Stability of twisted states in the continuum Kuramoto model

TL;DR

This paper investigates the stability of twisted states in a continuum Kuramoto model, providing conditions for stability and applying these results to small-world graph networks.

Contribution

It offers a new stability criterion for twisted states in nonlocal diffusion models and applies it to Kuramoto models on complex networks.

Findings

Derived a sufficient stability condition for twisted states

Applied stability analysis to small-world graph networks

Identified stability differences in Sobolev and BV spaces

Abstract

We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient condition for stability of twisted states with respect to perturbations in the Sobolev and BV spaces. As an application, we study stability of twisted states in the Kuramoto model on small-world graphs.