Collective Synchronization of Kuramoto-Oscillator Networks

Synchronization as a typical collective phenomenon emerges in many complex systems, and has attracted world-wide attention from science, engineering, sociology, and so forth. With the fast rising and development of network science, the Kuramoto-oscillator model is becoming one of the most pervasive paradigms for investigating collective synchronous behaviors. This review collects the latest advances of synchronization of Kuramoto-oscillator networks as well as several applications, such as locking of circuit oscillators, frequency synchronization in power grids, collective motion of self-propelled vehicles, and opinion synchronization in social networks. Besides, we specially address the intra-layer and inter-layer synchronization of multi-layer Kuramoto-oscillator networks, along with the stability analysis of Kuramoto-oscillator networkvs with and without control. Finally, we conclude this review with the discussions on some potential future directions for Kuramotooscillator networks.