Nonchaotic Behavior and Transition to Chaos in Lorenz-like Systems Having Invariant Algebraic Surfaces

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorMessias, Marcelo-
Autor(es): dc.creatorSilva, Rafael Paulino-
Data de aceite: dc.date.accessioned2025-08-21T17:37:01Z-
Data de disponibilização: dc.date.available2025-08-21T17:37:01Z-
Data de envio: dc.date.issued2023-03-01-
Data de envio: dc.date.issued2023-03-01-
Data de envio: dc.date.issued2022-03-01-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.51537/chaos.1022368-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/241167-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/241167-
Descrição: dc.descriptionThe famous and well-studied Lorenz system is considered a paradigm for chaotic behavior in three-dimensional continuous differential systems. After the appearance of such a system in 1963, several Lorenz-like chaotic systems have been proposed and studied in the related literature, as Rossler system, Chen- Ueta system, Rabinovich system, Rikitake system, among others. However, these systems are parameter dependent and are chaotic only for suitable combinations of parameter values. This raises the question of when such systems are not chaotic, which can be seen as a dual problem regarding chaotic systems. In this paper, we give sufficient algebraic conditions for a generalized class of Lorenz-like systems to be nonchaotic. Using the general results obtained, we give some examples of nonchaotic behavior of some classical chaotic Lorenz-like systems, including the Lorenz system itself. The nonchaotic differential systems presented here have invariant algebraic surfaces, which contain the stable (or unstable) invariant manifolds of their equilibrium points. We show that, in some cases, the deformation of these invariant manifolds through the destruction of the invariant algebraic surfaces, by perturbing the parameter values, can reorganize the global structure of the phase space, leading to a transition from nonchaotic to chaotic behavior of such differential systems.-
Descrição: dc.descriptionDepartamento de Matematica e Computacao Faculdade de Ciencias e Tecnologia Universidade Estadual Paulista (UNESP)-
Descrição: dc.descriptionDepartamento de Matematica e Computacao Faculdade de Ciencias e Tecnologia Universidade Estadual Paulista (UNESP)-
Formato: dc.format26-36-
Idioma: dc.languageen-
Relação: dc.relationChaos Theory and Applications-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectChaotic and nonchaotic dynamics-
Palavras-chave: dc.subjectDarboux invariant-
Palavras-chave: dc.subjectDarboux theory of integrability-
Palavras-chave: dc.subjectInvariant algebraic surface-
Palavras-chave: dc.subjectLorenz-like systems-
Palavras-chave: dc.subjectStable and unstable manifolds-
Título: dc.titleNonchaotic Behavior and Transition to Chaos in Lorenz-like Systems Having Invariant Algebraic Surfaces-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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