Self-similarities of periodic structures for a discrete model of a two-gene system.

Detalhes bibliográficos
Autor(a) principal: Souza, Silvio Luiz Thomaz de
Data de Publicação: 2012
Outros Autores: Lima, Angélica Alves, Caldas, Iberê Luiz, Torricos, Rene Orlando Medrano, Guimarães Filho, Zwinglio de Oliveira
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFOP
Texto Completo: http://www.repositorio.ufop.br/handle/123456789/3869
https://doi.org/10.1016/j.physleta.2012.02.036
Resumo: We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps.
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spelling Self-similarities of periodic structures for a discrete model of a two-gene system.Arnold tonguesShrimpsGolden ratioLyapunov exponentsTwo-gene modelWe report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps.2014-11-14T19:27:56Z2014-11-14T19:27:56Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfSOUZA, S. L. T. et al. Self-similarities of periodic structures for a discrete model of a two-gene system. Physics Letters. A (Print), v. 376, p. 1290-1294, 2012. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0375960112001715>. Acesso em: 20 ago. 2014.0375-9601http://www.repositorio.ufop.br/handle/123456789/3869https://doi.org/10.1016/j.physleta.2012.02.036O periódico Physics Letters. A concede permissão para depósito deste artigo no Repositório Institucional da UFOP. Número da licença: 3456021433058.info:eu-repo/semantics/openAccessSouza, Silvio Luiz Thomaz deLima, Angélica AlvesCaldas, Iberê LuizTorricos, Rene Orlando MedranoGuimarães Filho, Zwinglio de Oliveiraengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOP2019-05-10T15:06:51Zoai:repositorio.ufop.br:123456789/3869Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-05-10T15:06:51Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false
dc.title.none.fl_str_mv Self-similarities of periodic structures for a discrete model of a two-gene system.
title Self-similarities of periodic structures for a discrete model of a two-gene system.
spellingShingle Self-similarities of periodic structures for a discrete model of a two-gene system.
Souza, Silvio Luiz Thomaz de
Arnold tongues
Shrimps
Golden ratio
Lyapunov exponents
Two-gene model
title_short Self-similarities of periodic structures for a discrete model of a two-gene system.
title_full Self-similarities of periodic structures for a discrete model of a two-gene system.
title_fullStr Self-similarities of periodic structures for a discrete model of a two-gene system.
title_full_unstemmed Self-similarities of periodic structures for a discrete model of a two-gene system.
title_sort Self-similarities of periodic structures for a discrete model of a two-gene system.
author Souza, Silvio Luiz Thomaz de
author_facet Souza, Silvio Luiz Thomaz de
Lima, Angélica Alves
Caldas, Iberê Luiz
Torricos, Rene Orlando Medrano
Guimarães Filho, Zwinglio de Oliveira
author_role author
author2 Lima, Angélica Alves
Caldas, Iberê Luiz
Torricos, Rene Orlando Medrano
Guimarães Filho, Zwinglio de Oliveira
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Souza, Silvio Luiz Thomaz de
Lima, Angélica Alves
Caldas, Iberê Luiz
Torricos, Rene Orlando Medrano
Guimarães Filho, Zwinglio de Oliveira
dc.subject.por.fl_str_mv Arnold tongues
Shrimps
Golden ratio
Lyapunov exponents
Two-gene model
topic Arnold tongues
Shrimps
Golden ratio
Lyapunov exponents
Two-gene model
description We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps.
publishDate 2012
dc.date.none.fl_str_mv 2012
2014-11-14T19:27:56Z
2014-11-14T19:27:56Z
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 SOUZA, S. L. T. et al. Self-similarities of periodic structures for a discrete model of a two-gene system. Physics Letters. A (Print), v. 376, p. 1290-1294, 2012. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0375960112001715>. Acesso em: 20 ago. 2014.
0375-9601
http://www.repositorio.ufop.br/handle/123456789/3869
https://doi.org/10.1016/j.physleta.2012.02.036
identifier_str_mv SOUZA, S. L. T. et al. Self-similarities of periodic structures for a discrete model of a two-gene system. Physics Letters. A (Print), v. 376, p. 1290-1294, 2012. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0375960112001715>. Acesso em: 20 ago. 2014.
0375-9601
url http://www.repositorio.ufop.br/handle/123456789/3869
https://doi.org/10.1016/j.physleta.2012.02.036
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFOP
instname:Universidade Federal de Ouro Preto (UFOP)
instacron:UFOP
instname_str Universidade Federal de Ouro Preto (UFOP)
instacron_str UFOP
institution UFOP
reponame_str Repositório Institucional da UFOP
collection Repositório Institucional da UFOP
repository.name.fl_str_mv Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)
repository.mail.fl_str_mv repositorio@ufop.edu.br
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