Chaos. Write a program to study the following simple model for population growth, which might be…

Chaos. Write a program to study the following simple model
for population growth, which might be applied to study fish in a pond, bacteria
in a test tube, or any of a host of similar situations. We suppose that the
population ranges from 0 (extinct) to 1 (maximum population that can be sustained).
If the population at time t is x, then we suppose the population at time t + 1
to be r x (1- x), where the argument r, known as the fecundity parameter,
controls the rate of growth. Start with a small population—say, x = 0.01—and
study the result of iterating the model, for various values of r.
»

Chaos. Write a program to study the following simple model
for population growth, which might be applied to study fish in a pond, bacteria
in a test tube, or any of a host of similar situations. We suppose that the
population ranges from 0 (extinct) to 1 (maximum population that can be sustained).
If the population at time t is x, then we suppose the population at time t + 1
to be r x (1- x), where the argument r, known as the fecundity parameter,
controls the rate of growth. Start with a small population—say, x = 0.01—and
study the result of iterating the model, for various values of r. For which
values of r does the population stabilize at x = 1 – 1/r ? Can you say anything
about the population when r is 3.5? 3.8? 5?

»

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