Learning in and about Complex Systems
Dynamics of Multiple-Loop Systems (section 1.1.3)
It is best to pose this challenge in class, immediately after defining positive and negative
feedback loops using the chicken and egg illustration shown in Figure 1-5.
I usually ask people
first what the behavior of the system would be if the positive loop were the only loop active in
The vast majority of people correctly say that the chicken and egg population would
grow exponentially (as shown in Figure 1-5).
Then ask what the behavior of the chicken
population would be if the negative road-crossing loop were the only loop active.
people correctly conclude that the chicken population declines, and most of these will sketch an
asymptotic decline to zero, as shown in the figure.
Next, ask the group what the behavior of the system would be when both loops are active,
assuming the initial chicken population is fairly small, but includes at least one rooster.
experience, people will generate a number of different possibilities, including S-shaped growth,
S-shaped growth with oscillations, oscillations, overshoot and collapse, equilibrium, and perhaps
I sketch all these on the board as people suggest them until all the different suggested
trajectories are captured.
I then ask people to notice the differences of opinion about the behavior of the system, indicating
that even in a system with only two feedback loops, a system of incredible simplicity compared
to the systems and models we will be dealing with, it is not possible to infer correctly and
reliably the dynamics of the system from a representation of its structure.
Human beings do not
have the cognitive capability to simulate accurately the dynamics of complex systems.
people, examining the same model of a system, can come to quite different conclusions about the
implications of that model.
The only reliable way to determine the implications of such a model
is through computer simulation.
You should also note for the students that there is no single correct answer to this challenge.
Causal loop diagrams do not (and are not intended to) provide the precise specification of causal
relationships (as equations with parameter values) required to infer correctly the dynamics of a
To provide a unique answer it would be necessary to specify the functional relationships
for all the variables, the values of all parameters, and the initial conditions.
For example, if there
are no time delays in either loop, and if the probability of road crossing increases nonlinearly as
population density grows, then the behavior will be S-shaped growth.
The generic population
growth model in chapter 4 provides a framework to explore the different possibilities for the
dynamics of such a system as relationships and parameters vary.
Note, however, that even if we
provided the equations, parameters, and initial conditions for the chicken and egg model, most