Cluster Synchronization in Networked Phase Oscillators under Periodic Coupling

The synchronization behaviors of coupled oscillators under time-varying couplings are of both theoretical and practical significance. While recent studies show that synchronization is suppressed by time-varying coupling in general, the underlying mechanism is still not very clear. Here, by the kernel of sinusoidal coupling function, we revisit the effects of periodic coupling on the synchronization of networked phase oscillators. It is found that the suppressed synchronization by periodic coupling is attributed to the formation of synchronization clusters in the transition from desynchronization to global synchronization. The clusters are different in size and frequency but are all locked to the frequency of the periodic coupling. We demonstrate this phenomenon numerically in different network models and conduct a theoretical analysis on the numerical results based on the method of dimension reduction. The findings extend our knowledge on the dynamical responses of a complex network to external drivings, and shed lights on the mechanism of suppressed synchronization in periodically coupled oscillators.