Asymptotic Poincaré maps along the edges of polytopes
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/17360 |
Resumo: | For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope’s vertexes and edges. This piecewise linear flow is easy to compute even in higher dimensions, which allows the usage of numeric algorithms to find invariant dynamical structures such as periodic, homoclinic or heteroclinic orbits, which if robust persist as invariant dynamical structures of the original flow. We apply this method to prove the existence of chaotic behavior in some Hamiltonian replicator systems on the five dimensional simplex. |
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Asymptotic Poincaré maps along the edges of polytopesFor a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope’s vertexes and edges. This piecewise linear flow is easy to compute even in higher dimensions, which allows the usage of numeric algorithms to find invariant dynamical structures such as periodic, homoclinic or heteroclinic orbits, which if robust persist as invariant dynamical structures of the original flow. We apply this method to prove the existence of chaotic behavior in some Hamiltonian replicator systems on the five dimensional simplex.ISEG - REM - Research in Economics and MathematicsRepositório da Universidade de LisboaAlishah, Hassan NajafiDuarte, PedroPeixe, Telmo2019-02-14T13:11:34Z2019-022019-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/17360engAlishah, Hassan Najafi, Pedro Duarte e Telmo Peixe (2019). "Asymptotic Poincaré maps along the edges of polytopes". Instituto Superior de Economia e Gestão – REM Working paper nº 070 - 2019ISSN 2184-108Xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-06T14:47:02Zoai:www.repository.utl.pt:10400.5/17360Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:02:35.143927Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Asymptotic Poincaré maps along the edges of polytopes |
title |
Asymptotic Poincaré maps along the edges of polytopes |
spellingShingle |
Asymptotic Poincaré maps along the edges of polytopes Alishah, Hassan Najafi |
title_short |
Asymptotic Poincaré maps along the edges of polytopes |
title_full |
Asymptotic Poincaré maps along the edges of polytopes |
title_fullStr |
Asymptotic Poincaré maps along the edges of polytopes |
title_full_unstemmed |
Asymptotic Poincaré maps along the edges of polytopes |
title_sort |
Asymptotic Poincaré maps along the edges of polytopes |
author |
Alishah, Hassan Najafi |
author_facet |
Alishah, Hassan Najafi Duarte, Pedro Peixe, Telmo |
author_role |
author |
author2 |
Duarte, Pedro Peixe, Telmo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Alishah, Hassan Najafi Duarte, Pedro Peixe, Telmo |
description |
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope’s vertexes and edges. This piecewise linear flow is easy to compute even in higher dimensions, which allows the usage of numeric algorithms to find invariant dynamical structures such as periodic, homoclinic or heteroclinic orbits, which if robust persist as invariant dynamical structures of the original flow. We apply this method to prove the existence of chaotic behavior in some Hamiltonian replicator systems on the five dimensional simplex. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-02-14T13:11:34Z 2019-02 2019-02-01T00:00:00Z |
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://hdl.handle.net/10400.5/17360 |
url |
http://hdl.handle.net/10400.5/17360 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Alishah, Hassan Najafi, Pedro Duarte e Telmo Peixe (2019). "Asymptotic Poincaré maps along the edges of polytopes". Instituto Superior de Economia e Gestão – REM Working paper nº 070 - 2019 ISSN 2184-108X |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
ISEG - REM - Research in Economics and Mathematics |
publisher.none.fl_str_mv |
ISEG - REM - Research in Economics and Mathematics |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131115342004224 |