Some nonrobust bernoulli-shift rules

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)3407-3415
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume19
Issue number10
Publication statusPublished - Oct 2009

Abstract

In this paper, it is shown that elementary cellular automata rule 172, as a member of the Chua's robust period-1 rules and the Wolfram class I, is also a nonrobust Bernoulli-shift rule. This rule actually exhibits complex Bernoulli-shift dynamics in the bi-infinite binary sequence space. More precisely, in this paper, it is rigorously proved that rule 172 is topologically mixing and has positive topological entropy on a subsystem. Hence, rule 172 is chaotic in the sense of both LiYorke and Devaney. The method developed in this paper is also applicable to checking the subshifts contained in other robust period-1 rules, for example, rules 168 and 40, which also represent nonrobust Bernoulli-shift dynamics. © 2009 World Scientific Publishing Company.

Research Area(s)

  • Bernoulli-shift rule, Cellular automata, Chaos, Subshift, Topological entropy, Topologically mixing

Citation Format(s)

Some nonrobust bernoulli-shift rules. / Chen, Lin; Chen, Fangyue; Jin, Weifeng; Chen, Fangfang; Chen, Guanrong.

In: International Journal of Bifurcation and Chaos, Vol. 19, No. 10, 10.2009, p. 3407-3415.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review