Collective phase slips and phase synchronizations in coupled oscillator systems

Phase synchronization dynamics in coupled limit cycles with distributed natural frequencies are explored. A synchronization tree from free oscillations to local clustering and global phase locking is found. A desynchronization-induced transition to chaos is shown. Near the onset of various phase synchronization points, a simultaneous quantized stick-slip feature of the phases of oscillators is observed on the desynchronization side and heuristically interpreted in terms of a heteroclinic path instability.