Clustering as a prerequisite for chimera states in globally coupled systems

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.