained the economiccondition in the various regions Geographical distributionproportion age proportion and education proportion arepresented in Table 1

Complexity 5

Table 1 The statistical data of the fifth population consensus

Geographical distribution proportion ()East South West North Middle Southeast Northeast Southwest Northwest2286 1104 023 1177 2046 274 842 2095 153

Gender () Age ()Male Female Infants Child Juvenile Youth Middle-aged Elderly5163 4837 317 508 1467 3761 2976 971

Proportion of education among the juvenile () Proportion of education among the youth ()Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior268 7579 2153 0 204 2163 7035 598Proportion of education among the middle-aged () Proportion of education among the elderly ()

Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior888 3826 49 386 4755 3682 1358 205

The simulation environment is designed as follows

(1) Essential data of 1000 nodal attributes is generatedaccording to the statistical proportion of the fifthnational census

(2) The platform for essential data generation is devel-oped in C The simulation environment is Matlab2010b and the database is SQLServer 2008

(3) According to the fifth census data we can obtainthe individualrsquos physical location (119889max = 1000) Thephysical distance between agent 119894 and agent 119895 iscalculated from formula (4) The physical distancedistribution is shown in Figure 4

31The Comparison of HIModel and KHModel To comparethe differences between HI model and classical KH modelthis paper compares the opinion evolution of the two modelsin all connected networks and scale-free networks underthe same individual attributes (confidence radius physicaldistance and initial opinion) distribution Selections ofconfidence radius are 005 02 and 03 The initial opinionis random distribution between (0 1) Individual authorityand conformity are according to the distribution of Figures1 and 2 respectively As shown in Figure 4 80 of thephysical distance between two individuals is more than 600Therefore the interactive radius is set at 600

The evolution result in the full-connected network isshown in Figure 5The Figure indicates that the opinion evo-lution will be from discrete to polarization finally reaching aconsensus in bothHImodel andKHmodel with the increaseof confidence radius The evolutions of public opinion oftwo models are similar and the stable opinions are thesame However the convergence time is very different Theconvergence time of HImodel is longer than the convergencetime of KH mode As the limitation of the interactive radiusin HI model the evolution process tends to be slow

The evolution result in scale-free networks is shown inFigure 6 The opinion evolution will be from discrete topolarization finally reaching a consensus in both HI modeland KH model with the increase of confidence radiusHowever in a scale-free network no matter what kind of

0 100 200 300 400 500 600 700 800 900 1000 1100Distance

Distance

Fequ

ency

0

02

04

06

08

1

12

14

16

18

2

times105

Figure 4 The physical distance distribution

model the convergence time is longer than that in the full-connected network in the same situation This is because thenumber of individual joint nodes is reduced and it cannotreach a steady state in a short time which leads to an increasein the convergence time

From the above experimental result it shows that theevolution time will be longer when interactive radius limitsthe HI model In KH model without the limitation ofinteractive radius individuals can have more easy access toall other individual opinions in the system and update theiropinion in a relatively short time The global opinion couldreach a steady state quickly Also KH model ignores theinterpersonal influence and individual cognitive differencesand just puts the average value of the neighborrsquos opinionwhich is less than a confidence threshold with an ownopinion as for the next moment opinion However theinfluence of different neighbors on him is not the same whenindividual takes part in opinion interaction process in thereal world It makes the individual exchange opinion under

6 Complexity

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

Time

0

01

02

03

04

05

06

07

08

09

1

(a) 120576 = 005

10 20 30 40 50 60 70 80Time

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(b) 120576 = 02Time

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

Time10 20 30 40 50 60 70 80

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(c) 120576 = 03

Figure 5 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in full-connected network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(a) 120576 = 005

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(b) 120576 = 02

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 500Time

0010203040506070809

1

Opi

nion

(HI m

odel

)

(c) 120576 = 03

Figure 6 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in the scale-free network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

4 Complexity

in perspective Moreover the collection constituted by theseindividuals is called a reference collection of the individual119894 For a given time 119905 the physical distance radius 119889119894 ofthe individual 119894 defines the size of the reference collectionThe reference collection Distance(119894) of individual 119894 can becalculated as follows

Distance (119894) 119895 | 0 lt 119889 (119894 119895) lt 120575 1 le 119895 le 119873 119895 = 119894 (3)

In the above equation the physical distance radius 120575 is afixed constant

(2) Exchange Collection Calculation According to the size oftheir trust in the neighborhood an individual with a certainscope of opinion difference would be chosen The collectionconstituted by these individuals is called exchange collectionof the individual 119894 For a given time 119905 the exchange collectionNeighbor(119894) of node 119894 is decided by the radius of trust 120576119894and reference collection Distance(119894) Its can be calculated asfollows

Neighbor (119894) 119895 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 lt 120576119894 119895 isin Distance (119894) 119895 = 119894 (4)

As can be seen from the equation the individual isexcluded from the exchange collection by the filtration ofreference collection in HI model However the individualhimself must be included in the exchange collection of classi-cal limited trust model Therefore the exchange collection ofHI model may be empty

(3) Opinion Update When the exchange collection is deter-mined the system begins to exchange opinions In the nextmoment the individual 119894maintains his current opinion withprobability 1 minus 120582119894 and is affected by his trusted friend withprobability 120582119894 the influence of individual 119895 on individual 119894is proportional to the public authority PA119895 of the individual119895 When the exchange collection of individual 119894 is empty theopinion of the individual 119894 remains unchanged The opinionof individual 119894 at 119905 + 1 time is expressed as

119909119894 (119905 + 1)

= (1 minus 120582119894) 119909119894 (119905) + 120582119894sum

119895isin119873119894

PA119895sum119895 PA119895 times 119909119895 (119905) Neighbor (119894) = 120601

119909119894 (119905) Neighbor (119894) = 120601(5)

Opinion updating formula shows that the new opinion ofthe individual in the next moment is formed under the jointaction of the individualrsquos current opinion his personalitycharacteristics the opinion and public authority of trustedfriends

An algorithm flowchart of our proposed model is shownin Figure 3 Our model operates as follows

Step 1 (parameter initialization) Set appropriate parametersincluding the number of individuals physical distance radiusconfidence radius and evolution time

Beginning

Parameter initialization

Essential data generation

Calculate the exchangecollection

Opinion update

End

End of time or meetexternal terminationconditions

Evolution result output

Figure 3 HI model algorithm flowchart

Step 2 (essential data generation) According to statisticalproportion essential data is generated to initialize the basicattributes of each agent

Step 3 Calculate the exchange collection and the currentagent change opinion with according to (3) and (4)

Step 4 (opinion update is completed) If the exchange col-lection is not empty then the current individual updateshis opinion according to (5) at next step or his opinionwill remain unchanged Loop Steps 3 and 4 until all of theopinions achieve stable states Then the evolution is ended

Step 5 (evolution result output) Output the time evolutionresult of the individual opinions initial opinion distributioncurve and terminal opinion distribution curve

3 The Opinion Research ofHI Model in Full-Connected Networkand Scale-Free Network

According to the fifth population census data of China [17]this paper utilizes the statistical data of age proportionpopulation proportion in different geographical positionsand education level proportion respectively in juvenileyouth middle age and old age We obtained the economiccondition in the various regions Geographical distributionproportion age proportion and education proportion arepresented in Table 1

Complexity 5

Table 1 The statistical data of the fifth population consensus

Geographical distribution proportion ()East South West North Middle Southeast Northeast Southwest Northwest2286 1104 023 1177 2046 274 842 2095 153

Gender () Age ()Male Female Infants Child Juvenile Youth Middle-aged Elderly5163 4837 317 508 1467 3761 2976 971

Proportion of education among the juvenile () Proportion of education among the youth ()Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior268 7579 2153 0 204 2163 7035 598Proportion of education among the middle-aged () Proportion of education among the elderly ()

Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior888 3826 49 386 4755 3682 1358 205

The simulation environment is designed as follows

(1) Essential data of 1000 nodal attributes is generatedaccording to the statistical proportion of the fifthnational census

(2) The platform for essential data generation is devel-oped in C The simulation environment is Matlab2010b and the database is SQLServer 2008

(3) According to the fifth census data we can obtainthe individualrsquos physical location (119889max = 1000) Thephysical distance between agent 119894 and agent 119895 iscalculated from formula (4) The physical distancedistribution is shown in Figure 4

31The Comparison of HIModel and KHModel To comparethe differences between HI model and classical KH modelthis paper compares the opinion evolution of the two modelsin all connected networks and scale-free networks underthe same individual attributes (confidence radius physicaldistance and initial opinion) distribution Selections ofconfidence radius are 005 02 and 03 The initial opinionis random distribution between (0 1) Individual authorityand conformity are according to the distribution of Figures1 and 2 respectively As shown in Figure 4 80 of thephysical distance between two individuals is more than 600Therefore the interactive radius is set at 600

The evolution result in the full-connected network isshown in Figure 5The Figure indicates that the opinion evo-lution will be from discrete to polarization finally reaching aconsensus in bothHImodel andKHmodel with the increaseof confidence radius The evolutions of public opinion oftwo models are similar and the stable opinions are thesame However the convergence time is very different Theconvergence time of HImodel is longer than the convergencetime of KH mode As the limitation of the interactive radiusin HI model the evolution process tends to be slow

The evolution result in scale-free networks is shown inFigure 6 The opinion evolution will be from discrete topolarization finally reaching a consensus in both HI modeland KH model with the increase of confidence radiusHowever in a scale-free network no matter what kind of

0 100 200 300 400 500 600 700 800 900 1000 1100Distance

Distance

Fequ

ency

0

02

04

06

08

1

12

14

16

18

2

times105

Figure 4 The physical distance distribution

model the convergence time is longer than that in the full-connected network in the same situation This is because thenumber of individual joint nodes is reduced and it cannotreach a steady state in a short time which leads to an increasein the convergence time

From the above experimental result it shows that theevolution time will be longer when interactive radius limitsthe HI model In KH model without the limitation ofinteractive radius individuals can have more easy access toall other individual opinions in the system and update theiropinion in a relatively short time The global opinion couldreach a steady state quickly Also KH model ignores theinterpersonal influence and individual cognitive differencesand just puts the average value of the neighborrsquos opinionwhich is less than a confidence threshold with an ownopinion as for the next moment opinion However theinfluence of different neighbors on him is not the same whenindividual takes part in opinion interaction process in thereal world It makes the individual exchange opinion under

6 Complexity

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

Time

0

01

02

03

04

05

06

07

08

09

1

(a) 120576 = 005

10 20 30 40 50 60 70 80Time

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(b) 120576 = 02Time

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

Time10 20 30 40 50 60 70 80

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(c) 120576 = 03

Figure 5 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in full-connected network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(a) 120576 = 005

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(b) 120576 = 02

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 500Time

0010203040506070809

1

Opi

nion

(HI m

odel

)

(c) 120576 = 03

Figure 6 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in the scale-free network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

Complexity 5

Table 1 The statistical data of the fifth population consensus

Geographical distribution proportion ()East South West North Middle Southeast Northeast Southwest Northwest2286 1104 023 1177 2046 274 842 2095 153

Gender () Age ()Male Female Infants Child Juvenile Youth Middle-aged Elderly5163 4837 317 508 1467 3761 2976 971

Proportion of education among the juvenile () Proportion of education among the youth ()Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior268 7579 2153 0 204 2163 7035 598Proportion of education among the middle-aged () Proportion of education among the elderly ()

Illiteracy Primary Intermediate Senior Illiteracy Primary Intermediate Senior888 3826 49 386 4755 3682 1358 205

The simulation environment is designed as follows

(1) Essential data of 1000 nodal attributes is generatedaccording to the statistical proportion of the fifthnational census

(2) The platform for essential data generation is devel-oped in C The simulation environment is Matlab2010b and the database is SQLServer 2008

(3) According to the fifth census data we can obtainthe individualrsquos physical location (119889max = 1000) Thephysical distance between agent 119894 and agent 119895 iscalculated from formula (4) The physical distancedistribution is shown in Figure 4

31The Comparison of HIModel and KHModel To comparethe differences between HI model and classical KH modelthis paper compares the opinion evolution of the two modelsin all connected networks and scale-free networks underthe same individual attributes (confidence radius physicaldistance and initial opinion) distribution Selections ofconfidence radius are 005 02 and 03 The initial opinionis random distribution between (0 1) Individual authorityand conformity are according to the distribution of Figures1 and 2 respectively As shown in Figure 4 80 of thephysical distance between two individuals is more than 600Therefore the interactive radius is set at 600

The evolution result in the full-connected network isshown in Figure 5The Figure indicates that the opinion evo-lution will be from discrete to polarization finally reaching aconsensus in bothHImodel andKHmodel with the increaseof confidence radius The evolutions of public opinion oftwo models are similar and the stable opinions are thesame However the convergence time is very different Theconvergence time of HImodel is longer than the convergencetime of KH mode As the limitation of the interactive radiusin HI model the evolution process tends to be slow

The evolution result in scale-free networks is shown inFigure 6 The opinion evolution will be from discrete topolarization finally reaching a consensus in both HI modeland KH model with the increase of confidence radiusHowever in a scale-free network no matter what kind of

0 100 200 300 400 500 600 700 800 900 1000 1100Distance

Distance

Fequ

ency

0

02

04

06

08

1

12

14

16

18

2

times105

Figure 4 The physical distance distribution

model the convergence time is longer than that in the full-connected network in the same situation This is because thenumber of individual joint nodes is reduced and it cannotreach a steady state in a short time which leads to an increasein the convergence time

From the above experimental result it shows that theevolution time will be longer when interactive radius limitsthe HI model In KH model without the limitation ofinteractive radius individuals can have more easy access toall other individual opinions in the system and update theiropinion in a relatively short time The global opinion couldreach a steady state quickly Also KH model ignores theinterpersonal influence and individual cognitive differencesand just puts the average value of the neighborrsquos opinionwhich is less than a confidence threshold with an ownopinion as for the next moment opinion However theinfluence of different neighbors on him is not the same whenindividual takes part in opinion interaction process in thereal world It makes the individual exchange opinion under

6 Complexity

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

Time

0

01

02

03

04

05

06

07

08

09

1

(a) 120576 = 005

10 20 30 40 50 60 70 80Time

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(b) 120576 = 02Time

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

Time10 20 30 40 50 60 70 80

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(c) 120576 = 03

Figure 5 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in full-connected network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(a) 120576 = 005

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(b) 120576 = 02

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 500Time

0010203040506070809

1

Opi

nion

(HI m

odel

)

(c) 120576 = 03

Figure 6 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in the scale-free network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

6 Complexity

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

Time

0

01

02

03

04

05

06

07

08

09

1

(a) 120576 = 005

10 20 30 40 50 60 70 80Time

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

10 20 30 40 50 60 70 80Time

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(b) 120576 = 02Time

10 20 30 40 50 60 70 80

Opi

nion

s (H

I mod

el)

0

01

02

03

04

05

06

07

08

09

1

Time10 20 30 40 50 60 70 80

Opi

nion

s (KH

mod

el)

0

01

02

03

04

05

06

07

08

09

1

(c) 120576 = 03

Figure 5 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in full-connected network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(a) 120576 = 005

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(HI m

odel

)

(b) 120576 = 02

50 100 150 200 250 300 350 400 450 5000

010203040506070809

1

Time

Opi

nion

(KH

mod

el)

50 100 150 200 250 300 350 400 450 500Time

0010203040506070809

1

Opi

nion

(HI m

odel

)

(c) 120576 = 03

Figure 6 The comparison of public opinion evolution between KH model (the above three figures) and HI model (the three figures below)in the scale-free network 120576 (a) 120576 = 005 (b) 120576 = 02 and (c) 120576 = 03

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

Complexity 7

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

Opinions

KH model

Opi

nion

(KH

mod

el)

Freq

uenc

y (a

fter e

volu

tion)

(a) KH model

50 100 150 200 250 300 350 400 450 5000

01

02

03

04

05

06

07

08

09

1

Time

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

HI model

Opi

nion

(HI m

odel

)Fr

eque

ncy

(afte

r evo

lutio

n)

(b) HI model

Figure 7 The opinion evolution in scale-free network (a) KH model and (b) HI model 120576 = 02 120575 = 400

limited communication range increasing the difficulty ofthe individual to identify the overall environment of publicopinion It causes difficulty in forming their final opinionand public opinion convergence takes a long time Based onthe actual situation agents using the improved model canuse interactive choice agents to update their opinion underthe limitation of the individualrsquos heterogeneity and cognitiondegree although forming the consensus or a stable state needsa long time Eventually evolution effect such as discretepolarization and consensus is similar to classical KHmodel

32The Different Interactive Radius Experiments in HIModelIn real life the different physical distance will affect the inter-action between the individuals This paper considers evolu-tion under a different range of interactive radius betweenHI model and classical KH model Considering the scale-free network edge which is similar to individuals in real lifethe simulation experiments are conducted in the scale-freenetworks Because the opposition between two views (suchas vote) in real life namely the polarization phenomenon

is common the confidence radius of two models will be setto 02 which is easy to present the phenomenon The initialopinion distributions of two models are taking the samerandom distribution

Figure 7 shows the difference between the opinion evolu-tion of HI model (interactive radius 120575 = 400) and KHmodel

The figure shows that the convergence time of HI modelis slower than the convergence time of KH model and thefinal cluster number increase The main reason is due tothe limitation of confidence radius 120576 and interactive radius120575 which make the interactive agent number decrease in HImodel To describe the largest cluster in the steady state ofpublic opinion evolution Yang et al [18] defined 119878 index asthe ratio of the individual number of the largest cluster andoverall cluster Luo et al [19] defined 119866 index and Chen etal [11] defined 119862 as a final number of controlled agents Wechoose 119862 to describe the individual number of the largestcluster in the steady state Figure 8 shows under differentinteractive radius the individual number of the largest cluster(119862) in two models

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

8 Complexity

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

KH modelHI model

Freq

uenc

y (a

fter e

volu

tion)

(a) 120575 = 120

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(b) 120575 = 150

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(c) 120575 = 300

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(d) 120575 = 400

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(e) 120575 = 520

KH modelHI model

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000

Opinions

Freq

uenc

y (a

fter e

volu

tion)

(f) 120575 = 550

Figure 8 The final opinion distribution of HI model and KH model in scale-free network 120576 = 02 (a) 120575 = 120 (b) 120575 = 150 (c) 120575 = 300 (d) 120575= 400 (e) 120575 = 520 and (f) 120575 = 550

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

Complexity 9

Figure 8 shows thatwhen the interactive radius is between150 and 520 the individual number of the largest cluster (119862) ofHI model is greater than the individual number of the largestcluster (119862) of KHmodel Figure 8(a) shows that the individualnumber of the largest cluster (119862) of HI model is clearly lessthan the individual number of the largest cluster (119862) of KHmodel after interactive rate becomes less than 150 Figure 8(f)shows that after the interactive radius becomes greater than520 the HI model will eventually show the tendency of thepolarization and the individual number of the largest cluster(119862) is not better than the individual number of the largestcluster (119862) of KH model This means that the interactiveradius of HI model can influence the individual number ofthe largest cluster (119862) of public opinion In this case becauseof the limitation of interactive radius most of the nodes canbe in the direction of the consensus when confidence radiusis small

From the above when confidence radius is small mostagents will have a tendency to reach consensus in HI modelbut most agents appear to have the trend of opinionspolarization in KH model This is due to the fact that thepublic opinion evolution of KH model is only determinedby the confidence radius without considering the limitationof actual physical distance in the society In HI model bothinteractive radius and confidence radius affect the agentrsquosinteractive range When the two parameters are limited toa proper range most agents will be a consensus by localcommunication because of the mutual influence

4 Conclusion

Based on the classic KH model this paper proposes anew evolution model heterogeneous interaction model (HImodel) in the limitation of physical distance individualconformity and authorityTheHImodel conducts an opinionevolution in the full-connected network and the scale-freenetwork and the result is compared with the KHmodel Theresult of experiment reveals that the evolutional efficiencyof the network model will become slow after adding thelimitation of the interactive radius but the final evolutionalsituation of HI model and KH model is analogous In addi-tion when other conditions are consistent and interactiveradius is in a certain range most agents of HI model will beconsensus but the opinions of agents will be polarized in theKHmodel It means that we can limit the interactive radius tomakemost agents in consensus and control the final guidanceof public opinion

Based on the above experiments the results prove thatthe individual heterogeneity and interactive radius have asignificant influence in the public opinion evolution andunder the certain constraints of the condition it can controlthe individual number of the largest cluster (119862) of theevolution of public opinion Most of the previous researchesignore the individual heterogeneity and the physical distancebetween individuals and only consider the confidence radiusso it makes public opinion evolution model too simpleand the evolution process is different with the real-worldsituations HI model takes the individual heterogeneity and

interactive distance into account and the evolution processconforms to real-world data wherein the evolution timeincreases and the final point cluster increasesThismeans thatthe HI model is more reasonable in real life in describingthe evolution of public opinion and can more effectivelyobserve and predict the actual circumstances of the publicopinion evolution by the HI model In real life the finalresult of public opinion evolution is that winner is who havemore supporters namely the individual number of the largestcluster (119862) is more than 50 of the whole and HI modelcan effectively control the individual number of the largestcluster (119862) by controlling the largest interactive distance Tosome extent the public opinion evolution ofHImodel revealsthat the distance between the individuals has a significantinfluence on public opinion in consensus in real lifeThis alsomeans that in real life the authority can change the scope ofinteractive radius between the individuals to control the finaltrend of public opinion

After that we will conduct a more in-depth research inthe individual heterogeneity of the HI model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant nos 71571081 61540032and 91324203

References

[1] R Xiao and T Yu ldquoA multi-agent simulation approach torumor spread in virtual commnunity based on social networkrdquoIntelligent Automation and Soft Computing vol 17 no 7 pp859ndash869 2011

[2] R Xiao Y Zhang and Z Huang ldquoEmergent computation ofcomplex systems A comprehensive reviewrdquo International Jour-nal of Bio-Inspired Computation vol 7 no 2 pp 75ndash97 2015

[3] P Novoa-Hernandez C C Corona and D A Pelta ldquoSelf-adap-tation in dynamic environmentsmdashA survey and open issuesrdquoInternational Journal of Bio-Inspired Computation vol 8 no 1pp 1ndash13 2016

[4] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systemsvol 3 no 1ndash4 pp 87ndash98 2000

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 article 22002

[6] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[7] S Fortunato andD Stauffer ldquoComputer simulations of opinionsand their reactions to extreme eventsrdquo in Extreme Events inNature and Society pp 233ndash257 Springer Berlin Germany2006

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

10 Complexity

[8] D Stauffer ldquoSociophysics simulations II opinion dynamicsrdquoAIP Conference Proceedings vol 779 no 1 pp 56ndash68 2005

[9] G-R Chen W-D Cai H-J Xu P-X Yan and J-P WangldquoHigh-effect priority bounded confidence model for networkopinion evolutionrdquo Journal of Shanghai Jiaotong University vol47 no 1 pp 155ndash160 2013

[10] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[11] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos vol 26 no 8 Article ID 083105 2016

[12] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and Its Applications vol 392 no 9 pp2248ndash2256 2013

[13] M Jalili ldquoSocial power and opinion formation in complexnetworksrdquo Physica A Statistical Mechanics and Its Applicationsvol 392 no 4 pp 959ndash966 2013

[14] S Li and S Zhang ldquoLeader and follower agents in an opiniondynamics and bounded confidence model on the stochasticmovement worldrdquo in Proceedings of the 2nd International Con-ference on Computational Intelligence and Natural Computing(CINC rsquo10) pp 50ndash54 September 2010

[15] M A Javarone ldquoSocial influences in opinion dynamics therole of conformityrdquo Physica A Statistical Mechanics and ItsApplications vol 414 pp 19ndash30 2014

[16] X Chen L Zhang and W Li ldquoA network evolution modelfor chinese traditional acquaintance networksrdquo IEEE IntelligentSystems vol 29 no 5 pp 5ndash13 2014

[17] ldquoNational Bureau of Statistics of the Peoplersquos Republic ofChina[EBOL]rdquo httpwwwstatsgovcntjsjpcsj

[18] W Yang L Cao X Wang and X Li ldquoConsensus in a het-erogeneous influence networkrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 74 no 3 Article ID037101 2006

[19] S Luo Y Du P Liu Z Xuan and Y Wang ldquoA study oncoevolutionary dynamics of knowledge diffusion and socialnetwork structurerdquoExpert SystemswithApplications vol 42 no7 pp 3619ndash3633 2015

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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