The dynamics of chimera states in heterogeneous Kuramoto networks
type: Item
instance of: scholarly article
title: The dynamics of chimera states in heterogeneous Kuramoto networks
zbMATH Open document ID: 1185.34042
published in: Physica D
publication date: 2009-09-28T00:00:00Z
review text: The paper presents a number of analytical results concerning emergence and stability of chimera states in networks of coupled phase oscillators. The chimera states have previously been discovered as a surprise in networks of symmetrically coupled identical oscillators, where the population spontaneously splits into synchronized and desynchronized subpopulations. The present paper reports on the existence and stability of the chimera states for nonidentical oscillators if a heterogeneity of the natural frequencies is introduced. It is shown that a power-law ansatz for the probability density function recently discovered by Ott and Antonsen provides an effective tool for the investigation of stationary states of the evolutionary equation of the network. The paper addresses a variety of models including one- and two-dimensional oscillator arrays with non-local coupling, all-to-all coupled networks with inhomogeneous coupling strengths as well as delay-coupled oscillator ensembles. Bifurcation analysis of the stationary chimera states demonstrates that these states are robust with respect to small heterogeneity in the networks. The obtained analytical results are illustrated by numerical simulations.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D06
zbMATH DE Number: 5608104
zbMATH Keywords: Kuramoto
zbMATH Keywords: phase oscillators
zbMATH Keywords: synchrony
zbMATH Keywords: non-local coupling
zbMATH Keywords: bifurcation
author: Carlo Laing
reviewed by: Oleksandr Popovych
describes a project that uses: HomCont
describes a project that uses: AUTO
MaRDI profile type: Publication
full work available at URL: j.physd.2009.04.012
OpenAlex ID: W2148369470
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DOI: 10.1016/J.PHYSD.2009.04.012
description: scientific article; zbMATH DE number 5608104