Spiral wave chimeras induced by heterogeneity in phase lags and time delays

Abstract

A spiral wave chimera is a remarkable spatiotemporal pattern in a two-dimensional array of oscillators, for which the coherent spiral arms coexist with incoherent cores. So far the spiral wave chimeras have been known to occur in nonlocally coupled oscillators where the coupling strength between oscillators varies with the distance between them. Here we report on spiral wave chimeras for globally coupled phase oscillators with heterogeneous phase lags on the sphere. On the basis of Ott–Antonsen theory, we reduce our model to a low-dimensional system and present stability diagrams for different stationary states of the reduced system. We demonstrate the existence of spiral wave chimeras for the globally coupled phase oscillators with space-dependent interaction delays on the sphere, which are extended to appear also in the Stuart–Landau system of amplitude–phase oscillators. Chimeric behavior due to the heterogeneity in phase lags or time delays is peculiar to two-dimensional arrays of oscillators, which exhibits a self-emerging state in a wide parameter region. As an essential driving mechanism for the emergence of spiral chimeras, the space-dependent feature of interaction delays is omnipresent in nature and engineering systems, and we anticipate that our model and the related spiral chimera patterns will have widespread practical applications in the biological oscillatory networks.