Hierarchical Synchrony of Phase Oscillators in Modular Networks

TL;DR

This paper investigates how phase oscillators in modular networks synchronize at local and global levels, deriving low-dimensional equations to analyze bifurcations and the influence of coupling strengths on synchronization transitions.

Contribution

It introduces a low-dimensional framework for analyzing hierarchical synchrony in large modular networks using the Ott-Antonsen ansatz.

Findings

Local synchrony can be predicted from coupled low-dimensional equations.

Global synchrony description simplifies with many communities.

Transitions to synchrony depend on local and global coupling strengths.

Abstract

We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e., synchrony within and between communities, respectively. Using the recent ansatz of Ott and Antonsen, we find that the degree of local synchrony can be determined from a set of coupled low-dimensional equations. If the number of communities in the network is large, a low-dimensional description of global synchrony can be also found. Using these results, we study bifurcations between different types of synchrony. We find that, depending on the relative strength of local and global coupling, the transition to synchrony in the network can be mediated by local or global effects.