Chimeras in networks of planar oscillators

TL;DR

This paper extends the analysis of chimera states to networks of planar oscillators with amplitude and phase, revealing how bifurcations can destroy these states as attractivity decreases.

Contribution

It presents the first analysis of chimera states in planar oscillators, broadening understanding beyond phase-only models.

Findings

Chimeras are destroyed via saddle-node bifurcations as attractivity decreases.

Supercritical Hopf bifurcations of chimeras are observed.

Homoclinic bifurcations also lead to the destruction of chimeras.

Abstract

Chimera states occur in networks of coupled oscillators, and are characterized by having some fraction of the oscillators perfectly synchronized, while the remainder are desynchronized. Most chimera states have been observed in networks of phase oscillators with coupling via a sinusoidal function of phase differences, and it is only for such networks that any analysis has been performed. Here we present the first analysis of chimera states in a network of planar oscillators, each of which is described by both an amplitude and a phase. We find that as the attractivity of the underlying periodic orbit is reduced chimeras are destroyed in saddle-node bifurcations, and supercritical Hopf and homoclinic bifurcations of chimeras also occur.