Information geometry theory of bifurcations? A covariant formulation

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorDa Silva, V. B.-
Autor(es): dc.creatorVieira, J. P.-
Autor(es): dc.creatorLeonel, Edson D.-
Data de aceite: dc.date.accessioned2025-08-21T17:11:43Z-
Data de disponibilização: dc.date.available2025-08-21T17:11:43Z-
Data de envio: dc.date.issued2022-04-29-
Data de envio: dc.date.issued2022-04-29-
Data de envio: dc.date.issued2022-01-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1063/5.0069033-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/230489-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/230489-
Descrição: dc.descriptionThe 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.-
Descrição: dc.descriptionDepartment of Physics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio Claro-
Descrição: dc.descriptionDepartment of Mathematics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio Claro-
Descrição: dc.descriptionDepartment of Physics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio Claro-
Descrição: dc.descriptionDepartment of Mathematics Universidade Estadual Paulista Júlio de Mesquita Filho Campus de Rio Claro-
Idioma: dc.languageen-
Relação: dc.relationChaos-
???dc.source???: dc.sourceScopus-
Título: dc.titleInformation geometry theory of bifurcations? A covariant formulation-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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