Synchronization of stochastically coupled cellular automata

Abstract

We analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics. The coupling mechanism, characterized by a probability $p$, is stochastic. From numerical simulations, we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of $p$. This transition admits an approximate semianalytical description in terms of the evolution of the difference automaton, and is found both for symmetric and asymmetric coupling. It is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics.