loop drawings and examples

8/7/2019 Loop drawings and examples

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Feedback

A lthough stocks and flows are both necessary and sufficient for generating dynamic behavior, they arenot the only building blocks of dynamical systems. More precisely, the stocks and flows in real worldsystems are part of feedback loops , and the feedback loops are often joined together by nonlinear

couplings that often cause counterintuitive behavior.

From a system dynamics point of view, a system can be classified as either "open" or "closed." Opensystems have outputs that respond to, but have no influence upon, their inputs. Closed systems, on theother hand, have outputs that both respond to, and influence, their inputs. Closed systems are thusaware of their own performance and influenced by their past behavior, while open systems are not .

Of the two types of systems that exist in the world, the most prevalent and important, by far, are closedsystems. As shown in Figure 1, the feedback path for a closed system includes, in sequence, a stock,information about the stock, and a decision rule that controls the change in the flow . Figure 1 is adirect extension of the simple stock and flow configuration shown previously with the exception that an

information link added to close the feedback loop. In this case, an information link "transmits"information back to the flow variable about the state (or "level") of the stock variable. This informationis used to make decisions on how to alter the flow setting.

Figure 1: Simple System Dynamics Stock-Flow-Feedback Loop Structure.

It is important to note that the information about a system's state that is sent out by a stock is oftendelayed and/or distorted before it reaches the flow (which closes the loop and affects the stock). Figure2, for example, shows a more sophisticated stock-flow-feedback loop structure in which informationabout the stock is delayed in a second stock, representing the decision maker's perception of the stock (i.e., Perceived_Stock_Level), before being passed on. The decision maker's perception is thenmodified by a bias to form his or her opinion of the stock (i.e., Opinion_Of_Stock_Level). Finally, thedecision maker's opinion is compared to his or her desired level of the stock, which, in turn, influencesthe flow and alters the stock .

Given the fundamental role of feedback in the control of closed systems then, an important rule insystem dynamics modeling can be stated: Every feedback loop in a system dynamics model must contain at least one stock . .

http://www.systemdynamics.org/DL-IntroSysDyn/feed

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Figure 2: More Sophisticated Stock-Flow-Feedback Loop Structure

Positive and Negative Loops

Closed systems are controlled by two types of feedback loops: positive loops and negative loops .Positive loops portray self-reinforcing processes wherein an action creates a result that generates moreof the action, and hence more of the result. Anything that can be described as a vicious or virtuous

circle can be classified as a positive feedback process. Generally speaking, positive feedback processesdestabilize systems and cause them to "run away" from their current position. Thus, they areresponsible for the growth or decline of systems, although they can occasionally work to stabilize them.

Negative feedback loops, on the other hand, describe goal-seeking processes that generate actionsaimed at moving a system toward, or keeping a system at, a desired state. Generally speaking, negativefeedback processes stabilize systems, although they can occasionally destabilize them by causing themto oscillate.

Causal Loop Diagramming

In the field of system dynamics modeling, positive and negative feedback processes are often describedvia a simple technique known as causal loop diagramming. Causal loop diagrams are maps of cause andeffect relationships between individual system variables that, when linked, form closed loops.


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Figure 3, for example, presents a generic causal loopdiagram. In the figure, the arrows that link each variableindicate places where a cause and effect relationship exists,while the plus or minus sign at the head of each arrowindicates the direction of causality between the variableswhen all the other variables (conceptually) remain constant.More specifically, the variable at the tail of each arrow inFigure 3 causes a change in the variable at the head of eacharrow, ceteris paribus, in the same direction (in the case of a plus sign), or in the opposite direction (in the case of aminus sign) .

Figure 3: Generic causal loop diagram

The overall polarity of a feedback loop -- that is, whether the loop itself is positive or negative -- in acausal loop diagram, is indicated by a symbol in its center. A large plus sign indicates a positive loop; alarge minus sign indicates a negative loop. In Figure 3 the loop is positive and defines a self reinforcingprocess. This can be seen by tracing through the effect of an imaginary external shock as it propagatesaround the loop. For example, if a shock were to suddenly raise Variable A in Figure 3, Variable Bwould fall (i.e., move in the opposite direction as Variable A), Variable C would fall (i.e., move in thesame direction as Variable B), Variable D would rise (i.e., move in the opposite direction as VariableC), and Variable A would rise even further (i.e., move in the same direction as Variable D).

By contrast, Figure 4 presents a generic causal loopdiagram of a negative feedback loop structure. If anexternal shock were to make Variable A fall, Variable Bwould rise (i.e., move in the opposite direction asVariable A), Variable C would fall (i.e., move in theopposite direction as Variable B), Variable D would rise(i.e., move in the opposite directionas Variable C), and

Variable A would rise (i.e., move in the same direction asVariable D). The rise in Variable A after the shock propagates around the loop, acts to stabilize the system --i.e., move it back towards its state prior to the shock. Theshock is thus counteracted by the system's response.

Figure 4: Generic causal loop diagram of anegative feedback loop structure

Occasionally, causal loop diagrams are drawn in amanner slightly different from those shown in Figure 3and Figure 4. More specifically, some systemdynamicists prefer to place the letter "S" (for Samedirection) instead of a plus sign at the head of an arrowthat defines a positive relationship between twovariables. The letter "O" (for Opposite direction) is usedinstead of a minus sign at the head of an arrow to definea negative relationship between two variables. To definethe overall polarity of a loop system dynamicists oftenuse the letter "R" (for "Reinforcing") or an icon of asnowball rolling down a hill to indicate a positive loop.To indicate a negative loop, the letter "B" (for"Balancing"), the letter "C" (for "Counteracting"), or an Figure 5: Alternative Causal Loop


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icon of a teetertotter is used . Figure 5 illustrates thesedifferent causal loop diagramming conventions.

Diagramming Conventions

In order to make the notion of feedback a little more salient, Figure 6 to Figure 17 present a collectionof positive and negative loops. As these loops are shown in isolation (i.e., disconnected from the otherparts of the systems to which they belong), their individual behaviors are not necessarily the same asthe overall behaviors of the systems from which they are taken.

Positive Feedback Examples

Population Growth/Decline: Figure 6 showsthe feedback mechanism responsible for thegrowth of an elephant herd via births. In thissimple example we consider two systemvariables: Elephant Births and ElephantPopulation. For a given elephant herd, we saythat if the birth rate of the herd were to increase ,the Elephant Population would increase . In thissame way, we can say that if - over time - theElephant Population of the herd were toincrease , the birth rate of the herd wouldincrease . Thus, the Elephant Birth rate drivesthe Elephant Population that drives ElephantBirth rate - positive feedback.

Figure 6: Positive Loop Responsible for the Growth in anElephant Herd via Births

National Debt: Figure 7 is a positive loop thatshows the growth in the national debt due tothe compounding of interest payments. First,we note that that an increase in the amount of interest paid per year on the national debt(itself a cost within the federal budget ) willcause the overall national debt to increase. Inthis same way, an increase in the level of national debt will increase the amount of theinterest paid each year.

Figure 7: Positive Loop Showing Growth in the National DebtDue to Compounding Interest Payments


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Arms Race: Figure 8 shows a generic arms racebetween Country A and Country B. In itssimplest form, an "arms race" can be described asa self-sustaining competition for militarysuperiority. An arms race is driven by theperception that one's adversary has equal orgreater military strength. If Country A moves toincrease its military capability, Country Binterprets this as a threat and responds in-kindwith its own increase in military capability.Country B's action, in turn, causes Country A tofeel more threatened. Thus, Country A moves tofurther increase its military capability. Figure 8: Arms Race is a Positive Feedback Process.

Bank Panic: A common scene during the GreatDepression in the 1930s was that of a panicstricken crowd standing outside their local bank

waiting to withdraw what remained of theirsavings. Figure 8 shows the feedback mechanismresponsible for the spiraling decline of thebanking system during this period.

From the diagram, we see that the frequency of bank failures increases public concern and thefear of losing their money. In this case, we saythat the two system variables "move" in the same(S) or positive (+) direction. The relationshipbetween the "fear of not being able to withdraw

money" and the rate at which bank withdrawalsare made is also positive.

Figure 9: Bank panic is a positive feedback process.

The relationship between withdrawals and bank health is negative (-) or opposite (O). This means thatif the rate of bank withdrawals increases, the health of the bank decreases as capital reserves aredrawn down. The relationship between the banking industry's health and the rate of bank failures isalso negative. This means that if the health of the banking industry increases, the number of bank failures per year will decrease.

This vicious cycle was clearly seen during the 1930s. An overall economic downturn caused the rateof bank failures to increase. As more banks failed, the public's fear of not being able to withdraw theirown money increased. This, in turn, prompted many to withdraw their savings from banks, which

further reduced the banking industry's capital reserves. This caused even more banks to fail.


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Figure 10 depicts three interactingpositive feedback loops that arethought to be responsible for thegrowth in students taking drugs in highschool .

Figure 10: Feedback structure responsible for growth high school drug use

Negative Feedback Examples

Population Growth/Decline: In Figure 6, we sawhow an elephant population and its correspondingbirth rate form a positive feedback loop. Now, weconsider the other half of the equation, that is, thefeedback structure between Elephant Populationand Elephant Death rate. Figure 11 shows thenegative feedback process responsible for thedecline of an elephant herd via deaths. If theElephant Death rate increases , the ElephantPopulation will decrease . A negative signindicates this counteracting behavior. The causalinfluence of Elephant Population to ElephantDeath rate is just the opposite. An increase in thenumber of elephants in the herd means that aproportionally larger number of elephants will dieeach year, i.e., an increase in the herd's deathrate. A plus sign indicates this complimentarybehavior. These two relationships combinetogether to form a negative feedback loop.

Figure 11: Elephant population negative feedback loop.

Figure 12 and Figure 13 are two simple and familiar examples of negative feedback processes. Figure12 shows the negative feedback process responsible for the dissipation of Itching due to Scratching.Figure 13 considers the negative feedback involved in Eating to reduce Hunger. An increase in one'sHunger causes a person to eat more food. Increasing in the rate food consumption, in turn, reducesHunger.


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Figure 12: Scratching an itch and negative feedback Figure 13: Dissipation of hunger

Law Enforcement: Figure 14 depicts a negativefeedback process that maintains a balancebetween the number of drug dealers and thenumber of police officers in a neighborhood. Anincrease in the number of drug dealers in aneighborhood will prompt local officials toincrease the number of law enforcement personsas a counter measure. As the number of policeofficers increase , more arrests are made and thenumber of drug dealers is reduced .

Figure 14: Neighborhood drug intervention negative feedback

Car Pools: Figure 15 shows a negativefeedback process that maintains a balancebetween car pools and gasolineconsumption. An increase in gasolineconsumption increases gasoline price(supply reduction). A higher gasoline pricepushes many individual motorists to joincarpools, which reduces the total number of vehicles on the road. This, in turn, reducesgasoline consumption.

Figure 15: Gasoline consumption negative feedback

Implicit and Explicit Goals

The negative feedback loops presented in Figure 11 through Figure 15 are, in a sense, misleadingbecause the goals they are seeking are implicit rather than explicit. For example, the implicit goal of theloop in Figure 11 is zero elephants. That is, if the loop were to act, in isolation, for a substantial period


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of time, eventually all of the elephants would die and the population would be zero. The same sort of logic applies to Figure 12 and Figure 13, in which the loops implicitly seek goals of zero itching andzero hunger respectively.The logic gets even murkier in the case of Figure 14 and Figure 15. In Figure14, there is an implicit goal of an "acceptable" or "tolerable" level of drug dealers in the neighborhood,which may or may not be zero. In Figure 15, there is an implicit goal of an acceptable or tolerablegasoline price, which is certainly a lower price rather than a higher price, but is also (realistically) notzero.

Figure 16: Generic negative feedback structure with explicit goal

An alternative and (often) more desirable way to represent negative feedback processes via causal loopdiagrams is by explicitly identifying the goal of each loop. Figure 16, for example, shows a causal loopdiagram of a generic negative feedback structure with an explicit goal. The logic of this loop says that,

any time a discrepancy develops between the state of the system and the desired state of the system(i.e., goal), corrective action is called forth that moves the system back into line with its desired state.

A more concrete example of a negative feedback structure with an explicit goal is shown in Figure 17.In the figure, a distinction is drawn between the actual number of elephants in a herd and the desirednumber of elephants in the herd (presumably determined by a knowledge of the carrying capacity of the environment supporting the elephants). If the actual number of elephants begins to exceed thedesired number, corrective action -- i.e., hunting -- is called forth. This action reduces the size of theherd and brings it into line with the desired number of elephants.


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Figure 17: Example of negative feedback structure with an explicit goal

Examples of Interacting "Nests" of Positive and Negative Loops

In system dynamics modeling, causal loop diagrams are often used to display "nests" of interactingpositive and negative feedback loops. This is usually done when a system dynamicist is attempting to

present the basic ideas embodied in a model in a manner that is easily understood, without having todiscuss in detail.

As Figure 18 and Figure 19 show, when causal loop diagrams are used in this fashion, things can getrather complicated. Figure 18 is a causal loop diagram of a system dynamics model created to examineissues related to profitability in the paper and pulp industry. This figure has a number of features thatare important to mention. The first is that the authors have numbered each of the positive and negativeloops so that they can be easily referred to in a verbal or written discussion. The second is that theauthors have taken great care to choose variable names that have a clear sense of direction and havereal-life counterparts in the actual system . The last and most important feature is that, although thefigure provides a sweeping overview of the feedback structure that underlies profitability problems in

the paper and pulp industry, it cannot be used to determine the dynamic behavior of the model (or of the actual system). In other words, it is impossible for someone to accurately think through, or mentallysimulate, the dynamics of the paper and pulp system from Figure 18 alone.


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Figure 18: Causal Loop Diagram of a Model Examining Profitability in the Paper and Pulp Industry

Figure 19 is a causal loop diagram of a system dynamics model created to examine forces that may beresponsible for the growth or decline of life insurance companies in the United Kingdom. As withFigure 18, a number of this figure's features are worth mentioning. The first is that the model's negativefeedback loops are identified by "C's," which stand for "Counteracting" loops. The second is thatdouble slashes are used to indicate places where there is a significant delay between causes (i.e.,variables at the tails of arrows) and effects (i.e., variables at the heads of arrows). This is a commoncausal loop diagramming convention in system dynamics. Third, is that thicker lines are used to identifythe feedback loops and links that author wishes the audience to focus on. This is also a common systemdynamics diagramming convention . Last, as with Figure 18, it is clear that a decision maker would findit impossible to think through the dynamic behavior inherent in the model, from inspection of Figure 19alone.


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Figure 19: Causal Loop Diagram of a Model Examining the Growth or Decline of a Life InsuranceCompany .

Archetypes

An area of the field of system dynamics or, more precisely, of the much broader field of "systemsthinking," that has recently received a great deal of attention is archetypes . Archetypes are genericfeedback loop structures, presented via causal loop diagrams, that seem to describe many situations that

frequently appear in public and private sector organizations. Archetypes are thought to be useful whena decision maker notices that one of them is at work in his or her organization. Presumably, the decisionmaker can then attack the root causes of the problem from an holistic and systemic perspective .Currently, nine archetypes have been identified and cataloged by systems thinkers, including:

Balancing Process with Delay,Limits to Growth,Shifting the Burden,Eroding Goals,Escalation,Success to the Successful,

Tragedy of the Commons,Fixes that Fail, andGrowth and Underinvestment .

Recent efforts, however, have suggested that the number can be reduced to four:

Growth Intended-Stagnation/Decline Achieved,Control Intended-Unwanted Growth Achieved,Control Intended-Compromise Achieved, andGrowth Intended At Expense to Others .


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No matter what the true number archetypes is or will be, however, the central question remainsunanswered: How successful are archetypes in helping decision makers solve problems in theirorganizations?

Problems with Causal Loop Diagrams

Causal loop diagrams are an important tool in the field of system dynamics modeling. Almost all systemdynamicists use them and many system dynamics software packages support their creation and display.

Although some system dynamicists use causal loop diagrams for "brainstorming" and model creation,they are particularly helpful when used to present important ideas from a model that has already beencreated . The only potential problem with causal loop diagrams and archetypes then, occurs when adecision maker tries to use them, in lieu of simulation, to determine the dynamics of a system .

Causal loop diagrams are inherently weak because they do not distinguish between information flowsand conserved (noninformation) flows. As a result, they can blur direct causal relationships betweenflows and stocks. Further, it is impossible, in principle, to determine the behavior of a system solelyfrom the polarity of its feedback loops, because stocks and flows create dynamic behavior, notfeedback. Finally, since causal loop diagrams do not reveal a system's parameters, net rates, "hidden

loops," or nonlinear relationships, their usefulness as a tool for predicting and understanding dynamicbehavior is further weakened. The conclusion is that simulation is essential if a decision maker is to gaina complete understanding of the dynamics of a system .


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