SYNCHRONIZATION OF CHAOTIC SYSTEM

CONTENT CHAOTIC SYSTEM TENT MAP SYNCHRONIZATION HARDWARE IMPLEMENTATION ELECTRONIC IMPLEMENTATION OF TENT MAP SCHEMATIC DIA. OF TENT MAP ELECTRONIC CIRCUIT COMPONENTS SOFTWARE VRIFICATION CIRCUIT SYCHRONIZATION IMPLEMENTATION REFERENCE

CHAOTIC SYSTEM Chaotic systems are unstable since they tend not to

resist any outside disturbances but instead react in significant ways.

Chaotic systems are common in Nature.

CONTINUE…… Many natural phenomena can also be characterized

as being chaotic. They can be found in meteorology , solar system, heart and brain of living organisms and so on.

It is difficult for two chaotic systems to synchronize with each other, but if the two systems exchange information in just the right way, they can synchronize

TENT MAP The tent map with parameter μ is the real-valued

function fμ defined by:

 In particular, iterating a point x0 in [0, 1] gives rise to a sequence  :

where μ is a positive real constant.

CONTINUE…. This is called ‘tent map’ due to tent like shape of the

graph of fμ.

SYNCHRONIZATIONSynchronization between two system means feeding both the transmitter and the receiver with the same carrier signal for Demodulating the modulated signal accurately.

Need for Synchronization: Synchronization is one of the most important

requirements for designing a Digital Communication System

HARDWARE IMPLEMENTATION

Here we present one of the simplest electronic implementation of the tent map, which at same time is a good engineering model of the corresponding mathematical system.

Through the variation of tent map control parameter we are able to reproduce the theoretical diagram with high accuracy.

ELECTRONIC IMPLEMENTATION OF TENT MAP There are various processes for electrical

implementation of tent map-

1. Using analog multipliers 2. Using digital signal processor3. New approach [1]

SCHEMATIC DIAGRAM OF THE TENT MAP ELECTRONIC CIRCUIT

COMPONENTS The above diagram consists of- five operational amplifiers(from U1 to U5), four diodes (D1 - D4), thirteen resistors (from R1 to R13 a dc voltage source (Vdc). variable resisors R5 & R6(5kῼ) variable resistors R11(100kῼ) & R12(10kῼ)

SOFTWARE VERIFICATION OF CIRCUIT

OUTPUT

When y(n)=x(n) after around few iterations (say 5), f1=f2. [5]

SYNCHRONIZATION IMPLEMENTATION

SYNCHRONIZATION IN DIGITAL SYSTEM

CONCLUSION A very simple tent map electronic circuit has been presented

here and its implementation using only analog components as operational amplifiers, diodes, and resistors was also provided.

The circuit that replicates the whole known range of behaviors of the tent map has been determined.

The employed techniques are simple and the approach can be extended to other types of chaotic maps such.

Such circuit realizations have many potential applications, for example: random number generation, frequency hopping, ranging, and spread-spectrum communications.

Finally, we notice that this design can be manufactured in just one chip because the final electronic circuit contains only semiconductors and passive components.

REFERENCE1. Campos-Cantón, I., E. Campos-Cantón, J. S. Murguıa, and H. C. Rosu.

"A Simple Electronic Circuit Realization of the Tent Map." Chaos, Solitons & Fractals 42 (2009): 12-16.

2. May, Robert M. 1976. "Simple mathematical models with very complicated dynamics." Nature 261(5560):459-467.

3. Gleick, James (1987). Chaos: Making a New Science. Penguin Books.4. Strogatz, S. H. Nonlinear Dynamics and Chaos Perseus Books 1994.

ISBN 0-201-54344-35. Hardware Implementation of Tent Map, Debanjana Datta, Bidisha De

and Subhajit Paul, Submitted in ICETIC 20156.https://www.google.co.in/search?

q=block+diagram+of+digital+communication+system&biw=1024&bih=677&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjczNvIpZ_JAhVRTo4KHe1ZAQIQ_AUIBigB#imgrc=oFOLMrjZFT2HhM%3A

7.https://www.google.co.in/search?q=synchronisation+in+digital+communication&biw=1024&bih=677&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjWnLqrs5_JAhWCSo4KHcAoAmoQ_AUICCgD&dpr=1#imgrc=ty0UO-N891u2MM%3A