Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Resumen:
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
| 2015 | |
|
Linear stability analysis Coupled oscillators Dynamical systems Kuramoto models Measure theory Euclidean geometries Graph theory Vector fields Complex functions Cell lines |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/42646 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522940200157184 |
|---|---|
| author | Canale, Eduardo |
| author2 | Monzón, Pablo |
| author2_role | author |
| author_facet | Canale, Eduardo Monzón, Pablo |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Canale, Eduardo Monzón, Pablo |
| dc.date.accessioned.none.fl_str_mv | 2024-02-26T19:52:25Z |
| dc.date.available.none.fl_str_mv | 2024-02-26T19:52:25Z |
| dc.date.issued.es.fl_str_mv | 2015 |
| dc.date.submitted.es.fl_str_mv | 20240223 |
| dc.description.abstract.none.fl_txt_mv | This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work. |
| dc.description.es.fl_txt_mv | Trabajo publicado en Chaos. 25(2) 2015 |
| dc.identifier.citation.es.fl_str_mv | Canale, E, Monzón, P. "Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization" [Preprint] Publicado en: Chaos 25 (2), 2015 : 023106. https://doi.org/10.1063/1.4907952 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/42646 |
| 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 4.0) |
| 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.subject.es.fl_str_mv | Linear stability analysis Coupled oscillators Dynamical systems Kuramoto models Measure theory Euclidean geometries Graph theory Vector fields Complex functions Cell lines |
| dc.title.none.fl_str_mv | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| dc.type.es.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 publicado en Chaos. 25(2) 2015 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_4c9194d5f9e65340e379c6eb507543f1 |
| identifier_str_mv | Canale, E, Monzón, P. "Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization" [Preprint] Publicado en: Chaos 25 (2), 2015 : 023106. https://doi.org/10.1063/1.4907952 |
| 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:20.500.12008/42646 |
| publishDate | 2015 |
| 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 4.0) |
| spelling | 2024-02-26T19:52:25Z2024-02-26T19:52:25Z201520240223Canale, E, Monzón, P. "Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization" [Preprint] Publicado en: Chaos 25 (2), 2015 : 023106. https://doi.org/10.1063/1.4907952https://hdl.handle.net/20.500.12008/42646Trabajo publicado en Chaos. 25(2) 2015This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.Made available in DSpace on 2024-02-26T19:52:25Z (GMT). No. of bitstreams: 5 CM15.pdf: 339643 bytes, checksum: 694f958692c5f92c650ef2bdd23f65fc (MD5) license_text: 21936 bytes, checksum: 9833653f73f7853880c94a6fead477b1 (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) license.txt: 4244 bytes, checksum: 528b6a3c8c7d0c6e28129d576e989607 (MD5) Previous issue date: 2015enengLas 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 4.0)Linear stability analysisCoupled oscillatorsDynamical systemsKuramoto modelsMeasure theoryEuclidean geometriesGraph theoryVector fieldsComplex functionsCell linesExotic equilibria of Harary graphs and a new minimum degree lower bound for synchronizationPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCanale, EduardoMonzón, 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- Universidad de la Repúblicafalse |
| spellingShingle | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization Canale, Eduardo Linear stability analysis Coupled oscillators Dynamical systems Kuramoto models Measure theory Euclidean geometries Graph theory Vector fields Complex functions Cell lines |
| status_str | submittedVersion |
| title | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| title_full | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| title_fullStr | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| title_full_unstemmed | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| title_short | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| title_sort | Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization |
| topic | Linear stability analysis Coupled oscillators Dynamical systems Kuramoto models Measure theory Euclidean geometries Graph theory Vector fields Complex functions Cell lines |
| url | https://hdl.handle.net/20.500.12008/42646 |
