Recurrent synchronization of coupled oscillators with spontaneous phase reformation

Self-organizing and spontaneous breaking are seemingly opposite phenomena and hardly captured in a single model. We develop a second order Kuramoto model with phase-induced damping which shows phase locking together with spontaneous synchrony breaking and reformation. In a relatively large regime where the interacting force and the damping ratio are of the same order, the dynamics of the oscillators alternates in an irregular cycle of synchronization, formation-breaking, and reorganization. While the oscillators keep coming back to phase-locked states, their phase distribution repeatedly reforms. Also, the interevent time between bursty deviation from the synchronization states follows a power-law distribution, which implies that the synchronized states are maintained near a tipping point.