Synchronization Thresholds in an Ensemble of Kuramoto Phase Oscillators with Randomly Blinking Couplings

Abstract

We consider a network of Kuramoto phase oscillators with randomly blinking couplings. Applicability of the averaging method for small switching intervals is rigorously substantiated. Using this method, we analytically estimate the threshold coupling force for synchronizing the ensemble oscillators. The threshold synchronization is studied as a function of the switching interval for various network sizes. The effect of preserving synchronization for a significant increase in the switching interval is found, which is the key feature of the system since a slight increase in this interval usually leads to the synchronization failure. The intermittent-synchronization possibility for small network sizes and large switching intervals is shown. An increase in the network size is shown to result in a stability increase due to the decreasing probability of appearance of uncoupled configurations. The regions corresponding to the global synchronization of oscillators are singled out in the system-parameter space.