Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system

In this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of ho...

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Detalles Bibliográficos
Autores: Algaba Durán, Antonio, Fernández Sánchez, Fernando, Merino Morlesín, Manuel, Rodríguez Luis, Alejandro José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/162368
Acceso en línea:https://hdl.handle.net/11441/162368
https://doi.org/10.1016/j.chaos.2024.115248
Access Level:acceso abierto
Palabra clave:Degenerate heteroclinic cycle
Lorenz-like system
Homoclinic connection
Belyakov degeneracy
Triple-zero bifurcation
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spelling Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like systemAlgaba Durán, AntonioFernández Sánchez, FernandoMerino Morlesín, ManuelRodríguez Luis, Alejandro JoséDegenerate heteroclinic cycleLorenz-like systemHomoclinic connectionBelyakov degeneracyTriple-zero bifurcationIn this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of homoclinic connections arise from the point of the parameter plane where the degenerate heteroclinic cycle appears. The subsequent numerical study not only illustrates the presence of the first homoclinic orbits in the infinite succession but also allows to find other important local and global organizing centers of codimension two (Bogdanov–Takens bifurcations, degenerate homoclinic and heteroclinic connections, T-points) and three (triple-zero bifurcation, doubly-degenerate heteroclinic cycles, degenerate T-points).ElsevierMatemática Aplicada IITIC130: Investigación en Sistemas Dinámicos en IngenieríaMinisterio de Economía y Competitividad (MINECO). EspañaMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaJunta de Andalucía2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/162368https://doi.org/10.1016/j.chaos.2024.115248reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésChaos, Solitons & Fractals, 186 (115248).MTM2017-87915-C2-1-PPGC2018-096265-B-I00, PID2021- 123200NB-I00FQM-276TIC-0130P20_01160UHU-1260150https://www.sciencedirect.com/science/article/pii/S0960077924008002?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1623682026-06-17T12:51:07Z
dc.title.none.fl_str_mv Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
title Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
spellingShingle Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
Algaba Durán, Antonio
Degenerate heteroclinic cycle
Lorenz-like system
Homoclinic connection
Belyakov degeneracy
Triple-zero bifurcation
title_short Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
title_full Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
title_fullStr Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
title_full_unstemmed Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
title_sort Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
dc.creator.none.fl_str_mv Algaba Durán, Antonio
Fernández Sánchez, Fernando
Merino Morlesín, Manuel
Rodríguez Luis, Alejandro José
author Algaba Durán, Antonio
author_facet Algaba Durán, Antonio
Fernández Sánchez, Fernando
Merino Morlesín, Manuel
Rodríguez Luis, Alejandro José
author_role author
author2 Fernández Sánchez, Fernando
Merino Morlesín, Manuel
Rodríguez Luis, Alejandro José
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Ministerio de Economía y Competitividad (MINECO). España
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Junta de Andalucía
dc.subject.none.fl_str_mv Degenerate heteroclinic cycle
Lorenz-like system
Homoclinic connection
Belyakov degeneracy
Triple-zero bifurcation
topic Degenerate heteroclinic cycle
Lorenz-like system
Homoclinic connection
Belyakov degeneracy
Triple-zero bifurcation
description In this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of homoclinic connections arise from the point of the parameter plane where the degenerate heteroclinic cycle appears. The subsequent numerical study not only illustrates the presence of the first homoclinic orbits in the infinite succession but also allows to find other important local and global organizing centers of codimension two (Bogdanov–Takens bifurcations, degenerate homoclinic and heteroclinic connections, T-points) and three (triple-zero bifurcation, doubly-degenerate heteroclinic cycles, degenerate T-points).
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/162368
https://doi.org/10.1016/j.chaos.2024.115248
url https://hdl.handle.net/11441/162368
https://doi.org/10.1016/j.chaos.2024.115248
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Chaos, Solitons & Fractals, 186 (115248).
MTM2017-87915-C2-1-P
PGC2018-096265-B-I00, PID2021- 123200NB-I00
FQM-276
TIC-0130
P20_01160
UHU-1260150
https://www.sciencedirect.com/science/article/pii/S0960077924008002?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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