Solvable model for chimera states of coupled oscillators

TL;DR

This paper presents an exact analysis of chimera states in coupled oscillator networks, revealing their stability, dynamics, and bifurcations through a minimal two-population model.

Contribution

It provides the first exact results on the stability and bifurcations of chimera states using a simplified two-population oscillator model.

Findings

Stable and breathing chimera states identified

Bifurcations such as saddle-node, Hopf, and homoclinic analyzed

Exact stability results obtained for the minimal model

Abstract

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized sub-populations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf and homoclinic bifurcations of chimeras.