Travelling Wave in the Generalized Kuramoto Model with Inertia**Supported by the National Natural Science Foundation of China under Grant Nos 11447001 and 11247318, and the Key Project of Scientific and Technological Research of the Education Department of Henan Province under Grant Nos 16A140002 and 13A140025.

Abstract

We study the dynamics of the generalized Kuramoto model with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already displayed travelling wave states and π state in previous literature. The modulated travelling wave state may be characterized by the phase distributions of oscillators. Finally, the modulated travelling wave state and the travelling wave state of the model in the parameter space are presented.