On the population model with a sine function

Abstract

In the interval [0,1] function s_r(x) = r sin πx behaves similar to logistic function h _μ (x) = μx(1‐ x). We prove that for every r >  there exists subset ? ⊂ [0,1] such that s_r : ? → ? is a chaotic function. Since the logistic function is chaotic in another subset of [0,1] but both functions have similar graphs in [0,1] we conclude that it can lead to errors in practice.

First Published Online: 14 Oct 2010