The first of these runs generates a steady-state population of N ¼ 0.5, and the
second run yields a damped oscillation. With R ¼ 2 we have a situation in which the
population size can be thought of overshooting some carrying capacity, then gets
correct and falls below that carrying capacity, only to overshoot again—albeit to a
smaller extent—in the next period.
Increase R to 4. You should find that the population has left its regular pattern
and becomes chaotic—the curve never repeats itself (Fig. 4.4). Pause the model
halfway through its run and make a guess on the future path. Can you predict where
it is going, solely based on your observation of its past behavior and current position?
Fig. 4.3
Fig. 4.4
4.1 The Emergence of Chaos in Population Models
49
second run yields a damped oscillation. With R ¼ 2 we have a situation in which the
population size can be thought of overshooting some carrying capacity, then gets
correct and falls below that carrying capacity, only to overshoot again—albeit to a
smaller extent—in the next period.
Increase R to 4. You should find that the population has left its regular pattern
and becomes chaotic—the curve never repeats itself (Fig. 4.4). Pause the model
halfway through its run and make a guess on the future path. Can you predict where
it is going, solely based on your observation of its past behavior and current position?
Fig. 4.3
Fig. 4.4
4.1 The Emergence of Chaos in Population Models
49