Cellular automaton for chimera states

TL;DR

This paper introduces a simple cellular automaton model with a single parameter that can spontaneously generate chimera states, revealing their potential universality across elementary rules and coupling ranges.

Contribution

The authors present a minimalistic cellular automaton model that exhibits chimera states, highlighting their emergence from simple rules and broad applicability.

Findings

Chimera states appear after short transients for various initial conditions.

Stable domains of synchronized and incoherent behavior form with static boundaries.

Different periodic structures emerge when the coupling is local.

Abstract

A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent structures with different periodicities are formed.