Certification of almost global phase synchronization of all-to-all coupled phase oscillators

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dc.contributor.authorKudeyt, Mahmut
dc.contributor.authorKıvılcım, Ayşegül
dc.contributor.authorKöksal-Ersöz, Elif
dc.contributor.authorİlhan, Ferruh
dc.contributor.authorKarabacak, Özkan
dc.date.accessioned2025-02-20T08:46:29Z
dc.date.available2025-02-20T08:46:29Z
dc.date.issued2023
dc.departmentTürk-Alman Üniversitesien_US
dc.description.abstractCoupled oscillators may exhibit almost global phase synchronization, namely their phases tend to asymptotically overlap for almost all initial conditions. We consider certification of this property using Rantzer's dual Lyapunov approach with sum of squares (SOS) programming. To this aim, we use a stereographic transformation from a hypertorus to an Euclidean space. For the case of all-to-all coupling, this transformation converts the problem of certifying stability into the problem of certifying divergence of almost all solutions to infinity. We show that the latter can be solved using a polynomial Lyapunov density, which can be constructed via SOS programming. This leads to the certification of almost global phase synchronization of all-to-all coupled phase oscillators. We apply our method to an example of coupled phase oscillators and to an example of coupled van der Pol oscillators, and show that it can support the existing tools of local stability analysis by ensuring almost global phase synchronization. © 2023 Elsevier Ltd
dc.description.sponsorshipTUBITAK 1001 Research fund, (122E522)
dc.identifier.doi10.1016/j.chaos.2023.113838
dc.identifier.issn0960-0779
dc.identifier.scopus2-s2.0-85165528775
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.chaos.2023.113838
dc.identifier.urihttps://hdl.handle.net/20.500.12846/1740
dc.identifier.volume174en_US
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Ltd
dc.relation.ispartofChaos, Solitons and Fractals
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_Scopus_20250220
dc.subjectDual Lyapunov theoryen_US
dc.subjectKuramoto oscillatorsen_US
dc.subjectPhase synchronizationen_US
dc.subjectSum of squares programmingen_US
dc.titleCertification of almost global phase synchronization of all-to-all coupled phase oscillators
dc.typeArticle

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