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arXiv · 1903.02459

Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata

Marc Kesseböhmer·Jens D. M. Rademacher·Dennis Ulbrich
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Abstract

In this paper we analyse the non-wandering set of 1D-Greenberg-Hastings cellular automata models for excitable media with $e\geqslant 1$ excited and $r\geqslant 1$ refractory states and determine its (strictly positive) topological entropy. We show that it results from a Devaney-chaotic closed invariant subset of the non-wandering set that consists of colliding and annihilating travelling waves, which is conjugate to a skew-product dynamical system of coupled shift-dynamics. Moreover, we determine the remaining part of the non-wandering set explicitly as a Markov system with strictly less topological entropy that also scales differently for large $e,r$.

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Marc Kesseböhmer, Jens D. M. Rademacher, Dennis Ulbrich. 2019-03-06. Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata. https://doi.org/10.1017/etds.2020.18

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