Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

Detalhes bibliográficos
Autor(a) principal: Oliveira, Juliano A. de [UNESP]
Data de Publicação: 2013
Outros Autores: Papesso, Edson R. [UNESP], Leonel, Edson D. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.3390/e15104310
http://hdl.handle.net/11449/113117
Resumo: Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.
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spelling Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigationrelaxation to fixed pointsdissipative mappingcomplex systemcubic maplogistic mapConvergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.Univ Estadual Paulista, Dept Fis, UNESP, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, UNESP, BR-13874149 Sao Joao Da Bao Vista, SP, BrazilAbdus Salaam Int Ctr Theoret Phys, I-34151 Trieste, ItalyUniv Estadual Paulista, Dept Fis, UNESP, BR-13506900 Rio Claro, SP, BrazilUniv Estadual Paulista, UNESP, BR-13874149 Sao Joao Da Bao Vista, SP, BrazilMdpi AgUniversidade Estadual Paulista (Unesp)Abdus Salaam Int Ctr Theoret PhysOliveira, Juliano A. de [UNESP]Papesso, Edson R. [UNESP]Leonel, Edson D. [UNESP]2014-12-03T13:11:25Z2014-12-03T13:11:25Z2013-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article4310-4318application/pdfhttp://dx.doi.org/10.3390/e15104310Entropy. Basel: Mdpi Ag, v. 15, n. 10, p. 4310-4318, 2013.1099-4300http://hdl.handle.net/11449/11311710.3390/e15104310WOS:000328486900018WOS000328486900018.pdf6130644232718610Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengEntropy2.3050,592info:eu-repo/semantics/openAccess2023-12-07T06:15:02Zoai:repositorio.unesp.br:11449/113117Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:39:56.102187Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
title Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
spellingShingle Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
Oliveira, Juliano A. de [UNESP]
relaxation to fixed points
dissipative mapping
complex system
cubic map
logistic map
title_short Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
title_full Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
title_fullStr Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
title_full_unstemmed Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
title_sort Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
author Oliveira, Juliano A. de [UNESP]
author_facet Oliveira, Juliano A. de [UNESP]
Papesso, Edson R. [UNESP]
Leonel, Edson D. [UNESP]
author_role author
author2 Papesso, Edson R. [UNESP]
Leonel, Edson D. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Abdus Salaam Int Ctr Theoret Phys
dc.contributor.author.fl_str_mv Oliveira, Juliano A. de [UNESP]
Papesso, Edson R. [UNESP]
Leonel, Edson D. [UNESP]
dc.subject.por.fl_str_mv relaxation to fixed points
dissipative mapping
complex system
cubic map
logistic map
topic relaxation to fixed points
dissipative mapping
complex system
cubic map
logistic map
description Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.
publishDate 2013
dc.date.none.fl_str_mv 2013-10-01
2014-12-03T13:11:25Z
2014-12-03T13:11:25Z
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 http://dx.doi.org/10.3390/e15104310
Entropy. Basel: Mdpi Ag, v. 15, n. 10, p. 4310-4318, 2013.
1099-4300
http://hdl.handle.net/11449/113117
10.3390/e15104310
WOS:000328486900018
WOS000328486900018.pdf
6130644232718610
url http://dx.doi.org/10.3390/e15104310
http://hdl.handle.net/11449/113117
identifier_str_mv Entropy. Basel: Mdpi Ag, v. 15, n. 10, p. 4310-4318, 2013.
1099-4300
10.3390/e15104310
WOS:000328486900018
WOS000328486900018.pdf
6130644232718610
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Entropy
2.305
0,592
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 4310-4318
application/pdf
dc.publisher.none.fl_str_mv Mdpi Ag
publisher.none.fl_str_mv Mdpi Ag
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129104081321984

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