Chimera states on a flat torus

TL;DR

This paper derives conditions for the emergence of two-dimensional chimera states on a flat torus and investigates their stability through numerical simulations, contributing to understanding these complex spatiotemporal patterns.

Contribution

It provides the first asymptotic derivation of conditions for 2D chimera states on a flat torus and analyzes their stability via numerical methods.

Findings

Conditions for 2D chimera formation derived mathematically

Numerical simulations identify stable chimera configurations

Chimera states can persist under specific parameter regimes

Abstract

Discovered numerically by Kuramoto and Battogtokh in 2002, chimera states are spatiotemporal patterns in which regions of coherence and incoherence coexist. These mathematical oddities were recently reproduced in a laboratory setting sparking a flurry of interest in their properties. Here we use asymptotic methods to derive the conditions under which two-dimensional chimeras, similar to those observed in the experiments, can appear in a periodic space. We also use numerical integration to explore the dynamics of these chimeras and determine which are dynamically stable.