Stability of phase difference trajectories of networks of kuramoto oscillators with time-varying couplings and intrinsic frequencies

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buir.contributor.authorAtay, Fatihcan M.
dc.citation.epage483en_US
dc.citation.issueNumber1en_US
dc.citation.spage457en_US
dc.citation.volumeNumber17en_US
dc.contributor.authorLu, W.en_US
dc.contributor.authorAtay, Fatihcan M.en_US
dc.date.accessioned2019-02-21T16:06:35Z
dc.date.available2019-02-21T16:06:35Z
dc.date.issued2018en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe study dynamics of phase differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In the case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable if there exists T > 0 such that the aggregation of the time-varying graphs across any time interval of length T has a spanning tree. We also consider the situation that the coupling coefficients may be negative and provide sufficient conditions for the asymptotic stability of the PD dynamics. Due to time variations, the PDs are asymptotic to time-varying patterns rather than constant values. Hence, the PD dynamics can be regarded as a generalization of the well-known phase-locking phenomena. We explicitly investigate several particular cases of time-varying graph structures, including asymptotically periodic PDs due to periodic coupling coefficients and intrinsic frequencies, small perturbations, and fast-switching near constant coupling and frequencies, which lead to PD dynamics close to a phase-locked one. Numerical examples are provided to illustrate the theoretical results.
dc.description.sponsorshipAcknowledgments. The authors thank the anonymous reviewers for their constructive comments that helped improve the paper significantly. The authors gratefully acknowledge the support of the ZiF, the Center for Interdisciplinary Research of Bielefeld University, where part of this research was conducted under the cooperation program Discrete and Continuous Models in the Theory of Networks.
dc.identifier.doi10.1137/16M1084390
dc.identifier.issn1536-0040
dc.identifier.urihttp://hdl.handle.net/11693/50319
dc.language.isoEnglish
dc.publisherSociety for Industrial and Applied Mathematics Publications
dc.relation.isversionofhttps://doi.org/10.1137/16M1084390
dc.relation.projectNational Aerospace Science Foundation of China: 91630314 - Fudan University - Bilkent Üniversitesi - Chinese Academy of Sciences, CAS - National Natural Science Foundation of China, NSFC: 61673119
dc.source.titleSIAM Journal on Applied Dynamical Systemsen_US
dc.subjectAsymptotic stabilityen_US
dc.subjectKuramoto oscillatorsen_US
dc.subjectPhase differenceen_US
dc.subjectTime-varying couplingsen_US
dc.titleStability of phase difference trajectories of networks of kuramoto oscillators with time-varying couplings and intrinsic frequenciesen_US
dc.typeArticleen_US
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