Chimera states in heterogeneous networks

TL;DR

This paper investigates how heterogeneity in natural frequencies affects chimera states in coupled oscillator networks, revealing conditions under which heterogeneity destroys, preserves, or destabilizes these states.

Contribution

It provides exact results for heterogeneous networks by reducing the problem to finite differential equations, extending understanding beyond identical oscillators.

Findings

Heterogeneity can destroy chimera states.

Heterogeneity can preserve or destabilize chimerae.

Destabilization occurs via Hopf bifurcations.

Abstract

Chimera states in networks of coupled oscillators occur when some fraction of the oscillators synchronise with one another, while the remaining oscillators are incoherent. Several groups have studied chimerae in networks of identical oscillators, but here we study these states in a heterogeneous model for which the natural frequencies of the oscillators are chosen from a distribution. We obtain exact results by reduction to a finite set of differential equations. We find that heterogeneity can destroy chimerae, destroy all states except chimerae, or destabilise chimerae in Hopf bifurcations, depending on the form of the heterogeneity.