Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1142/S0218127420501175 http://hdl.handle.net/11449/197101 |
Resumo: | In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form (x) triple over dot = j(x, (x)over dot, (x)double over dot), called jerk equations, where j is a polynomial of degree n. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations. |
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Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk EquationsDarboux theory of integrabilityinvariant algebraic surfaceDarboux invariantchaotic and nonchaotic dynamicsjerk equationIn this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form (x) triple over dot = j(x, (x)over dot, (x)double over dot), called jerk equations, where j is a polynomial of degree n. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.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)FCT UNESP, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP, BrazilIBILCE UNESP, Inst Biocincias Letras & Cincias Exatas, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilFCT UNESP, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP, BrazilIBILCE UNESP, Inst Biocincias Letras & Cincias Exatas, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilFAPESP: 2019/10269-3CNPq: 311355/2018-8World Scientific Publ Co Pte LtdUniversidade Estadual Paulista (Unesp)Messias, Marcelo [UNESP]Silva, Rafael Paulino [UNESP]2020-12-10T20:06:13Z2020-12-10T20:06:13Z2020-06-30info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article12http://dx.doi.org/10.1142/S0218127420501175International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 30, n. 8, 12 p., 2020.0218-1274http://hdl.handle.net/11449/19710110.1142/S0218127420501175WOS:000551351100011Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal Of Bifurcation And Chaosinfo:eu-repo/semantics/openAccess2024-06-19T14:31:49Zoai:repositorio.unesp.br:11449/197101Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:45:18.199372Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
title |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
spellingShingle |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations Messias, Marcelo [UNESP] Darboux theory of integrability invariant algebraic surface Darboux invariant chaotic and nonchaotic dynamics jerk equation |
title_short |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
title_full |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
title_fullStr |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
title_full_unstemmed |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
title_sort |
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations |
author |
Messias, Marcelo [UNESP] |
author_facet |
Messias, Marcelo [UNESP] Silva, Rafael Paulino [UNESP] |
author_role |
author |
author2 |
Silva, Rafael Paulino [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Messias, Marcelo [UNESP] Silva, Rafael Paulino [UNESP] |
dc.subject.por.fl_str_mv |
Darboux theory of integrability invariant algebraic surface Darboux invariant chaotic and nonchaotic dynamics jerk equation |
topic |
Darboux theory of integrability invariant algebraic surface Darboux invariant chaotic and nonchaotic dynamics jerk equation |
description |
In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form (x) triple over dot = j(x, (x)over dot, (x)double over dot), called jerk equations, where j is a polynomial of degree n. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-10T20:06:13Z 2020-12-10T20:06:13Z 2020-06-30 |
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/10.1142/S0218127420501175 International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 30, n. 8, 12 p., 2020. 0218-1274 http://hdl.handle.net/11449/197101 10.1142/S0218127420501175 WOS:000551351100011 |
url |
http://dx.doi.org/10.1142/S0218127420501175 http://hdl.handle.net/11449/197101 |
identifier_str_mv |
International Journal Of Bifurcation And Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 30, n. 8, 12 p., 2020. 0218-1274 10.1142/S0218127420501175 WOS:000551351100011 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal Of Bifurcation And Chaos |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
12 |
dc.publisher.none.fl_str_mv |
World Scientific Publ Co Pte Ltd |
publisher.none.fl_str_mv |
World Scientific Publ Co Pte Ltd |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1808128271984885760 |