The Logistic-Like Map

Detalhes bibliográficos
Autor(a) principal: Leonel, Edson Denis [UNESP]
Data de Publicação: 2021
Tipo de documento: Capítulo de livro
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/978-981-16-3544-1_4
http://hdl.handle.net/11449/233497
Resumo: This chapter is dedicated to discuss some dynamical properties of a generalized version of the logistic map called as logistic-like map. The fixed points and their stability are discussed as well as the convergence to the stationary state at and near at the bifurcations. We show the critical exponents defining the convergence to stationary state for the transcritical and supercritical pitchfork bifurcations are not universal and do depend on the nonlinearity of the mapping. On the other hand the critical exponents obtained for the period doubling bifurcations are universal and are independent on the nonlinearity of the map. We use both phenomenological approach with a set of scaling hypothesis and also an approximation transforming the equation of differences into a differential equation in which the solution gives analytically the critical exponents.
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spelling The Logistic-Like MapThis chapter is dedicated to discuss some dynamical properties of a generalized version of the logistic map called as logistic-like map. The fixed points and their stability are discussed as well as the convergence to the stationary state at and near at the bifurcations. We show the critical exponents defining the convergence to stationary state for the transcritical and supercritical pitchfork bifurcations are not universal and do depend on the nonlinearity of the mapping. On the other hand the critical exponents obtained for the period doubling bifurcations are universal and are independent on the nonlinearity of the map. We use both phenomenological approach with a set of scaling hypothesis and also an approximation transforming the equation of differences into a differential equation in which the solution gives analytically the critical exponents.Departmamento de Física Sao Paulo State UniversityDepartmamento de Física Sao Paulo State UniversityUniversidade Estadual Paulista (UNESP)Leonel, Edson Denis [UNESP]2022-05-01T08:45:07Z2022-05-01T08:45:07Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart45-55http://dx.doi.org/10.1007/978-981-16-3544-1_4Nonlinear Physical Science, p. 45-55.1867-84591867-8440http://hdl.handle.net/11449/23349710.1007/978-981-16-3544-1_42-s2.0-85114352556Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Physical Scienceinfo:eu-repo/semantics/openAccess2022-05-01T08:45:07Zoai:repositorio.unesp.br:11449/233497Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-05-01T08:45:07Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The Logistic-Like Map
title The Logistic-Like Map
spellingShingle The Logistic-Like Map
Leonel, Edson Denis [UNESP]
title_short The Logistic-Like Map
title_full The Logistic-Like Map
title_fullStr The Logistic-Like Map
title_full_unstemmed The Logistic-Like Map
title_sort The Logistic-Like Map
author Leonel, Edson Denis [UNESP]
author_facet Leonel, Edson Denis [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Leonel, Edson Denis [UNESP]
description This chapter is dedicated to discuss some dynamical properties of a generalized version of the logistic map called as logistic-like map. The fixed points and their stability are discussed as well as the convergence to the stationary state at and near at the bifurcations. We show the critical exponents defining the convergence to stationary state for the transcritical and supercritical pitchfork bifurcations are not universal and do depend on the nonlinearity of the mapping. On the other hand the critical exponents obtained for the period doubling bifurcations are universal and are independent on the nonlinearity of the map. We use both phenomenological approach with a set of scaling hypothesis and also an approximation transforming the equation of differences into a differential equation in which the solution gives analytically the critical exponents.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-05-01T08:45:07Z
2022-05-01T08:45:07Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/978-981-16-3544-1_4
Nonlinear Physical Science, p. 45-55.
1867-8459
1867-8440
http://hdl.handle.net/11449/233497
10.1007/978-981-16-3544-1_4
2-s2.0-85114352556
url http://dx.doi.org/10.1007/978-981-16-3544-1_4
http://hdl.handle.net/11449/233497
identifier_str_mv Nonlinear Physical Science, p. 45-55.
1867-8459
1867-8440
10.1007/978-981-16-3544-1_4
2-s2.0-85114352556
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Physical Science
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 45-55
dc.source.none.fl_str_mv Scopus
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_ 1803046414404550656

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