Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment

TL;DR

This paper demonstrates that spiral wave chimeras can exist in populations of oscillators coupled to a slowly varying diffusive environment, expanding understanding of chimera states beyond the previously studied rapid environment coupling.

Contribution

It shows the existence of spiral wave chimeras in oscillator-environment systems with large characteristic time scale, supported by simulations with Stuart-Landau and FitzHugh-Nagumo oscillators.

Findings

Spiral wave chimeras persist for large environment time scales.

Transitions between chimeras and regular spiral waves are characterized.

Chimera states are confirmed in different oscillator models.

Abstract

Chimera states are firstly discovered in nonlocally coupled oscillator systems. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scale $\tau$ is so small (i.e., $\tau \rightarrow 0$) that it could be eliminated adiabatically. Nevertheless, whether the chimera states still exist in the opposite situation (i.e., $\tau \gg 1$) is unknown. Here, by coupling large populations of Stuart-Landau oscillators to a diffusive environment, we demonstrate that spiral wave chimeras do exist in this oscillator-environment coupling system even when $\tau$ is very large. Various transitions such as from spiral wave chimeras to spiral waves or unstable spiral wave chimeras as functions of the system parameters are explored. A physical picture for explaining the formation of spiral wave chimeras is also provided. The existence of spiral wave chimeras is further confirmed in ensembles of FitzHugh-Nagumo oscillators with the similar oscillator-environment coupling mechanism. Our results provide an affirmative answer to the observation of spiral wave chimeras in populations of oscillators mediated via a slowly changing environment and give important hints to generate chimera patterns in both laboratory and realistic chemical or biological systems.