The multiplex decomposition: An analytic framework for multilayer dynamical networks

dc.contributor.authorBerner, Rico
dc.contributor.authorMehrmann, Volker
dc.contributor.authorSchöll, Eckehard
dc.contributor.authorYanchuk, Serhiy
dc.date.accessioned2021-12-22T09:49:55Z
dc.date.available2021-12-22T09:49:55Z
dc.date.issued2021
dc.descriptionFirst Published in SIAM Journal on Applied Dynamical Systems in Volume 20, Issue 4 (2021), published by the Society for Industrial and Applied Mathematics (SIAM).Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.en
dc.description.abstractMultiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the adjacency matrices for each layer are simultaneously triagonalizable. For such networks, we derive the relation between the spectrum of the multiplex network and the eigenvalues of the individual layers. As an application, we propose a generalized master stability approach that allows for a simplified, low-dimensional description of the stability of synchronized solutions in multiplex networks. We illustrate our result with a duplex network of FitzHugh--Nagumo oscillators. In particular, we show how interlayer interaction can lead to stabilization or destabilization of the synchronous state. Finally, we give explicit conditions for the stability of synchronous solutions in duplex networks of linear diffusive systems.en
dc.description.sponsorshipDFG, 411803875, Dynamik gekoppelter Systeme mit Zeitverzögerungen und deren Anwendungenen
dc.description.sponsorshipDFG, 440145547, Komplexe dynamische Netzwerke: Effekte von Heterogenität, Adaptivität und Topologie der Kopplungenen
dc.identifier.eissn1536-0040
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15996
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14769
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc530 Physikde
dc.subject.othermultiplex networksen
dc.subject.othermultiplex decompositionen
dc.subject.othercoupled oscillatorsen
dc.subject.othermaster stability functionen
dc.subject.othercomplex networksen
dc.titleThe multiplex decomposition: An analytic framework for multilayer dynamical networksen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1137/21M1406180en
dcterms.bibliographicCitation.issue4en
dcterms.bibliographicCitation.journaltitleSIAM Journal on Applied Dynamical Systemsen
dcterms.bibliographicCitation.originalpublishernameSIAMen
dcterms.bibliographicCitation.originalpublisherplacePhiladelphia, Pa.en
dcterms.bibliographicCitation.pageend1772en
dcterms.bibliographicCitation.pagestart1752en
dcterms.bibliographicCitation.volume20en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Theoretische Physik::FG Nichtlineare Dynamik und Kontrollede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Nichtlineare Dynamik und Kontrollede
tub.affiliation.instituteInst. Theoretische Physikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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