Chimeras with uniformly distributed heterogeneity: two coupled populations

TL;DR

This paper investigates the existence and stability of chimera states in two coupled oscillator populations with one population's parameters uniformly distributed, revealing that increasing heterogeneity destabilizes chimeras.

Contribution

It generalizes previous models to include heterogeneity in oscillator parameters and analyzes how this affects chimera stability in large networks.

Findings

Heterogeneity destroys stable chimeras via saddle-node bifurcation.

Chimeras are less robust as oscillator heterogeneity increases.

Results extend understanding of chimera robustness in realistic networks.

Abstract

Chimeras occur in networks of two coupled populations of oscillators when the oscillators in one population synchronise while those in the other are asynchronous. We consider chimeras of this form in networks of planar oscillators for which one parameter associated with the dynamics of an oscillator is randomly chosen from a uniform distribution. A generalisation of the approach in [C.R. Laing, Physical Review E, 100, 042211, 2019], which dealt with identical oscillators, is used to investigate the existence and stability of chimeras for these heterogeneous networks in the limit of an infinite number of oscillators. In all cases, making the oscillators more heterogeneous destroys the stable chimera in a saddle-node bifurcation. The results help us understand the robustness of chimeras in networks of general oscillators to heterogeneity.