Chimera patterns in the Kuramoto-Battogtokh model

TL;DR

This paper investigates chimera patterns in the Kuramoto-Battogtokh model, discovering various rotating solutions, analyzing their stability, and providing analytical solutions in certain coupling limits.

Contribution

It introduces a new approach to find and analyze rotating chimera patterns as solutions of differential equations, including analytical solutions in specific coupling regimes.

Findings

Multiple rotating chimera patterns identified

Only simplest chimeras with one synchronous region are stable

Analytical solutions derived for neutral coupling limit

Abstract

Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After reformulation in terms of local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating periodic in space chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in form of one- and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only simplest chimeras with one synchronous region are stable.