Templex-based dynamical units for a taxonomy of chaos

Autores
Mosto, Caterina; Charó, Gisela Daniela; Letellier, Christophe; Sciamarella, Denisse
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented BraMAH cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a “minimal” form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (Rössler, Lorenz, and Burke–Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated.
Fil: Mosto, Caterina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina
Fil: Charó, Gisela Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina. Laboratoire des Sciences du Climat et de l’Environnement; Francia
Fil: Letellier, Christophe. Rouen Normandie University; Francia
Fil: Sciamarella, Denisse. Centre National de la Recherche Scientifique; Francia. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina
Materia
TOPOLOGICAL DATA ANALYSIS
DYNAMICAL SYSTEMS
CHAOTIC ATTRACTORS
ALGEBRAIC TOPOLOGY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/261028
Acceder
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spelling Templex-based dynamical units for a taxonomy of chaosMosto, CaterinaCharó, Gisela DanielaLetellier, ChristopheSciamarella, DenisseTOPOLOGICAL DATA ANALYSISDYNAMICAL SYSTEMSCHAOTIC ATTRACTORSALGEBRAIC TOPOLOGYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented BraMAH cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a “minimal” form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (Rössler, Lorenz, and Burke–Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated.Fil: Mosto, Caterina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; ArgentinaFil: Charó, Gisela Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina. Laboratoire des Sciences du Climat et de l’Environnement; FranciaFil: Letellier, Christophe. Rouen Normandie University; FranciaFil: Sciamarella, Denisse. Centre National de la Recherche Scientifique; Francia. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; ArgentinaAmerican Institute of Physics2024-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/261028Mosto, Caterina; Charó, Gisela Daniela; Letellier, Christophe; Sciamarella, Denisse; Templex-based dynamical units for a taxonomy of chaos; American Institute of Physics; Chaos; 34; 11; 11-2024; 1-181054-1500CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://pubs.aip.org/cha/article/34/11/113111/3319161/Templex-based-dynamical-units-for-a-taxonomy-ofinfo:eu-repo/semantics/altIdentifier/doi/10.1063/5.0233160info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:04:31Zoai:ri.conicet.gov.ar:11336/261028instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:04:31.306CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Templex-based dynamical units for a taxonomy of chaos
title Templex-based dynamical units for a taxonomy of chaos
spellingShingle Templex-based dynamical units for a taxonomy of chaos
Mosto, Caterina
TOPOLOGICAL DATA ANALYSIS
DYNAMICAL SYSTEMS
CHAOTIC ATTRACTORS
ALGEBRAIC TOPOLOGY
title_short Templex-based dynamical units for a taxonomy of chaos
title_full Templex-based dynamical units for a taxonomy of chaos
title_fullStr Templex-based dynamical units for a taxonomy of chaos
title_full_unstemmed Templex-based dynamical units for a taxonomy of chaos
title_sort Templex-based dynamical units for a taxonomy of chaos
dc.creator.none.fl_str_mv Mosto, Caterina
Charó, Gisela Daniela
Letellier, Christophe
Sciamarella, Denisse
author Mosto, Caterina
author_facet Mosto, Caterina
Charó, Gisela Daniela
Letellier, Christophe
Sciamarella, Denisse
author_role author
author2 Charó, Gisela Daniela
Letellier, Christophe
Sciamarella, Denisse
author2_role author
author
author
dc.subject.none.fl_str_mv TOPOLOGICAL DATA ANALYSIS
DYNAMICAL SYSTEMS
CHAOTIC ATTRACTORS
ALGEBRAIC TOPOLOGY
topic TOPOLOGICAL DATA ANALYSIS
DYNAMICAL SYSTEMS
CHAOTIC ATTRACTORS
ALGEBRAIC TOPOLOGY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented BraMAH cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a “minimal” form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (Rössler, Lorenz, and Burke–Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated.
Fil: Mosto, Caterina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina
Fil: Charó, Gisela Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina. Laboratoire des Sciences du Climat et de l’Environnement; Francia
Fil: Letellier, Christophe. Rouen Normandie University; Francia
Fil: Sciamarella, Denisse. Centre National de la Recherche Scientifique; Francia. Instituto Franco-Argentino sobre Estudios del Clima y sus Impactos; Argentina
description Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to three-dimensional objects based on knot theory. To deal with higher-dimensional chaos, we recently introduced the templex combining a flow-oriented BraMAH cell complex and a directed graph (a digraph). There is no dimensional limitation in the concept of templex. Here, we show that a templex can be automatically reduced into a “minimal” form to provide a comprehensive and synthetic view of the main properties of chaotic attractors. This reduction allows for the development of a taxonomy of chaos in terms of two elementary units: the oscillating unit (O-unit) and the switching unit (S-unit). We apply this approach to various well-known attractors (Rössler, Lorenz, and Burke–Shaw) as well as a non-trivial four-dimensional attractor. A case of toroidal chaos (Deng) is also treated.
publishDate 2024
dc.date.none.fl_str_mv 2024-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/261028
Mosto, Caterina; Charó, Gisela Daniela; Letellier, Christophe; Sciamarella, Denisse; Templex-based dynamical units for a taxonomy of chaos; American Institute of Physics; Chaos; 34; 11; 11-2024; 1-18
1054-1500
CONICET Digital
CONICET
url http://hdl.handle.net/11336/261028
identifier_str_mv Mosto, Caterina; Charó, Gisela Daniela; Letellier, Christophe; Sciamarella, Denisse; Templex-based dynamical units for a taxonomy of chaos; American Institute of Physics; Chaos; 34; 11; 11-2024; 1-18
1054-1500
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://pubs.aip.org/cha/article/34/11/113111/3319161/Templex-based-dynamical-units-for-a-taxonomy-of
info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0233160
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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