Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/6180 |
Resumo: | In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps. |
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Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth modelsBig bang bifurcationFold and flip bifurcation curvesKneading sequencesSymbolic dynamicsWeibull-Gompertz-Fréchet's growth modelsIn this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.Natural Sciences Publishing CoRCIPLRocha, J. LeonelTaha, Abdel KaddousFournier-Prunaret, Danièle2016-05-10T14:17:06Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6180engROCHA, J. Leonel; TAHA, Abdel Kaddous; FOURNIER-PRUNARET, Danièle Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models. Applied Mathematics and Information Sciences. ISSN. 1935-0090. Vol. 9 Nr. 5, (2015), 2377-2388.1935-009010.12785/amis/090520metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:40Zoai:repositorio.ipl.pt:10400.21/6180Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:21.834768Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
title |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
spellingShingle |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models Rocha, J. Leonel Big bang bifurcation Fold and flip bifurcation curves Kneading sequences Symbolic dynamics Weibull-Gompertz-Fréchet's growth models |
title_short |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
title_full |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
title_fullStr |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
title_full_unstemmed |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
title_sort |
Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models |
author |
Rocha, J. Leonel |
author_facet |
Rocha, J. Leonel Taha, Abdel Kaddous Fournier-Prunaret, Danièle |
author_role |
author |
author2 |
Taha, Abdel Kaddous Fournier-Prunaret, Danièle |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Rocha, J. Leonel Taha, Abdel Kaddous Fournier-Prunaret, Danièle |
dc.subject.por.fl_str_mv |
Big bang bifurcation Fold and flip bifurcation curves Kneading sequences Symbolic dynamics Weibull-Gompertz-Fréchet's growth models |
topic |
Big bang bifurcation Fold and flip bifurcation curves Kneading sequences Symbolic dynamics Weibull-Gompertz-Fréchet's growth models |
description |
In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z 2016-05-10T14:17:06Z |
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 |
http://hdl.handle.net/10400.21/6180 |
url |
http://hdl.handle.net/10400.21/6180 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
ROCHA, J. Leonel; TAHA, Abdel Kaddous; FOURNIER-PRUNARET, Danièle Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models. Applied Mathematics and Information Sciences. ISSN. 1935-0090. Vol. 9 Nr. 5, (2015), 2377-2388. 1935-0090 10.12785/amis/090520 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
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metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Natural Sciences Publishing Co |
publisher.none.fl_str_mv |
Natural Sciences Publishing Co |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799133412070522880 |