Synchronization of Kuramoto oscillators in networks of networks

TL;DR

This paper analyzes how synchronization occurs in complex modular networks of Kuramoto oscillators, providing a low-dimensional model that predicts different synchronization regimes and matches simulations.

Contribution

It introduces a simplified low-dimensional model for community-level synchronization in modular networks of oscillators, including multilayer structures.

Findings

The model accurately predicts bifurcations between incoherence, local, and global synchrony.

Synchronization dynamics can be described as coupled planar oscillators.

The model's predictions agree well with simulations of heterogeneous networks.

Abstract

We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble of coupled planar oscillators. In the limit of a large number of communities, we find a low dimensional description of the level of synchronization between the communities. In this limit, we describe bifurcations between incoherence, local synchrony, and global synchrony. We compare the predictions of this simplified model with simulations of heterogeneous networks in which the internal structure of each community is preserved and find excellent agreement. Finally, we investigate synchronization in networks where several layers of communities within communities may be present.