Synchronization of coupled oscillators on small-world networks
type: Item
instance of: scholarly article
title: Synchronization of coupled oscillators on small-world networks
zbMATH Open document ID: 1190.34060
author: Fumito Mori
author: Takashi Odagaki
published in: Physica D
publication date: 2009-08-12T00:00:00Z
review text: The paper studies the dynamics of networks of coupled phase oscillators \[ \frac{d\theta_n}{dt} = \omega_n - K\sum_{m=1}^N A_{nm} \sin(\theta_n - \theta_m), \] where \(\theta_n\) and \(\omega_n\) are the phase and the natural frequency of oscillator \(n\), respectively. The coupling strength is controlled by the parameter \(K\) and the coupling structure of the network by the matrix \((A_{nk})_{n,k=1,\dots,N}\) with elements 1 or 0. The authors consider the Watts-Strogatz type small-world networks, which are defined as follows. First, a one-dimensional ring of \(N\) sites connected with all its \(k\) neighbors is prepared. Next, each edge is rewired with probability \(p\). In the case when the probability is not too big (about 0.01 for \(N=1000\)), the network has the properties of a small-world network. Using mainly numerical integration, the authors focus on the two types of synchronization: frequency and phase synchronization. The main result of the paper is to show that the critical coupling strength for the phase synchronization is larger than that of the frequency synchronization. Moreover, the critical coupling strengths for the both types of synchronization diverges as the structure of the network approaches the regular one (\(p\to 0\)). This behavior is shown to obey a power low.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 5593881
zbMATH Keywords: coupled oscillator
zbMATH Keywords: small-world network
zbMATH Keywords: critical exponent
zbMATH Keywords: Watts-Strogatz
zbMATH Keywords: Kuramoto oscillator
zbMATH Keywords: phase oscillator
zbMATH Keywords: frequency
zbMATH Keywords: phase synchronization
MaRDI profile type: Publication
full work available at URL: j.physd.2009.04.002
OpenAlex ID: W2039127699
cites work: Synchronization: a universal concept in nonlinear sciences
cites work: Global and local synchrony of coupled neurons in small-world networks
cites work: Chemical oscillations, waves, and turbulence
cites work: Collective dynamics of ‘small-world’ networks
cites work: Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators
DOI: 10.1016/J.PHYSD.2009.04.002
description: scientific article; zbMATH DE number 5593881