Synchronization and structure in an adaptive oscillator network

TL;DR

This paper investigates how adaptive rewiring based on oscillator synchronization leads to the emergence of small-world network structures and synchronized groups, revealing a relationship between coupling strength and network topology.

Contribution

It introduces a model where network structure evolves according to oscillator coherence, demonstrating the formation of small-world networks with synchronized clusters.

Findings

Network reaches small-world structure during adaptation

Maximum clustering occurs at intermediate coupling strength

Synchronized groups correspond to network clusters

Abstract

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.