Policiclos em sistemas de Filippov planares
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/13037 |
Resumo: | In this work, we study the local structure of planar Filippov systems around low codi mension Σ−singularities and we analyze systems presenting polycycles passing through Σ−singularities. In this way, we analyze Poincaré maps (associated with such polycycles) and determine bifurcation diagrams of Filippov systems around these minimal sets. More specifically, we study the generic bifurcation of a Filippov system around a global con nection passing through a visible fold-regular singularity, the so-called critical crossing cycle and we show that, under smale pertubations, such connection breaks originating étther a sliding cycle or a crossing limit cycle. We also study a planar Filippov system model around a certain Σ−singularity called Fold-Cusp, where a fold and a cusp meet and we show the existence of a critical crossing cycle bifurcations from such singularity in an unfolding of this system. In addition, we exhibit the bifurcation diagram of this unfolding. |
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Gomide, Otávio Marçal Leandrohttp://lattes.cnpq.br/6665788071640310Gomide, Otávio Marçal LeandroCristiano, RonyLima, Dahisy Valadão de Souzahttp://lattes.cnpq.br/8466538997176999Souza, Alessandra Carlos de2023-09-08T11:51:31Z2023-09-08T11:51:31Z2023-07-27SOUZA, A. C. Policiclos em sistemas de Filippov planares. 2023. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023.http://repositorio.bc.ufg.br/tede/handle/tede/13037In this work, we study the local structure of planar Filippov systems around low codi mension Σ−singularities and we analyze systems presenting polycycles passing through Σ−singularities. In this way, we analyze Poincaré maps (associated with such polycycles) and determine bifurcation diagrams of Filippov systems around these minimal sets. More specifically, we study the generic bifurcation of a Filippov system around a global con nection passing through a visible fold-regular singularity, the so-called critical crossing cycle and we show that, under smale pertubations, such connection breaks originating étther a sliding cycle or a crossing limit cycle. We also study a planar Filippov system model around a certain Σ−singularity called Fold-Cusp, where a fold and a cusp meet and we show the existence of a critical crossing cycle bifurcations from such singularity in an unfolding of this system. In addition, we exhibit the bifurcation diagram of this unfolding.Neste trabalho, estudamos a estrutura local de sistemas de Filippov planares ao redor de Σ-singularidades de codimensão baixa e analisamos sistemas que apresentam policiclos passando por Σ-singularidades. Neste processo, analisamos mapas de Poincaré (associa dos a estes policiclos) e determinamos diagramas de bifurcação de sistemas de Filippov ao redor destes conjuntos minimais. Mais especificamente, estudamos a bifurcação ge nérica de um sistema de Filippov ao redor de uma conexão global que passa por uma singularidade do tipo dobra-regular visível, conhecida como ciclo limite costurante crí- tico e mostramos que, sob pequenas perturbações, essa conexão se rompe e origina um ciclo deslizante ou um ciclo limite costurante. Também estudamos um modelo de sis tema de Filippov planar ao redor de uma certa Σ-singularidade chamada dobra-cúspide, e mostramos a existência de um ciclo costurante crítico que bifurca desta singularidade em um desdobramento deste sistema. Além disso, exibimos o diagrama de bifurcação deste desdobramento.Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2023-09-06T19:50:54Z No. of bitstreams: 2 Dissertação - Alessandra Carlos de Souza - 2023.pdf: 2529129 bytes, checksum: d7f3ae711087130a7ce88b9009695048 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2023-09-08T11:51:31Z (GMT) No. of bitstreams: 2 Dissertação - Alessandra Carlos de Souza - 2023.pdf: 2529129 bytes, checksum: d7f3ae711087130a7ce88b9009695048 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Made available in DSpace on 2023-09-08T11:51:31Z (GMT). No. of bitstreams: 2 Dissertação - Alessandra Carlos de Souza - 2023.pdf: 2529129 bytes, checksum: d7f3ae711087130a7ce88b9009695048 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Previous issue date: 2023-07-27Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RMG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessSistemas de FilippovSistemas dinâmicosBifurcaçõesPolicicloSingularidade dobra-regularSingularidade dobra-cúspideFilippov systemsDynamical systemsBifurcationsPolycycleFold-regular singularityFold-cusp singularityCIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADAPoliciclos em sistemas de Filippov planaresPolycycles in Filippov systems planarsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis70500500500500277951reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGORIGINALDissertação - Alessandra Carlos de Souza - 2023.pdfDissertação - Alessandra Carlos de Souza - 2023.pdfapplication/pdf2529129http://repositorio.bc.ufg.br/tede/bitstreams/2763bb6b-bfca-4ffe-b6ab-1a19eca7ae05/downloadd7f3ae711087130a7ce88b9009695048MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/b936e309-e7f0-4bb9-8a3c-c45ea3feb851/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/c4542a07-dc35-4197-9721-3dc692b946e4/download4460e5956bc1d1639be9ae6146a50347MD52tede/130372023-09-08 08:51:31.597http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/13037http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2023-09-08T11:51:31Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
dc.title.pt_BR.fl_str_mv |
Policiclos em sistemas de Filippov planares |
dc.title.alternative.eng.fl_str_mv |
Polycycles in Filippov systems planars |
title |
Policiclos em sistemas de Filippov planares |
spellingShingle |
Policiclos em sistemas de Filippov planares Souza, Alessandra Carlos de Sistemas de Filippov Sistemas dinâmicos Bifurcações Policiclo Singularidade dobra-regular Singularidade dobra-cúspide Filippov systems Dynamical systems Bifurcations Polycycle Fold-regular singularity Fold-cusp singularity CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA |
title_short |
Policiclos em sistemas de Filippov planares |
title_full |
Policiclos em sistemas de Filippov planares |
title_fullStr |
Policiclos em sistemas de Filippov planares |
title_full_unstemmed |
Policiclos em sistemas de Filippov planares |
title_sort |
Policiclos em sistemas de Filippov planares |
author |
Souza, Alessandra Carlos de |
author_facet |
Souza, Alessandra Carlos de |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Gomide, Otávio Marçal Leandro |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6665788071640310 |
dc.contributor.referee1.fl_str_mv |
Gomide, Otávio Marçal Leandro |
dc.contributor.referee2.fl_str_mv |
Cristiano, Rony |
dc.contributor.referee3.fl_str_mv |
Lima, Dahisy Valadão de Souza |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8466538997176999 |
dc.contributor.author.fl_str_mv |
Souza, Alessandra Carlos de |
contributor_str_mv |
Gomide, Otávio Marçal Leandro Gomide, Otávio Marçal Leandro Cristiano, Rony Lima, Dahisy Valadão de Souza |
dc.subject.por.fl_str_mv |
Sistemas de Filippov Sistemas dinâmicos Bifurcações Policiclo Singularidade dobra-regular Singularidade dobra-cúspide |
topic |
Sistemas de Filippov Sistemas dinâmicos Bifurcações Policiclo Singularidade dobra-regular Singularidade dobra-cúspide Filippov systems Dynamical systems Bifurcations Polycycle Fold-regular singularity Fold-cusp singularity CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA |
dc.subject.eng.fl_str_mv |
Filippov systems Dynamical systems Bifurcations Polycycle Fold-regular singularity Fold-cusp singularity |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA |
description |
In this work, we study the local structure of planar Filippov systems around low codi mension Σ−singularities and we analyze systems presenting polycycles passing through Σ−singularities. In this way, we analyze Poincaré maps (associated with such polycycles) and determine bifurcation diagrams of Filippov systems around these minimal sets. More specifically, we study the generic bifurcation of a Filippov system around a global con nection passing through a visible fold-regular singularity, the so-called critical crossing cycle and we show that, under smale pertubations, such connection breaks originating étther a sliding cycle or a crossing limit cycle. We also study a planar Filippov system model around a certain Σ−singularity called Fold-Cusp, where a fold and a cusp meet and we show the existence of a critical crossing cycle bifurcations from such singularity in an unfolding of this system. In addition, we exhibit the bifurcation diagram of this unfolding. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-09-08T11:51:31Z |
dc.date.available.fl_str_mv |
2023-09-08T11:51:31Z |
dc.date.issued.fl_str_mv |
2023-07-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SOUZA, A. C. Policiclos em sistemas de Filippov planares. 2023. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/13037 |
identifier_str_mv |
SOUZA, A. C. Policiclos em sistemas de Filippov planares. 2023. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/13037 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
70 |
dc.relation.confidence.fl_str_mv |
500 500 500 500 |
dc.relation.department.fl_str_mv |
27 |
dc.relation.cnpq.fl_str_mv |
795 |
dc.relation.sponsorship.fl_str_mv |
1 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Matemática (IME) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RMG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
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Repositório Institucional da UFG |
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