Solutions1 - Business Dynamics Instructors Manual Chapter 1...

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Business Dynamics Instructor’s Manual Chapter 1 1 1 Learning in and about Complex Systems 1.1 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 system. 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. Again, most 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. In my 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 others. 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. Different 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 system. 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 people would still not be able to infer correctly what the dynamics would be.
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