Mat Lab

In the previous problem, we looked at the logistic map: P(t+1) = rP(1)(1 - PO) where P(0) = 8 and K = 20. In particular, we found that when r = 2.5, the population density P(t) approached a constant value as t grew. This constant value is called a stable equilibrium of the logistic map. We also found that P(t) did not approach a single constant value as t grew when r = 3.2 or when r = 3.5. We therefore know that the logistic map does not have a stable equilibrium for these r values. In this problem, we would like to determine which values of r lead to a stable equilibrium for the logistic map. As a somewhat crude method, we can check if the population densities stop changing (or at least do not change very much) after a long enough wait. We will say that the logistic map has a stable equilibrium if P(501) P(500) is sufficiently small. In particular, the logistic map has a stable equilibrium if 10-8