Naimark-Sacker bifurcations in a delay quartic map

Bibliographic Details
Main Author: Rech P.C.*
Publication Date: 2008
Format: Article
Language: eng
Source: Repositório Institucional da Udesc
dARK ID: ark:/33523/001300000qn3j
Download full: https://repositorio.udesc.br/handle/UDESC/10174
Summary: In this paper, we consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via numerical simulations, phenomena associated with the appearance, in the phase-space, of closed invariant curves involved in the Naimark-Sacker bifurcation. Lyapunov exponents, parameter-space and phase-space diagrams are used to show that the transition from quasiperiodic to chaotic states generally do not happen in this case. We determine numerically the location of the parameter sets where the Naimark-Sacker bifurcation occurs. © 2006 Elsevier Ltd. All rights reserved.
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spelling Naimark-Sacker bifurcations in a delay quartic mapIn this paper, we consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via numerical simulations, phenomena associated with the appearance, in the phase-space, of closed invariant curves involved in the Naimark-Sacker bifurcation. Lyapunov exponents, parameter-space and phase-space diagrams are used to show that the transition from quasiperiodic to chaotic states generally do not happen in this case. We determine numerically the location of the parameter sets where the Naimark-Sacker bifurcation occurs. © 2006 Elsevier Ltd. All rights reserved.2024-12-06T19:25:06Z2008info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlep. 387 - 3920960-077910.1016/j.chaos.2006.08.029https://repositorio.udesc.br/handle/UDESC/10174ark:/33523/001300000qn3jChaos, Solitons and Fractals372Rech P.C.*engreponame:Repositório Institucional da Udescinstname:Universidade do Estado de Santa Catarina (UDESC)instacron:UDESCinfo:eu-repo/semantics/openAccess2024-12-07T21:07:14Zoai:repositorio.udesc.br:UDESC/10174Biblioteca Digital de Teses e Dissertaçõeshttps://pergamumweb.udesc.br/biblioteca/index.phpPRIhttps://repositorio-api.udesc.br/server/oai/requestri@udesc.bropendoar:63912024-12-07T21:07:14Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)false
dc.title.none.fl_str_mv Naimark-Sacker bifurcations in a delay quartic map
title Naimark-Sacker bifurcations in a delay quartic map
spellingShingle Naimark-Sacker bifurcations in a delay quartic map
Rech P.C.*
title_short Naimark-Sacker bifurcations in a delay quartic map
title_full Naimark-Sacker bifurcations in a delay quartic map
title_fullStr Naimark-Sacker bifurcations in a delay quartic map
title_full_unstemmed Naimark-Sacker bifurcations in a delay quartic map
title_sort Naimark-Sacker bifurcations in a delay quartic map
author Rech P.C.*
author_facet Rech P.C.*
author_role author
dc.contributor.author.fl_str_mv Rech P.C.*
description In this paper, we consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via numerical simulations, phenomena associated with the appearance, in the phase-space, of closed invariant curves involved in the Naimark-Sacker bifurcation. Lyapunov exponents, parameter-space and phase-space diagrams are used to show that the transition from quasiperiodic to chaotic states generally do not happen in this case. We determine numerically the location of the parameter sets where the Naimark-Sacker bifurcation occurs. © 2006 Elsevier Ltd. All rights reserved.
publishDate 2008
dc.date.none.fl_str_mv 2008
2024-12-06T19:25:06Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv 0960-0779
10.1016/j.chaos.2006.08.029
https://repositorio.udesc.br/handle/UDESC/10174
dc.identifier.dark.fl_str_mv ark:/33523/001300000qn3j
identifier_str_mv 0960-0779
10.1016/j.chaos.2006.08.029
ark:/33523/001300000qn3j
url https://repositorio.udesc.br/handle/UDESC/10174
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Chaos, Solitons and Fractals
37
2
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv p. 387 - 392
dc.source.none.fl_str_mv reponame:Repositório Institucional da Udesc
instname:Universidade do Estado de Santa Catarina (UDESC)
instacron:UDESC
instname_str Universidade do Estado de Santa Catarina (UDESC)
instacron_str UDESC
institution UDESC
reponame_str Repositório Institucional da Udesc
collection Repositório Institucional da Udesc
repository.name.fl_str_mv Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)
repository.mail.fl_str_mv ri@udesc.br
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