Arnold tongues and quasiperiodicity in a prey-predator model

Detalhes bibliográficos
Autor(a) principal: Rosa C.*
Data de Publicação: 2009
Outros Autores: Correia M.J.*, Rech P.C.*
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da Udesc
dARK ID: ark:/33523/0013000004b6r
Texto Completo: https://repositorio.udesc.br/handle/UDESC/9931
Resumo: We consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via analytical and numerical simulations, phenomena associated with the appearance, in the parameter-space, of structures like Arnold tongues involved in the Naimark-Sacker bifurcation. We determine analytically the location of the parameter sets where Naimark-Sacker bifurcation occurs, and the location on this line where tongues of arbitrary period are born. Lyapunov exponents, bifurcation diagrams, parameter-space and phase-space diagrams are used to show the transition from quasiperiodic to chaotic states. © 2007 Elsevier Ltd. All rights reserved.
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spelling Arnold tongues and quasiperiodicity in a prey-predator modelWe consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via analytical and numerical simulations, phenomena associated with the appearance, in the parameter-space, of structures like Arnold tongues involved in the Naimark-Sacker bifurcation. We determine analytically the location of the parameter sets where Naimark-Sacker bifurcation occurs, and the location on this line where tongues of arbitrary period are born. Lyapunov exponents, bifurcation diagrams, parameter-space and phase-space diagrams are used to show the transition from quasiperiodic to chaotic states. © 2007 Elsevier Ltd. All rights reserved.2024-12-06T19:20:34Z2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlep. 2041 - 20460960-077910.1016/j.chaos.2007.09.094https://repositorio.udesc.br/handle/UDESC/9931ark:/33523/0013000004b6rChaos, Solitons and Fractals404Rosa C.*Correia M.J.*Rech P.C.*engreponame:Repositório Institucional da Udescinstname:Universidade do Estado de Santa Catarina (UDESC)instacron:UDESCinfo:eu-repo/semantics/openAccess2024-12-07T21:06:07Zoai:repositorio.udesc.br:UDESC/9931Biblioteca Digital de Teses e Dissertaçõeshttps://pergamumweb.udesc.br/biblioteca/index.phpPRIhttps://repositorio-api.udesc.br/server/oai/requestri@udesc.bropendoar:63912024-12-07T21:06:07Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)false
dc.title.none.fl_str_mv Arnold tongues and quasiperiodicity in a prey-predator model
title Arnold tongues and quasiperiodicity in a prey-predator model
spellingShingle Arnold tongues and quasiperiodicity in a prey-predator model
Rosa C.*
title_short Arnold tongues and quasiperiodicity in a prey-predator model
title_full Arnold tongues and quasiperiodicity in a prey-predator model
title_fullStr Arnold tongues and quasiperiodicity in a prey-predator model
title_full_unstemmed Arnold tongues and quasiperiodicity in a prey-predator model
title_sort Arnold tongues and quasiperiodicity in a prey-predator model
author Rosa C.*
author_facet Rosa C.*
Correia M.J.*
Rech P.C.*
author_role author
author2 Correia M.J.*
Rech P.C.*
author2_role author
author
dc.contributor.author.fl_str_mv Rosa C.*
Correia M.J.*
Rech P.C.*
description We consider a two-dimensional map in which one of the fixed points is destabilized via a supercritical Naimark-Sacker bifurcation. We investigate, via analytical and numerical simulations, phenomena associated with the appearance, in the parameter-space, of structures like Arnold tongues involved in the Naimark-Sacker bifurcation. We determine analytically the location of the parameter sets where Naimark-Sacker bifurcation occurs, and the location on this line where tongues of arbitrary period are born. Lyapunov exponents, bifurcation diagrams, parameter-space and phase-space diagrams are used to show the transition from quasiperiodic to chaotic states. © 2007 Elsevier Ltd. All rights reserved.
publishDate 2009
dc.date.none.fl_str_mv 2009
2024-12-06T19:20:34Z
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.2007.09.094
https://repositorio.udesc.br/handle/UDESC/9931
dc.identifier.dark.fl_str_mv ark:/33523/0013000004b6r
identifier_str_mv 0960-0779
10.1016/j.chaos.2007.09.094
ark:/33523/0013000004b6r
url https://repositorio.udesc.br/handle/UDESC/9931
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Chaos, Solitons and Fractals
40
4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv p. 2041 - 2046
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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