Solvable Model of Spiral Wave Chimeras

TL;DR

This paper introduces an analytical model for spiral wave chimeras in nonlocally coupled oscillators, providing formulas for their rotation speed and core size, advancing understanding of complex spatiotemporal patterns.

Contribution

It presents the first analytical description of spiral wave chimeras, including perturbation-based calculations of their key properties.

Findings

Derived formulas for rotation speed of spiral wave chimeras

Calculated size of the incoherent core

Provided analytical insight into nonlocal oscillator dynamics

Abstract

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here we provide the first analytical description of such a spiral wave chimera, and use perturbation theory to calculate its rotation speed and the size of its incoherent core.