Information geometry theory of bifurcations? A covariant formulation
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1063/5.0069033 http://hdl.handle.net/11449/230489 |
Resumo: | The conventional local bifurcation theory (CBT) fails to present a complete characterization of the stability and general aspects of complex phenomena. After all, the CBT only explores the behavior of nonlinear dynamical systems in the neighborhood of their fixed points. Thus, this limitation imposes the necessity of non-trivial global techniques and lengthy numerical solutions. In this article, we present an attempt to overcome these problems by including the Fisher information theory in the study of bifurcations. Here, we investigate a Riemannian metrical structure of local and global bifurcations described in the context of dynamical systems. The introduced metric is based on the concept of information distance. We examine five contrasting models in detail: saddle-node, transcritical, supercritical pitchfork, subcritical pitchfork, and homoclinic bifurcations. We found that the metric imposes a curvature scalar R on the parameter space. Also, we discovered that R diverges to infinity while approaching bifurcation points. We demonstrate that the local stability conditions are recovered from the interpretations of the curvature R, while global stability is inferred from the character of the Fisher metric. The results are a clear improvement over those of the conventional theory. |
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Repositório Institucional da UNESP |
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Information geometry theory of bifurcations? A covariant formulationThe conventional local bifurcation theory (CBT) fails to present a complete characterization of the stability and general aspects of complex phenomena. After all, the CBT only explores the behavior of nonlinear dynamical systems in the neighborhood of their fixed points. Thus, this limitation imposes the necessity of non-trivial global techniques and lengthy numerical solutions. In this article, we present an attempt to overcome these problems by including the Fisher information theory in the study of bifurcations. Here, we investigate a Riemannian metrical structure of local and global bifurcations described in the context of dynamical systems. The introduced metric is based on the concept of information distance. We examine five contrasting models in detail: saddle-node, transcritical, supercritical pitchfork, subcritical pitchfork, and homoclinic bifurcations. We found that the metric imposes a curvature scalar R on the parameter space. Also, we discovered that R diverges to infinity while approaching bifurcation points. We demonstrate that the local stability conditions are recovered from the interpretations of the curvature R, while global stability is inferred from the character of the Fisher metric. The results are a clear improvement over those of the conventional theory.Department of Physics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio ClaroDepartment of Mathematics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio ClaroDepartment of Physics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio ClaroDepartment of Mathematics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio ClaroUniversidade Estadual Paulista (UNESP)Da Silva, V. B. [UNESP]Vieira, J. P. [UNESP]Leonel, Edson D. [UNESP]2022-04-29T08:40:16Z2022-04-29T08:40:16Z2022-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1063/5.0069033Chaos, v. 32, n. 2, 2022.1089-76821054-1500http://hdl.handle.net/11449/23048910.1063/5.00690332-s2.0-85125588605Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengChaosinfo:eu-repo/semantics/openAccess2022-04-29T08:40:16Zoai:repositorio.unesp.br:11449/230489Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:40:16Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Information geometry theory of bifurcations? A covariant formulation |
title |
Information geometry theory of bifurcations? A covariant formulation |
spellingShingle |
Information geometry theory of bifurcations? A covariant formulation Da Silva, V. B. [UNESP] |
title_short |
Information geometry theory of bifurcations? A covariant formulation |
title_full |
Information geometry theory of bifurcations? A covariant formulation |
title_fullStr |
Information geometry theory of bifurcations? A covariant formulation |
title_full_unstemmed |
Information geometry theory of bifurcations? A covariant formulation |
title_sort |
Information geometry theory of bifurcations? A covariant formulation |
author |
Da Silva, V. B. [UNESP] |
author_facet |
Da Silva, V. B. [UNESP] Vieira, J. P. [UNESP] Leonel, Edson D. [UNESP] |
author_role |
author |
author2 |
Vieira, J. P. [UNESP] Leonel, Edson D. [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Da Silva, V. B. [UNESP] Vieira, J. P. [UNESP] Leonel, Edson D. [UNESP] |
description |
The conventional local bifurcation theory (CBT) fails to present a complete characterization of the stability and general aspects of complex phenomena. After all, the CBT only explores the behavior of nonlinear dynamical systems in the neighborhood of their fixed points. Thus, this limitation imposes the necessity of non-trivial global techniques and lengthy numerical solutions. In this article, we present an attempt to overcome these problems by including the Fisher information theory in the study of bifurcations. Here, we investigate a Riemannian metrical structure of local and global bifurcations described in the context of dynamical systems. The introduced metric is based on the concept of information distance. We examine five contrasting models in detail: saddle-node, transcritical, supercritical pitchfork, subcritical pitchfork, and homoclinic bifurcations. We found that the metric imposes a curvature scalar R on the parameter space. Also, we discovered that R diverges to infinity while approaching bifurcation points. We demonstrate that the local stability conditions are recovered from the interpretations of the curvature R, while global stability is inferred from the character of the Fisher metric. The results are a clear improvement over those of the conventional theory. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-04-29T08:40:16Z 2022-04-29T08:40:16Z 2022-02-01 |
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/10.1063/5.0069033 Chaos, v. 32, n. 2, 2022. 1089-7682 1054-1500 http://hdl.handle.net/11449/230489 10.1063/5.0069033 2-s2.0-85125588605 |
url |
http://dx.doi.org/10.1063/5.0069033 http://hdl.handle.net/11449/230489 |
identifier_str_mv |
Chaos, v. 32, n. 2, 2022. 1089-7682 1054-1500 10.1063/5.0069033 2-s2.0-85125588605 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Chaos |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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_ |
1799964751434874880 |