The Kuramoto model on power law graphs

2017/05/14 by Georgi S. Medvedev, Medvedev, Georgi S., Xuezhi Tang +1
Computer Science · #Adaptation and Self-Organizing Systems (nlin.AO) #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1705.04905

openalex publication_date 2017/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Kuramoto model (KM) of coupled phase oscillators on scale free graphs is analyzed in this work. The W-random graph model is used to define a convergent family of sparse graphs with power law degree distribution. For the KM on this family of graphs, we derive the mean field description of the system's dynamics in the limit as the size of the network tends to infinity. The mean field equation is used to study two problems: synchronization in the coupled system with randomly distributed intrinsic frequencies and existence and bifurcations of chimera states in the KM with repulsive coupling. The analysis of both problems highlights the role of the scale free network organization in shaping dynamics of the coupled system. The analytical results are complemented with the results of numerical simulations.

Citations

• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators

Related

• The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas
• The mean field equation for the Kuramoto model on graph sequences with\n non-Lipschitz limit
• The mean field analysis of the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations
• Stability and bifurcation of mixing in the Kuramoto model with inertia
• Capturing the critical coupling of large random Kuramoto networks with graphons