The Kuramoto model on power law graphs

TL;DR

This paper investigates the dynamics of the Kuramoto model on scale-free power law graphs, deriving a mean field description and analyzing synchronization and chimera states influenced by network topology.

Contribution

It introduces a mean field framework for the Kuramoto model on sparse scale-free graphs and analyzes how network structure affects synchronization and chimera states.

Findings

Mean field equation derived for large networks.

Network topology influences synchronization patterns.

Chimera states depend on coupling and degree distribution.

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.