Sequences -- Chaos -- Answers

1. Because this is an open-ended question many different answers are possible. Any logistic model of the form

   p(n + 1) = 4 [1 - b p(n)] p(n)

   exhibits chaos unless p(1) is exactly an equilibrium point or a cycle.

   Logistic models of the form

   p(n + 1) = a [1 - b p(n)] p(n)

   where a is close to 4 also exhibit chaos. It is interesting and somewhat difficult to determine how close a must be to 4 to have chaos.