Spiral wave chimeras in locally coupled oscillator systems

TL;DR

This paper demonstrates the existence of spiral wave chimeras in reaction-diffusion systems with local coupling, expanding the understanding of chimera states beyond non-local or global coupling scenarios.

Contribution

First numerical evidence of spiral wave chimeras in locally coupled reaction-diffusion systems, revealing new dynamics and transition behaviors.

Findings

Spiral wave chimeras rotate inwardly with propagating waves toward the core.

A continuous transition from smooth spiral waves to chimeras occurs with changing local dynamics.

Spiral wave chimeras may naturally occur in systems modeled by diffusive coupling.

Abstract

The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. This fascinating chimera state has until now been found only in non-local or globally coupled oscillator systems. In this work, we for the first time show numerical evidence of the existence of spiral wave chimeras in reaction-diffusion systems where each element is locally coupled by diffusion. This spiral wave chimera rotates inwardly, i.e., coherent waves propagate toward the phase randomized core. A continuous transition from spiral waves with smooth core to spiral wave chimeras is found as we change the local dynamics of the system. Our findings on the spiral wave chimera in locally coupled oscillator systems largely improve our understanding of the chimera state and suggest that spiral chimera states may be found in natural systems which can be modeled by a set of oscillators indirectly coupled by a diffusive environment.