Filippov trajectories and clustering in the Kuramoto model with singular couplings
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Park, Jinyeong | - |
dc.contributor.author | Poyato, David | - |
dc.contributor.author | Soler, Juan | - |
dc.date.accessioned | 2022-07-07T09:18:50Z | - |
dc.date.available | 2022-07-07T09:18:50Z | - |
dc.date.created | 2021-07-14 | - |
dc.date.issued | 2021 | - |
dc.identifier.issn | 1435-9855 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/144076 | - |
dc.description.abstract | We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the interaction between oscillators is enhanced by the approach of phases. First, we study the well-posedness problem for the singular weighted Kuramoto systems in which the Lipschitz continuity fails to hold. We present the dynamics of the system equipped with singular weights in all the subcritical, critical and supercritical regimes of the singularity. A key fact is that solutions in the most singular cases must be considered in Filippov's sense. We characterize sticking of phases in the subcritical and critical case and we exhibit a continuation criterion for classical solutions after any collision state in the supercritical regime. Second, we prove that strong solutions to these systems of differential inclusions can be recovered as singular limits of regular weights. We also study the emergence of synchronous dynamics for the singular and regular weighted Kuramoto models. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | EUROPEAN MATHEMATICAL SOC-EMS | - |
dc.title | Filippov trajectories and clustering in the Kuramoto model with singular couplings | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Park, Jinyeong | - |
dc.identifier.doi | 10.4171/JEMS/1081 | - |
dc.identifier.scopusid | 2-s2.0-85117426059 | - |
dc.identifier.wosid | 000663332000001 | - |
dc.identifier.bibliographicCitation | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v.23, no.10, pp.3193 - 3278 | - |
dc.relation.isPartOf | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | - |
dc.citation.title | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 23 | - |
dc.citation.number | 10 | - |
dc.citation.startPage | 3193 | - |
dc.citation.endPage | 3278 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | PHASE-LOCKED STATES | - |
dc.subject.keywordPlus | MEAN-FIELD LIMIT | - |
dc.subject.keywordPlus | OSCILLATORS | - |
dc.subject.keywordPlus | SYNCHRONIZATION | - |
dc.subject.keywordPlus | PROPAGATION | - |
dc.subject.keywordPlus | EQUATIONS | - |
dc.subject.keywordPlus | DYNAMICS | - |
dc.subject.keywordPlus | SYSTEMS | - |
dc.subject.keywordAuthor | Kuramoto models | - |
dc.subject.keywordAuthor | adaptive coupling | - |
dc.subject.keywordAuthor | singular interactions | - |
dc.subject.keywordAuthor | Hebbian learning | - |
dc.subject.keywordAuthor | Filippov-type solutions | - |
dc.subject.keywordAuthor | clustering | - |
dc.subject.keywordAuthor | finite-time synchronization | - |
dc.subject.keywordAuthor | sticking | - |
dc.subject.keywordAuthor | Cucker-Smale | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
222, Wangsimni-ro, Seongdong-gu, Seoul, 04763, Korea+82-2-2220-1365
COPYRIGHT © 2021 HANYANG UNIVERSITY.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.