Clustering as a prerequisite for chimera states in globally coupled systems

TL;DR

This paper investigates the conditions under which chimera states emerge in globally coupled oscillators, highlighting that initial clustering into groups is a necessary step for their formation and that these states derive properties from cluster states.

Contribution

It demonstrates that clustering is a prerequisite for chimera states in globally coupled systems and shows their relation to cluster and chaotic states.

Findings

Clustering is essential for chimera state formation.

Chimera states inherit properties from cluster states.

Chimera states can exist between cluster and chaotic or synchronized states.

Abstract

The coexistence of coherently and incoherently oscillating parts in a system of identical oscillators with symmetrical coupling, i.e., a chimera state, is even observable with uniform global coupling. We address the question of the prerequisites for these states to occur in globally coupled systems. By analyzing two different types of chimera states found for nonlinear global coupling, we show that a clustering mechanism to split the ensemble into two groups is needed as a first step. In fact, the chimera states inherit properties from the cluster states in which they originate. Remarkably, they can exist in parameter space between cluster and chaotic states, as well as between cluster and synchronized states.