Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition

TL;DR

This paper introduces a DMD-based method to identify functional communities in networks of coupled oscillators, revealing how synchronization patterns form and evolve in complex networks.

Contribution

The paper develops a novel DMD algorithm for detecting functional communities in heterogeneous oscillator networks, advancing analysis of dynamic synchronization.

Findings

Community membership correlates with oscillator locking.

Forest graphs illustrate complex association patterns.

Method works on Watts--Strogatz and Barabási--Albert networks.

Abstract

Dynamic-mode decomposition (DMD) is a versatile framework for model-free analysis of time series that are generated by dynamical systems. We develop a DMD-based algorithm to investigate the formation of "functional communities" in networks of coupled, heterogeneous Kuramoto oscillators. In these functional communities, the oscillators in the network have similar dynamics. We consider two common random-graph models (Watts--Strogatz networks and Barab\'asi--Albert networks) with different amounts of heterogeneities among the oscillators. In our computations, we find that membership in a community reflects the extent to which there is establishment and sustainment of locking between oscillators. We construct forest graphs that illustrate the complex ways in which the heterogeneous oscillators associate and disassociate with each other.