Dynamics of the Kuramoto Model with Bimodal Frequency Distribution on Complex Networks

Abstract

We introduce a piecewise uniform frequency distribution to model a symmetrical bimodal natural frequency distribution and investigate the dynamics in the Kuramoto model on complex networks. We find that the scenario of the synchronization transition depends on the network topology. For an ER network, the incoherent state, standing wave states and stationary synchronous states are encountered successively with the increase of the coupling strength. However, for an SF network, there exists another type of synchronous states, traveling wave states, between the standing wave states and the stationary synchronous states.