Stability of twisted states in the continuum Kuramoto model

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.

References in corpus (3)

• The nonlinear heat equation on W-random graphs
• Small-world networks of Kuramoto oscillators
• Stability of twisted states in the Kuramoto model on Cayley and random graphs

Cited by in corpus (6)

• Bifurcations in the Kuramoto model on graphs
• Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations
• Dynamical Systems on Graph Limits and Their Symmetries
• The Kuramoto model on power law graphs
• Capturing the critical coupling of large random Kuramoto networks with graphons
• Persistence of steady-states for dynamical systems on large networks