Emergence of local synchronization in an ensemble of heterogeneous Kuramoto oscillators
type: Item
instance of: scholarly article
title: Emergence of local synchronization in an ensemble of heterogeneous Kuramoto oscillators
zbMATH Open document ID: 1364.34078
author: Seung-Yeal Ha
author: Zhuchun Li
author: Jae-Seung Lee
published in: Networks and Heterogeneous Media
publication date: 2017-03-13T00:00:00Z
review text: The authors consider two groups of generalised Kuramoto oscillators. Specifically, there are two groups of phase oscillators, each group having identical local (i.e.,~uncoupled) dynamics, but different local dynamics for the two groups. The within group coupling is all-to-all through sines of phase differences, as is the between group coupling. Much of the paper concerns the conditions under which local exponential synchronization occurs. In this form of synchronization, all phases in one group tend to a common value as \(t\rightarrow\infty\), as do the phases in the other group, but the two groups do not have the same final phases. They also consider ``practical synchronization'' in which the maximum difference in phases over the whole ensemble is uniformly bounded by some constant inversely proportional to the coupling strength. They generalise their results to more than two groups and also provide numerical results to confirm their analyses.
Mathematics Subject Classification ID: 34D06
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 92B25
zbMATH DE Number: 6693914
zbMATH Keywords: Kuramoto oscillators
zbMATH Keywords: interacting groups
zbMATH Keywords: local exponential synchronization
zbMATH Keywords: practical synchronization
reviewed by: Carlo Laing
MaRDI profile type: Publication
full work available at URL: nhm.2017001
OpenAlex ID: W2589338611
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DOI: 10.3934/NHM.2017001
description: scientific article; zbMATH DE number 6693914