Topologically Mixing and Chaos of One Class of Bernoulli-Shift Cellular Automata Rules

Abstract

This paper is devoted to an in-depth study of Chua's Bernoulli-shift rules 11, 14, 43 and 142 from the viewpoint of symbolic dynamics. It is shown that each of these four rules identifies two chaotic dynamical subsystems and presents very rich and complicated dynamical properties. In particular, they are topologically mixing and possess the positive topological entropies on their two subsystems. Therefore, they are chaotic in the sense of both Li-Yorke and Devaney on the subsystems. The method proposed in this work is also gives some support for investigating the dynamics of subsystems of other rules, especially the hyper-Bernoulli-shift rules therein.