Periodic coupling suppresses synchronization in coupled phase oscillators

The responses of complex dynamical systems to external perturbations are of both theoretical importance and practical significance. Different from the conventional studies in which perturbations are added on to the system variables, here we consider the scenario of perturbed couplings. Specifically, by the scheme of periodic coupling in which the coupling strength varies periodically with time, we investigate how the synchronization behaviors of an ensemble of phase oscillators are affected by the properties of periodic coupling, including the coupling frequency and amplitude. It is found that, by comparison with the constant coupling scenario, the presence of period coupling will suppress synchronization in general and, with a decrease in the frequency (or the increase of the amplitude) of the periodic coupling, the synchronization performance gradually deteriorates. The influences of periodic coupling on synchronization are demonstrated by numerical simulations in different network models, and the underlying mechanism is analyzed by the method of dimension reduction.