Dynamics in the Kuramoto Model with a Discontinuous Bimodal Distribution of Natural Frequencies

Abstract

We consider a Kuramoto model in which the natural frequencies of oscillators follow a discontinuous bimodal distribution constructed from a Lorentzian one. Different synchronous dynamics (such as different types of travelling wave states, standing wave states, and stationary synchronous states) are identified and the transitions between them are investigated. We find that increasing the asymmetry in frequency distribution brings the critical coupling strength to a low value and that strong asymmetry is unfavorable to standing wave states.