Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation

We study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and t...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Makhlouf, Ammar
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:204386
Acceso en línea:https://ddd.uab.cat/record/204386
https://dx.doi.org/urn:doi:10.1007/s12591-017-0375-5
Access Level:acceso abierto
Palabra clave:Periodic orbit
Third-order differential equation
Quadratic system
Averaging theory
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spelling Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential EquationLlibre, Jaume|||0000-0002-9511-5999Makhlouf, AmmarPeriodic orbitThird-order differential equationQuadratic systemAveraging theoryWe study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and their kind of stability. The Hopf bifurcations of these differential systems were studied in [5], here we complete these studies adding their zero-Hopf bifurcations. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/204386https://dx.doi.org/urn:doi:10.1007/s12591-017-0375-5reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2043862026-06-06T12:50:31Z
dc.title.none.fl_str_mv Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
title Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
spellingShingle Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
Llibre, Jaume|||0000-0002-9511-5999
Periodic orbit
Third-order differential equation
Quadratic system
Averaging theory
title_short Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
title_full Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
title_fullStr Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
title_full_unstemmed Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
title_sort Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Makhlouf, Ammar
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Makhlouf, Ammar
author_role author
author2 Makhlouf, Ammar
author2_role author
dc.subject.none.fl_str_mv Periodic orbit
Third-order differential equation
Quadratic system
Averaging theory
topic Periodic orbit
Third-order differential equation
Quadratic system
Averaging theory
description We study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and their kind of stability. The Hopf bifurcations of these differential systems were studied in [5], here we complete these studies adding their zero-Hopf bifurcations.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/204386
https://dx.doi.org/urn:doi:10.1007/s12591-017-0375-5
url https://ddd.uab.cat/record/204386
https://dx.doi.org/urn:doi:10.1007/s12591-017-0375-5
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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