Testing for Basins of Wada

Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has the Wada property and initial conditions near that boundary are even more unpredictable....

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Authors: Daza, Alvar, Wagemakers, Alexandre, Sanjuán, Miguel A. F., Yorke, James A.
Format: article
Publication Date:2015
Country:España
Institution:Universidad Rey Juan Carlos
Repository:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/26255
Online Access:https://hdl.handle.net/10115/26255
Access Level:Open access
Keyword:Chaos
Wada
Fractal boundaries
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spelling Testing for Basins of WadaDaza, AlvarWagemakers, AlexandreSanjuán, Miguel A. F.Yorke, James A.ChaosWadaFractal boundariesNonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has the Wada property and initial conditions near that boundary are even more unpredictable. Many physical systems of interest with this topological property appear in the literature. However, so far the only approach to study Wada basins has been restricted to two-dimensional phase spaces. Here we report a simple algorithm whose purpose is to look for the Wada property in a given dynamical system. Another benefit of this procedure is the possibility to classify and study intermediate situations known as partially Wada boundaries.Nature202320232015info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/26255reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/262552026-06-24T12:48:17Z
dc.title.none.fl_str_mv Testing for Basins of Wada
title Testing for Basins of Wada
spellingShingle Testing for Basins of Wada
Daza, Alvar
Chaos
Wada
Fractal boundaries
title_short Testing for Basins of Wada
title_full Testing for Basins of Wada
title_fullStr Testing for Basins of Wada
title_full_unstemmed Testing for Basins of Wada
title_sort Testing for Basins of Wada
dc.creator.none.fl_str_mv Daza, Alvar
Wagemakers, Alexandre
Sanjuán, Miguel A. F.
Yorke, James A.
author Daza, Alvar
author_facet Daza, Alvar
Wagemakers, Alexandre
Sanjuán, Miguel A. F.
Yorke, James A.
author_role author
author2 Wagemakers, Alexandre
Sanjuán, Miguel A. F.
Yorke, James A.
author2_role author
author
author
dc.subject.none.fl_str_mv Chaos
Wada
Fractal boundaries
topic Chaos
Wada
Fractal boundaries
description Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has the Wada property and initial conditions near that boundary are even more unpredictable. Many physical systems of interest with this topological property appear in the literature. However, so far the only approach to study Wada basins has been restricted to two-dimensional phase spaces. Here we report a simple algorithm whose purpose is to look for the Wada property in a given dynamical system. Another benefit of this procedure is the possibility to classify and study intermediate situations known as partially Wada boundaries.
publishDate 2015
dc.date.none.fl_str_mv 2015
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/26255
url https://hdl.handle.net/10115/26255
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Atribución 4.0 Internacional
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución 4.0 Internacional
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Nature
publisher.none.fl_str_mv Nature
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869406327711727616
score 15.812429

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