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

dc.authorid Koksal-Ersoz, Elif/0000-0003-3696-7953
dc.authorid Kivilcim, Aysegul/0000-0002-4442-568X
dc.authorwosid Kivilcim, Aysegul/A-4185-2019
dc.contributor.author Karabacak, Özkan
dc.contributor.author Kudeyt, Mahmut
dc.contributor.author Koksal-Ersoz, Elif
dc.contributor.author Ilhan, Ferruh
dc.contributor.author Karabacak, Ozkan
dc.contributor.other Mechatronics Engineering
dc.contributor.other Core Program
dc.date.accessioned 2023-10-19T15:12:12Z
dc.date.available 2023-10-19T15:12:12Z
dc.date.issued 2023
dc.department-temp [Kudeyt, Mahmut] Kadir Has Univ, Core Program, TR-34083 Istanbul, Turkiye; [Kivilcim, Aysegul] Aalborg Univ, Dept Math Sci, Skjernvej 4A, DK-9220 Aalborg, Denmark; [Koksal-Ersoz, Elif] Univ Rennes, INSERM, LTSI, UMR 1099, F-35000 Rennes, France; [Ilhan, Ferruh] Univ Turkish German Univ, Dept Elect Engn, TR-34820 Istanbul, Turkiye; [Karabacak, Ozkan] Kadir Has Univ, Dept Mechatron Engn, TR-34083 Istanbul, Turkiye en_US
dc.description.abstract Coupled oscillators may exhibit almost global phase synchronization, namely their phases tend to asymp-totically 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. en_US
dc.identifier.citationcount 0
dc.identifier.doi 10.1016/j.chaos.2023.113838 en_US
dc.identifier.issn 0960-0779
dc.identifier.issn 1873-2887
dc.identifier.scopus 2-s2.0-85165528775 en_US
dc.identifier.scopusquality Q1
dc.identifier.uri https://doi.org/10.1016/j.chaos.2023.113838
dc.identifier.uri https://hdl.handle.net/20.500.12469/5373
dc.identifier.volume 174 en_US
dc.identifier.wos WOS:001053981700001 en_US
dc.identifier.wosquality Q1
dc.khas 20231019-WoS en_US
dc.language.iso en en_US
dc.publisher Pergamon-Elsevier Science Ltd en_US
dc.relation.ispartof Chaos Solitons & Fractals en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 1
dc.subject Dissipative Dynamical-Systems En_Us
dc.subject Response Curves En_Us
dc.subject Stability En_Us
dc.subject Verification En_Us
dc.subject Sensitivity En_Us
dc.subject Networks En_Us
dc.subject Kuramoto En_Us
dc.subject Dissipative Dynamical-Systems
dc.subject Response Curves
dc.subject Stability
dc.subject Verification
dc.subject Dual Lyapunov theory en_US
dc.subject Sensitivity
dc.subject Kuramoto oscillators en_US
dc.subject Networks
dc.subject Phase synchronization en_US
dc.subject Kuramoto
dc.subject Sum of squares programming en_US
dc.title Certification of almost global phase synchronization of all-to-all coupled phase oscillators en_US
dc.type Article en_US
dc.wos.citedbyCount 1
dspace.entity.type Publication
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