Chimera states in coupled map lattices: Spatiotemporally intermittent behavior and an equivalent cellular automaton

TL;DR

This paper investigates chimera states in a globally coupled sine circle map lattice, revealing conditions for their emergence, characterizing their spatiotemporal structures, and establishing an equivalent cellular automaton model that replicates these behaviors.

Contribution

It introduces a cellular automaton model equivalent to the coupled map lattice and derives a mean field equation that captures the chimera state dynamics.

Findings

Chimera states emerge from random initial conditions at specific parameters.

The phase diagram identifies regions supporting different phase configurations.

The cellular automaton replicates the space-time behavior of the CML and matches the mean field analysis.

Abstract

We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random initial condition evolves to chimera states, having a phase synchronised and a phase desynchronised group, where the space time variation of the phases of the maps in the desynchronised group shows structures similar to spatiotemporally intermittent regions. Using the complex order parameter we obtain a phase diagram that identifies the region in the parameter space which supports chimera states of this type, as well as other types of phase configurations. An equivalent cellular automaton is obtained which shows space time behaviour similar to the CML. We also derive a mean field equation for this cellular automaton and compare its solutions with the corresponding phase configurations obtained in the parameter space, and show that it matches with the behavior seen for the CML.