Isochronous bifurcations in second-order delay differential equations

Autores
Bel, Andrea Liliana; Reartes, Walter
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time t minus the position at the delayed time t−τ. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
Fil: Bel, Andrea Liliana. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Reartes, Walter. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
DELAY DIFFERENTIAL EQUATIONS
HOPF BIFURCATION
ISOCHRONOUS CYCLES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/31285
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Isochronous bifurcations in second-order delay differential equationsBel, Andrea LilianaReartes, WalterDELAY DIFFERENTIAL EQUATIONSHOPF BIFURCATIONISOCHRONOUS CYCLEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time t minus the position at the delayed time t−τ. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.Fil: Bel, Andrea Liliana. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Reartes, Walter. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaTexas State University2014-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31285Reartes, Walter; Bel, Andrea Liliana; Isochronous bifurcations in second-order delay differential equations; Texas State University; Electronic Journal of Differential Equations; 2014; 162; 6-2014; 1-121072-6691CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ejde.math.txstate.edu/Volumes/2014/162/abstr.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:42:42Zoai:ri.conicet.gov.ar:11336/31285instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:42:42.925CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Isochronous bifurcations in second-order delay differential equations
title Isochronous bifurcations in second-order delay differential equations
spellingShingle Isochronous bifurcations in second-order delay differential equations
Bel, Andrea Liliana
DELAY DIFFERENTIAL EQUATIONS
HOPF BIFURCATION
ISOCHRONOUS CYCLES
title_short Isochronous bifurcations in second-order delay differential equations
title_full Isochronous bifurcations in second-order delay differential equations
title_fullStr Isochronous bifurcations in second-order delay differential equations
title_full_unstemmed Isochronous bifurcations in second-order delay differential equations
title_sort Isochronous bifurcations in second-order delay differential equations
dc.creator.none.fl_str_mv Bel, Andrea Liliana
Reartes, Walter
author Bel, Andrea Liliana
author_facet Bel, Andrea Liliana
Reartes, Walter
author_role author
author2 Reartes, Walter
author2_role author
dc.subject.none.fl_str_mv DELAY DIFFERENTIAL EQUATIONS
HOPF BIFURCATION
ISOCHRONOUS CYCLES
topic DELAY DIFFERENTIAL EQUATIONS
HOPF BIFURCATION
ISOCHRONOUS CYCLES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time t minus the position at the delayed time t−τ. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
Fil: Bel, Andrea Liliana. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Reartes, Walter. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time t minus the position at the delayed time t−τ. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
publishDate 2014
dc.date.none.fl_str_mv 2014-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/31285
Reartes, Walter; Bel, Andrea Liliana; Isochronous bifurcations in second-order delay differential equations; Texas State University; Electronic Journal of Differential Equations; 2014; 162; 6-2014; 1-12
1072-6691
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31285
identifier_str_mv Reartes, Walter; Bel, Andrea Liliana; Isochronous bifurcations in second-order delay differential equations; Texas State University; Electronic Journal of Differential Equations; 2014; 162; 6-2014; 1-12
1072-6691
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ejde.math.txstate.edu/Volumes/2014/162/abstr.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Texas State University
publisher.none.fl_str_mv Texas State University
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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