Feedback
A lthough stocks and flows are both necessary and sufficient for generating dynamic behavior, they are not the only building blocks of dynamical systems. More precisely, the stocks and flows in real world systems 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." Open systems
have outputs that respond to, but have no influence upon, their inputs.
Closed systems, on the other hand, have outputs that both respond to, and
influence, their inputs. Closed systems are thus aware of their own performance
and influenced by their past behavior, while open systems are not
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Of the two types of systems that exist in the world, the most prevalent
and important, by far, are closed systems. 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 a direct 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 information is 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 often delayed and/or distorted before it
reaches the flow (which closes the loop and affects the stock). Figure 2, for example, shows a more sophisticated stock-flow-feedback loop structure
in which information about 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 then modified by a
bias to form his or her opinion of the stock (i.e., Opinion_Of_Stock_Level). Finally,
the decision maker's opinion is compared to his or her desired level of
the stock, which, in turn, influences the flow and alters the stock.
Given the fundamental role of feedback in the control of closed systems
then, an important rule in system dynamics modeling can be stated: Every
feedback loop in a system dynamics model must contain at least one stock.
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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 more of 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 processes
destabilize systems and cause them to "run away" from their current position.
Thus, they are responsible 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 actions aimed at moving a system toward, or keeping a system at, a desired state. Generally speaking, negative feedback processes stabilize systems, although they can occasionally destabilize them by causing them to oscillate.
Causal Loop Diagramming
In the field of system dynamics modeling, positive and negative feedback processes are often described via a simple technique known as causal loop diagramming. Causal loop diagrams are maps of cause and effect relationships between individual system variables that, when linked, form closed loops.
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Figure 3, for example, presents a generic causal loop diagram. In the figure, the
arrows that link each variable indicate places where a cause and effect
relationship exists, while the plus or minus sign at the head of each arrow
indicates the direction of causality between the variables when all the
other variables (conceptually) remain constant. More specifically, the variable
at the tail of each arrow in Figure 3 causes a change in the variable at
the head of each arrow, ceteris paribus, in the same direction (in the
case of a plus sign), or in the opposite direction (in the case of a minus
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 a causal loop diagram, is indicated by a symbol in its center. A large plus sign indicates a positive loop; a large minus sign indicates a negative loop. In Figure 3 the loop is positive and defines a self reinforcing process. This can be seen by tracing through the effect of an imaginary external shock as it propagates around the loop. For example, if a shock were to suddenly raise Variable A in Figure 3, Variable B would fall (i.e., move in the opposite direction as Variable A), Variable C would fall (i.e., move in the same direction as Variable B), Variable D would rise (i.e., move in the opposite direction as Variable C), 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 loop diagram of a negative feedback loop structure. If an external shock were to make Variable A fall, Variable B would rise (i.e., move in the opposite direction as Variable A), Variable C would fall (i.e., move in the opposite 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 as Variable 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. The shock is thus counteracted by the system's response. |
Figure 4: Generic causal loop diagram of a negative feedback loop structure |
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Occasionally, causal loop diagrams are drawn in a manner slightly different
from those shown in Figure 3 and Figure 4. More specifically, some system
dynamicists prefer to place the letter "S" (for Same direction)
instead of a plus sign at the head of an arrow that defines a positive
relationship between two variables. The letter "O" (for Opposite
direction) is used instead of a minus sign at the head of an arrow to define
a negative relationship between two variables. To define the overall
polarity of a loop system dynamicists often use the letter "R" (for "Reinforcing")
or an icon of a snowball 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 icon of a teetertotter is used |
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In order to make the notion of feedback a little more salient, Figure 6 to Figure 17 present a collection of positive and negative loops. As these loops are shown in isolation (i.e., disconnected from the other parts of the systems to which they belong), their individual behaviors are not necessarily the same as the overall behaviors of the systems from which they are taken.
Positive Feedback Examples
| Population Growth/Decline: Figure 6 shows the feedback mechanism responsible for the growth of an elephant herd via births. In this simple example we consider two system variables: Elephant Births and Elephant Population. For a given elephant herd, we say that if the birth rate of the herd were to increase, the Elephant Population would increase. In this same way, we can say that if - over time - the Elephant Population of the herd were to increase, the birth rate of the herd would increase. Thus, the Elephant Birth rate drives the Elephant Population that drives Elephant Birth rate - positive feedback. |
Figure 6: Positive Loop Responsible for the Growth in an Elephant Herd via Births |
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National Debt: Figure 7 is a positive loop that shows the growth in the national debt due to the 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 ) will cause the overall national debt to increase. In this same way, an increase in the level of national debt will increase the amount of the interest paid each year. |
Figure 7: Positive Loop Showing Growth in the National Debt Due to Compounding Interest Payments |
| Arms Race: Figure 8 shows a generic arms race between Country A and Country B. In its simplest form, an "arms race" can be described as a self-sustaining competition for military superiority. An arms race is driven by the perception that one's adversary has equal or greater military strength. If Country A moves to increase its military capability, Country B interprets this as a threat and responds in-kind with its own increase in military capability. Country B's action, in turn, causes Country A to feel more threatened. Thus, Country A moves to further increase its military capability. |
Figure 8: Arms Race is a Positive Feedback Process. |
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Bank Panic: A common scene during the Great Depression in the 1930s was that of a panic stricken crowd standing outside their local bank waiting to withdraw what remained of their savings. Figure 8 shows the feedback mechanism responsible for the spiraling decline of the banking system during this period. From the diagram, we see that the frequency of bank failures increases public concern and the fear of losing their money. In this case, we say that the two system variables "move" in the same (S) or positive (+) direction. The relationship between the "fear of not being able to withdraw money" and the rate at which bank withdrawals are made is also positive. |
Figure 9: Bank panic is a positive feedback process. |
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The relationship between withdrawals and bank health is negative (-) or opposite (O). This means that if the rate of bank withdrawals increases, the health of the bank decreases as capital reserves are drawn down. The relationship between the banking industry's health and the rate of bank failures is also 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 rate of bank failures to increase. As more banks failed, the public's fear of not being able to withdraw their own 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 interacting positive feedback loops that
are thought to be responsible for the growth in students taking drugs in
high school |
Figure 10: Feedback structure responsible for growth high school drug use |
Negative Feedback Examples
Population Growth/Decline:In Figure 6, we saw how an elephant population and its corresponding birth rate form a positive feedback loop. Now, we consider the other half of the equation, that is, the feedback structure between Elephant Population and Elephant Death rate. Figure 11 shows the negative feedback process responsible for the decline of an elephant herd via deaths. If the Elephant Death rate increases, the Elephant Population will decrease. A negative sign indicates this counteracting behavior. The causal influence of Elephant Population to Elephant Death rate is just the opposite. An increase in the number of elephants in the herd means that a proportionally larger number of elephants will die each year, i.e., an increase in the herd's death rate. A plus sign indicates this complimentary behavior. These two relationships combine together 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. Figure 12 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's Hunger causes a person to eat more food. Increasing in the rate food consumption, in turn, reduces Hunger. | |
Figure 12: Scratching an itch and negative feedback |
Figure 13: Dissipation of hunger |
| Law Enforcement:Figure 14 depicts a negative feedback process that maintains a balance between the number of drug dealers and the number of police officers in a neighborhood. An increase in the number of drug dealers in a neighborhood will prompt local officials to increase the number of law enforcement persons as a counter measure. As the number of police officers increase, more arrests are made and the number of drug dealers is reduced. |
Figure 14: Neighborhood drug intervention negative feedback |
| Car Pools:Figure 15 shows a negative feedback process that maintains a balance between car pools and gasoline consumption. An increase in gasoline consumption increases gasoline price (supply reduction). A higher gasoline price pushes many individual motorists to join carpools, which reduces the total number of vehicles on the road. This, in turn, reduces gasoline 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, misleading because the goals they are seeking are implicit rather than explicit. For example, the implicit goal of the loop in Figure 11 is zero elephants. That is, if the loop were to act, in isolation, for a substantial period 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 and zero hunger respectively.The logic gets even murkier in the case of Figure 14 and Figure 15. In Figure 14, 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 tolerable gasoline price, which is certainly a lower price rather than a higher price, but is also (realistically) not zero.
Figure 16: Generic negative feedback structure with explicit goal
An alternative and (often) more desirable way to represent negative feedback processes via causal loop diagrams is by explicitly identifying the goal of each loop. Figure 16, for example, shows a causal loop diagram 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 desired number 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 the desired number, corrective action -- i.e., hunting -- is called forth. This action reduces the size of the herd and brings it into line with the desired number of elephants.
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 interacting positive 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 to discuss in detail.
As Figure 18 and Figure 19 show, when causal loop diagrams are used
in this fashion, things can get rather complicated. Figure 18 is a causal
loop diagram of a system dynamics model created to examine issues related
to profitability in the paper and pulp industry. This figure has a number
of features that are important to mention. The first is that the authors
have numbered each of the positive and negative
loops so that they can be easily referred to in a verbal or written discussion.
The second is that the authors have taken great care to choose variable
names that have a clear sense of direction and have real-life counterparts
in the actual system.
The last and most important feature is that, although the figure 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 mentally simulate,
the dynamics of the paper and pulp system from Figure 18 alone.
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 be responsible for the growth or decline of
life insurance companies in the United Kingdom. As with Figure 18, a number
of this figure's features are worth mentioning. The first is that the model's
negative feedback loops are identified by "C's," which stand
for "Counteracting" loops. The second is that double 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 common causal loop diagramming convention
in system dynamics. Third, is that thicker lines are used to identify the
feedback loops and links that author wishes the audience to focus on. This
is also a common system dynamics diagramming convention.
Last, as with Figure 18, it is clear that a decision maker would find it
impossible to think through the dynamic behavior inherent in the model,
from inspection of Figure 19 alone.
Figure 19: Causal Loop Diagram of a Model Examining the Growth
or Decline of a Life Insurance Company.
Archetypes
An area of the field of system dynamics or, more precisely, of the much
broader field of "systems thinking," that has recently received
a great deal of attention is archetypes.
Archetypes are generic feedback 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 when a decision maker notices that one of them is at work in his
or her organization. Presumably, the decision maker 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:
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Recent efforts, however, have suggested that the number can be reduced to four:
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No matter what the true number archetypes is or will be, however, the central question remains unanswered: How successful are archetypes in helping decision makers solve problems in their organizations?
Problems with Causal Loop Diagrams
Causal loop diagrams are an important tool in the field of system dynamics modeling. Almost all system dynamicists 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 been created.
The only potential problem with causal loop diagrams and archetypes then,
occurs when a decision 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 flows and conserved (noninformation) flows. As a result,
they can blur direct causal relationships between flows and stocks. Further,
it is impossible, in principle, to determine the behavior of a system solely
from the polarity of its feedback loops, because stocks and flows create
dynamic behavior, not feedback. 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 dynamic behavior is further weakened. The conclusion is that
simulation is essential if a decision maker is to gain a complete understanding
of the dynamics of a system.
