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

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.