Graph partitions and cluster synchronization in networks of oscillators

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Title: Graph partitions and cluster synchronization in networks of oscillators
Authors: Schaub, MT
O'Clery, N
Billeh, YN
Delvenne, J-C
Lambiotte, R
Barahona, M
Item Type: Journal Article
Abstract: Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.
Issue Date: 19-Aug-2016
Date of Acceptance: 1-Aug-2016
ISSN: 1089-7682
Publisher: American Institute of Physics
Journal / Book Title: Chaos
Volume: 26
Copyright Statement: © 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license ( licenses/by/4.0/). []
Sponsor/Funder: Wellcome Trust
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: 086764/Z/08/Z
Keywords: physics.soc-ph
Fluids & Plasmas
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0299 Other Physical Sciences
Publication Status: Published
Article Number: 094821
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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