Synchronization and control of cellular automata

TL;DR

This paper explores methods to control and synchronize cellular automata, a class of extended discrete systems, by leveraging their unique properties to improve control efficiency and address challenges posed by stable chaos.

Contribution

It introduces novel control strategies tailored for cellular automata, highlighting how system characteristics can be exploited to reduce control effort in complex, high-dimensional discrete systems.

Findings

Control methods can effectively synchronize cellular automata.

Exploiting system characteristics reduces control effort.

Traditional chaos indicators may be misleading for cellular automata.

Abstract

The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the control may be concentrated on the most expanding directions. This scheme is hard to follow for high-dimensional (extended) systems. This is particularly true for extended systems that exhibit stable chaos, that is, systems which are not chaotic in the usual sense, but are unpredictable for finite perturbations. Prototypical of this class are cellular automata, aka completely discrete dynamical systems. Although usual indicators of chaoticity such as the maximum Lyapunov exponent may be defined for such systems, we show that the usual approach may lead to counter intuitive results, and that it is possible to exploit the characteristics of the system in order to reduce the distance between two replicas with less control.