Sliding Shilnikov connection in Filippov-type predator–prey model

Detalhes bibliográficos
Autor(a) principal: Carvalho, Tiago
Data de Publicação: 2020
Outros Autores: Duarte Novaes, Douglas, Gonçalves, Luiz Fernando [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11071-020-05672-w
http://hdl.handle.net/11449/198854
Resumo: Recently, a piecewise smooth differential system was derived as a model of a 1 predator–2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic behavior was numerically found. Here, we revisit this model and prove the existence of a Shilnikov sliding connection when the parameters are taken in a codimension one submanifold of the parameter space. As a consequence of this connection, we conclude, analytically, that the model behaves chaotically for an open region of the parameter space.
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spelling Sliding Shilnikov connection in Filippov-type predator–prey modelChaosPiecewise smooth vector fieldsPrey switching modelShilnikov connectionSliding dynamicsRecently, a piecewise smooth differential system was derived as a model of a 1 predator–2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic behavior was numerically found. Here, we revisit this model and prove the existence of a Shilnikov sliding connection when the parameters are taken in a codimension one submanifold of the parameter space. As a consequence of this connection, we conclude, analytically, that the model behaves chaotically for an open region of the parameter space.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Departamento de Computação e Matemática Faculdade de Filosofia Ciências e Letras de Ribeirão Preto Universidade de São Paulo, Av. Bandeirantes, 3900Departamento de Matemática Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda 651, Cidade Universitária Zeferino VazInstituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265FAPESP: 2017/00883-0FAPESP: 2018/13481-0FAPESP: 2018/16430-8FAPESP: 2019/10269-3CNPq: 306649/2018-7CNPq: 438975/2018-9CAPES: Finance Code 001Universidade de São Paulo (USP)Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)Carvalho, TiagoDuarte Novaes, DouglasGonçalves, Luiz Fernando [UNESP]2020-12-12T01:23:47Z2020-12-12T01:23:47Z2020-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2973-2987http://dx.doi.org/10.1007/s11071-020-05672-wNonlinear Dynamics, v. 100, n. 3, p. 2973-2987, 2020.1573-269X0924-090Xhttp://hdl.handle.net/11449/19885410.1007/s11071-020-05672-w2-s2.0-85084981056Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Dynamicsinfo:eu-repo/semantics/openAccess2021-10-22T20:42:44Zoai:repositorio.unesp.br:11449/198854Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462021-10-22T20:42:44Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Sliding Shilnikov connection in Filippov-type predator–prey model
title Sliding Shilnikov connection in Filippov-type predator–prey model
spellingShingle Sliding Shilnikov connection in Filippov-type predator–prey model
Carvalho, Tiago
Chaos
Piecewise smooth vector fields
Prey switching model
Shilnikov connection
Sliding dynamics
title_short Sliding Shilnikov connection in Filippov-type predator–prey model
title_full Sliding Shilnikov connection in Filippov-type predator–prey model
title_fullStr Sliding Shilnikov connection in Filippov-type predator–prey model
title_full_unstemmed Sliding Shilnikov connection in Filippov-type predator–prey model
title_sort Sliding Shilnikov connection in Filippov-type predator–prey model
author Carvalho, Tiago
author_facet Carvalho, Tiago
Duarte Novaes, Douglas
Gonçalves, Luiz Fernando [UNESP]
author_role author
author2 Duarte Novaes, Douglas
Gonçalves, Luiz Fernando [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Carvalho, Tiago
Duarte Novaes, Douglas
Gonçalves, Luiz Fernando [UNESP]
dc.subject.por.fl_str_mv Chaos
Piecewise smooth vector fields
Prey switching model
Shilnikov connection
Sliding dynamics
topic Chaos
Piecewise smooth vector fields
Prey switching model
Shilnikov connection
Sliding dynamics
description Recently, a piecewise smooth differential system was derived as a model of a 1 predator–2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic behavior was numerically found. Here, we revisit this model and prove the existence of a Shilnikov sliding connection when the parameters are taken in a codimension one submanifold of the parameter space. As a consequence of this connection, we conclude, analytically, that the model behaves chaotically for an open region of the parameter space.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T01:23:47Z
2020-12-12T01:23:47Z
2020-05-01
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/10.1007/s11071-020-05672-w
Nonlinear Dynamics, v. 100, n. 3, p. 2973-2987, 2020.
1573-269X
0924-090X
http://hdl.handle.net/11449/198854
10.1007/s11071-020-05672-w
2-s2.0-85084981056
url http://dx.doi.org/10.1007/s11071-020-05672-w
http://hdl.handle.net/11449/198854
identifier_str_mv Nonlinear Dynamics, v. 100, n. 3, p. 2973-2987, 2020.
1573-269X
0924-090X
10.1007/s11071-020-05672-w
2-s2.0-85084981056
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Dynamics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2973-2987
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 repositoriounesp@unesp.br
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