Global considerations on the Kuramoto model of sinusoidally coupled oscillators
Resumen:
In this article we study global stability properties of the Kuramoto model of sinusoidally coupled oscillators. We base our analysis on previous results by the con-trol community that analyze local properties of the consensus point of different kinds of Kuramoto models. We prove that for the complete symmetric case, the consensus point is almost globally stable, that is, the set of trajectories that do not converge to it has zero measure. We present a counter-example of that when the completeness hypothesis is removed. We also show that the general non-symmetric case is more complex and we analyze the particular case of oscillators coupled in a ring structure, where we can establish some global stability properties.
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| 2005 | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/21193 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND) |
| _version_ | 1807523048566292480 |
|---|---|
| author | Paganini, Fernando |
| author2 | Monzón, Pablo |
| author2_role | author |
| author_facet | Paganini, Fernando Monzón, Pablo |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Paganini, Fernando Monzón, Pablo |
| dc.date.accessioned.none.fl_str_mv | 2019-07-03T16:35:57Z |
| dc.date.available.none.fl_str_mv | 2019-07-03T16:35:57Z |
| dc.date.issued.es.fl_str_mv | 2005 |
| dc.date.submitted.es.fl_str_mv | 20190703 |
| dc.description.abstract.none.fl_txt_mv | In this article we study global stability properties of the Kuramoto model of sinusoidally coupled oscillators. We base our analysis on previous results by the con-trol community that analyze local properties of the consensus point of different kinds of Kuramoto models. We prove that for the complete symmetric case, the consensus point is almost globally stable, that is, the set of trajectories that do not converge to it has zero measure. We present a counter-example of that when the completeness hypothesis is removed. We also show that the general non-symmetric case is more complex and we analyze the particular case of oscillators coupled in a ring structure, where we can establish some global stability properties. nbsp, |
| dc.description.es.fl_txt_mv | Trabajo presentado a 44th IEEE Conference on Decision and Control, Seville, Spain, 2005 |
| dc.identifier.citation.es.fl_str_mv | Paganini, F , Monzón, P. Global considerations on the Kuramoto model of sinusoidally coupled oscillators [Preprint] Publicado en Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005. doi 10.1109/CDC.2005.1582774 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/21193 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.title.none.fl_str_mv | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| dc.type.en.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Trabajo presentado a 44th IEEE Conference on Decision and Control, Seville, Spain, 2005 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_40b87fedc2b9ffb1573ceccd75d1121f |
| identifier_str_mv | Paganini, F , Monzón, P. Global considerations on the Kuramoto model of sinusoidally coupled oscillators [Preprint] Publicado en Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005. doi 10.1109/CDC.2005.1582774 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/21193 |
| publishDate | 2005 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND) |
| spelling | 2019-07-03T16:35:57Z2019-07-03T16:35:57Z200520190703Paganini, F , Monzón, P. Global considerations on the Kuramoto model of sinusoidally coupled oscillators [Preprint] Publicado en Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 2005. doi 10.1109/CDC.2005.1582774https://hdl.handle.net/20.500.12008/21193Trabajo presentado a 44th IEEE Conference on Decision and Control, Seville, Spain, 2005In this article we study global stability properties of the Kuramoto model of sinusoidally coupled oscillators. We base our analysis on previous results by the con-trol community that analyze local properties of the consensus point of different kinds of Kuramoto models. We prove that for the complete symmetric case, the consensus point is almost globally stable, that is, the set of trajectories that do not converge to it has zero measure. We present a counter-example of that when the completeness hypothesis is removed. We also show that the general non-symmetric case is more complex and we analyze the particular case of oscillators coupled in a ring structure, where we can establish some global stability properties.nbsp,Made available in DSpace on 2019-07-03T16:35:57Z (GMT). No. of bitstreams: 5 MP05.pdf: 144352 bytes, checksum: 82e68f5b63ca9bc03d8ea54b74679100 (MD5) license_text: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) license.txt: 4267 bytes, checksum: 6429389a7df7277b72b7924fdc7d47a9 (MD5) Previous issue date: 2005enengLas obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad De La República. (Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución – No Comercial – Sin Derivadas (CC - By-NC-ND)Global considerations on the Kuramoto model of sinusoidally coupled oscillatorsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaPaganini, FernandoMonzón, 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- Universidad de la Repúblicafalse |
| spellingShingle | Global considerations on the Kuramoto model of sinusoidally coupled oscillators Paganini, Fernando |
| status_str | submittedVersion |
| title | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| title_full | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| title_fullStr | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| title_full_unstemmed | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| title_short | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| title_sort | Global considerations on the Kuramoto model of sinusoidally coupled oscillators |
| url | https://hdl.handle.net/20.500.12008/21193 |
