Synchronization of Kuramoto model with time-varying forcing in complex networks

In this paper، a generalization of the Kuramoto model is introduced by explicit consideration of deterministically time-varying periodic external force. In this model، the oscillator''s natural frequencies and amplitude of collective oscillations are influenced by external forces with constant or random strengths. Then، the synchronization behavior of forced Kuramoto model is studied in some complex networks. In the model، a new collective dynamics behavior is observed، i. e.، all the oscillators are synchronized at one second، and after a little time، all of them become unsynchronized. Also، a distinct behavior of small-world networks is observed. When the strength of external force has a bimodal distribution، a resonant behavior in small-world network is seen.