Synchronization Dynamics in a System of Multiple Interacting Populations of Phase Oscillators

We study the synchronization dynamics in a system of multiple interacting populations of phase oscillators. Using the dimensionality-reduction technique of Ott and Antonsen, we explore different types of synchronization dynamics when the incoherent state becomes unstable. We find that the inter-population coupling is crucial to the synchronization. When the intra-population interaction is repulsive, the local synchronization can still be maintained through the inter-population coupling. For attractive inter-population coupling, the local order parameters in different populations are of in-phase while the local synchronization are of anti-phase for repulsive inter-population coupling.