Construction of chaotic dynamical system

Abstract

The first‐order difference equation x_n+ 1 = f(x_n ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S ₂. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic.

First published online: 09 Jun 2011