Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity

We consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis a...

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Author: García, I. A. (Isaac A.)
Format: article
Status:Published version
Publication Date:2022
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/84117
Online Access:https://doi.org/10.1007/s10884-022-10208-4
http://hdl.handle.net/10459.1/84117
Access Level:Open access
Keyword:Zero-Hopf singularity
Periodic orbits
Poincaré map
ν-cyclicity
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spelling Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf SingularityGarcía, I. A. (Isaac A.)Zero-Hopf singularityPeriodic orbitsPoincaré mapν-cyclicityWe consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis and then returns to the initial point closing the orbit. When the parameters of the family are restricted to certain explicitly computable open semi-algebraic sets , we characterize those parameters that give rise to the appearance of local two-dimensional periodic invariant manifolds through the singularity. Also we use a Bautin-type analysis to study the maximum number of small-amplitude ν-limit cycles that can be made to bifurcate from the equilibrium when the parameters of the family are restricted to . We obtain global upper bounds on the number of bifurcated ν-limit cycles.The author is partially supported by a MICINN Grant Number PID2020-113758GB-I00 and an AGAUR Grant Number 2017SGR-1276.Springer202220222024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1007/s10884-022-10208-4http://hdl.handle.net/10459.1/84117http://hdl.handle.net/10459.1/84117reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00Reproducció del document publicat a https://doi.org/10.1007/s10884-022-10208-4Journal of Dynamics and Differential Equations, 2024, vol. 36, p. 1325-1346cc-by (c) Isaac A. García, 2024info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:recercat.cat:10459.1/841172026-05-29T05:05:01Z
dc.title.none.fl_str_mv Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
title Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
spellingShingle Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
García, I. A. (Isaac A.)
Zero-Hopf singularity
Periodic orbits
Poincaré map
ν-cyclicity
title_short Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
title_full Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
title_fullStr Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
title_full_unstemmed Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
title_sort Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
dc.creator.none.fl_str_mv García, I. A. (Isaac A.)
author García, I. A. (Isaac A.)
author_facet García, I. A. (Isaac A.)
author_role author
dc.subject.none.fl_str_mv Zero-Hopf singularity
Periodic orbits
Poincaré map
ν-cyclicity
topic Zero-Hopf singularity
Periodic orbits
Poincaré map
ν-cyclicity
description We consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis and then returns to the initial point closing the orbit. When the parameters of the family are restricted to certain explicitly computable open semi-algebraic sets , we characterize those parameters that give rise to the appearance of local two-dimensional periodic invariant manifolds through the singularity. Also we use a Bautin-type analysis to study the maximum number of small-amplitude ν-limit cycles that can be made to bifurcate from the equilibrium when the parameters of the family are restricted to . We obtain global upper bounds on the number of bifurcated ν-limit cycles.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
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://doi.org/10.1007/s10884-022-10208-4
http://hdl.handle.net/10459.1/84117
http://hdl.handle.net/10459.1/84117
url https://doi.org/10.1007/s10884-022-10208-4
http://hdl.handle.net/10459.1/84117
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00
Reproducció del document publicat a https://doi.org/10.1007/s10884-022-10208-4
Journal of Dynamics and Differential Equations, 2024, vol. 36, p. 1325-1346
dc.rights.none.fl_str_mv cc-by (c) Isaac A. García, 2024
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) Isaac A. García, 2024
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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