Randomly connected cellular automata: A search for critical connectivities

TL;DR

This paper investigates the behavior of Chate-Manneville cellular automata on randomly connected lattices, revealing critical connectivities, decay of autocorrelations, and a new chaotic phase, extending understanding of complex dynamics in high-dimensional systems.

Contribution

It demonstrates that macroscopic behaviors of these automata persist on infinite-dimensional lattices and identifies critical connectivity thresholds and a novel chaotic phase.

Findings

Lower critical connectivity at C=4

Autocorrelations decay as a power-law with exponent ~-2.5

Existence of a new intermittent chaotic phase

Abstract

I study the Chate-Manneville cellular automata rules on randomly connected lattices. The periodic and quasi-periodic macroscopic behaviours associated with these rules on finite-dimensional lattices persist on an infinite-dimensional lattice with finite connectivity and symmetric bonds. The lower critical connectivity for these models is at C=4 and the mean-field connectivity, if finite, is not smaller than C=100. Autocorrelations are found to decay as a power-law with a connectivity independent exponent approx. equal to -2.5. A new intermitten chaotic phase is also discussed.