Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators.

Hideaki Yamamoto,Fabio A. Shimizu,Shigeru Kubota,Michio Niwano,Ayumi Hirano-Iwata

doi:10.3389/fncom.2018.00017

Abstract

A system consisting of interconnected networks, or a network of networks (NoN), appears diversely in many real-world systems, including the brain. In this study, we consider NoNs consisting of heterogeneous phase oscillators and investigate how the topology of subnetworks affects the global synchrony of the network. The degree of synchrony and the effect of subnetwork topology are evaluated based on the Kuramoto order parameter and the minimum coupling strength necessary for the order parameter to exceed a threshold value, respectively. In contrast to an isolated network in which random connectivity is favorable for achieving synchrony, NoNs synchronize with weaker interconnections when the degree distribution of subnetworks is heterogeneous, suggesting the major role of the high-degree nodes. We also investigate a case in which subnetworks with different average natural frequencies are coupled to show that direct coupling of subnetworks with the largest variation is effective for synchronizing the whole system. In real-world NoNs like the brain, the balance of synchrony and asynchrony is critical for its function at various spatial resolutions. Our work provides novel insights into the topological basis of coordinated dynamics in such networks.

Highlights

Many biological, social, and technological systems comprise of interacting subsystems and can be modeled as a network of networks (NoN) (Gao et al, 2012; Boccaletti et al, 2014; Kivelä et al, 2014)
We show that in networks of heterogenous phase oscillators, the optimal topology varies between a single network and a NoN
We investigated the effect of the subnetwork topology on the synchronization of interconnected networks, or NoNs

Summary

Introduction

Social, and technological systems comprise of interacting subsystems and can be modeled as a network of networks (NoN) (Gao et al, 2012; Boccaletti et al, 2014; Kivelä et al, 2014). Synchronization in NoNs and modular networks has been explored theoretically based several models, including phase oscillators (Arenas et al, 2006, 2008; Barreto et al, 2008; Laing, 2009; Zhao et al, 2010; Louzada et al, 2013), chaotic oscillators (Zhao et al, 2011; Aguirre et al, 2014; Leyva et al, 2017), and various neuron models (Zhao et al, 2010; Batista et al, 2012; Prado et al, 2014), especially from the viewpoint of competition of global and local synchronizations depending. The case of globally coupled NoNs has been analytically investigated in more detail, for instance, using a self-consistent analysis (Barreto et al, 2008) or the Ott-Antonsen ansatz (Ott and Antonsen, 2008; Laing, 2009)

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Results

Conclusion