## Thursday, January 19, 2017

### The "causal loops" of system dynamics

Excerpts from Introduction to Computer Simulation: A System Dynamics Modeling Approach by Nancy Roberts, David Anderson, Ralph Deal, Michael Garet, and William Shaffer. Addison-Wesley Publishing Company. Copyright (c) 1983 Lesley College.

Page 16, on causal loops:
One way to clarify the representation of a system is to focus on circular chains or causal loops. Within a causal loop, an initial cause ripples through the entire chain of causes and effects until the initial cause eventually becomes an indirect effect of itself. This process whereby an initial cause ripples through a chain of causation ultimately to reaffect itself is called feedback.

Pages 23-24, on positive and negative feedback loops:
Another approach to better understanding the implications of a closed-loop diagram is "walking through" the links. Take, for example, the "Tired-Sleep" loop shown here.

It can be read: "The more tired I am, the more I sleep. The more I sleep, the less tired I am. The less tired I am, the less I sleep," and so forth around the loop.

If this loop were walked through as it is talked through, stepping in the same direction each time saying the same word (more or less), or reversing direction as the words changed, a distinct two-directional pattern would develop. The tired-sleep loop would produce the pattern of footprints shown below.

The up-and-down pattern is symptomatic of compensating causal loops...

The "Cry-Depressed" loop provides another and different type of example for "walking through."

The footsteps produce the distinct one-directional pattern shown below,

The one-directional pattern is symptomatic of reinforcing causal loops...

So there are compensating loops, and reinforcing loops. Compensating loops undermine the tendency to move away from some equilibrium level. Reinforcing loops reinforce the tendency to move away from equilibrium.

Compensating loops are called negative feedback loops. Reinforcing loops are called positive feedback loops.

Page 43, on positive feedback loops:
The general pattern is that if some quantity within a positive feedback loop begins to increase, then a "snowball" effect takes over, and that quantity continues to increase...

The "snowball" effect of a positive loop can also work in reverse. If a quantity in a positive loop begins to decline, that can lead to a continuing decline...

Occasionally, the equilibrium point is not difficult to determine. In the bank balance problem in figure 3.1, for example, it is easy to see that the equilibrium point is zero. If any amount of money above zero is deposited in a bank account earning 10 percent interest compounded annually, it will grow without bound. But if exactly zero dollars are placed in the account, the balance will remain constant at zero.

Page 44, on negative feedback loops:
Previous examples have indicated that negative feedback loops tend to produce behavior over time that is "stable" and "goal-seeking." For example, a heating system in a house always tends to maintain the house at the same temperature under wide variations in the temperature outside...

The behavior of a negative feedback loop cam be described more easily by referring to the system's equilibrium point. Recall that if a quantity in a positive loop ... is above the equilibrium point, it generally will grow at an accelerating rate; and if it is below the equilibrium point, it will decline at an accelerating rate. Thus the equilibrium point in a positive loop is unstable.

In a negative loop, the situation is just the reverse.

// Related post: Negative Feedback