Sampling period, statistical complexity, and chaotic attractors

Autores
de Micco, Luciana; Fernandez, Juana Graciela; Larrondo, Hilda Angela; Plastino, Ángel Luis; Rosso, Osvaldo Anibal
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period T and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period T. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens´ one in a delay-time embedding, on one hand, and the exact Nyquist-Shannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens´ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension D2 between 2 and 3. One recent experiment confirms the analysis presented here.
Fil: de Micco, Luciana. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Fernandez, Juana Graciela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina
Fil: Larrondo, Hilda Angela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rosso, Osvaldo Anibal. Universidade Federal de Minas Gerais; Brasil. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
chaos
sampling
Nyquist reconstruction
Takens reconstruction
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/278249
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/278249
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sampling period, statistical complexity, and chaotic attractorsde Micco, LucianaFernandez, Juana GracielaLarrondo, Hilda AngelaPlastino, Ángel LuisRosso, Osvaldo AnibalchaossamplingNyquist reconstructionTakens reconstructionhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period T and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period T. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens´ one in a delay-time embedding, on one hand, and the exact Nyquist-Shannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens´ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension D2 between 2 and 3. One recent experiment confirms the analysis presented here.Fil: de Micco, Luciana. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Fernandez, Juana Graciela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; ArgentinaFil: Larrondo, Hilda Angela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Rosso, Osvaldo Anibal. Universidade Federal de Minas Gerais; Brasil. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2012-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/278249de Micco, Luciana; Fernandez, Juana Graciela; Larrondo, Hilda Angela; Plastino, Ángel Luis; Rosso, Osvaldo Anibal; Sampling period, statistical complexity, and chaotic attractors; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 391; 8; 4-2012; 2564-25750378-4371CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437111009782#info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2011.12.042info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T14:31:46Zoai:ri.conicet.gov.ar:11336/278249instacron: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:34982025-12-23 14:31:46.791CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sampling period, statistical complexity, and chaotic attractors
title Sampling period, statistical complexity, and chaotic attractors
spellingShingle Sampling period, statistical complexity, and chaotic attractors
de Micco, Luciana
chaos
sampling
Nyquist reconstruction
Takens reconstruction
title_short Sampling period, statistical complexity, and chaotic attractors
title_full Sampling period, statistical complexity, and chaotic attractors
title_fullStr Sampling period, statistical complexity, and chaotic attractors
title_full_unstemmed Sampling period, statistical complexity, and chaotic attractors
title_sort Sampling period, statistical complexity, and chaotic attractors
dc.creator.none.fl_str_mv de Micco, Luciana
Fernandez, Juana Graciela
Larrondo, Hilda Angela
Plastino, Ángel Luis
Rosso, Osvaldo Anibal
author de Micco, Luciana
author_facet de Micco, Luciana
Fernandez, Juana Graciela
Larrondo, Hilda Angela
Plastino, Ángel Luis
Rosso, Osvaldo Anibal
author_role author
author2 Fernandez, Juana Graciela
Larrondo, Hilda Angela
Plastino, Ángel Luis
Rosso, Osvaldo Anibal
author2_role author
author
author
author
dc.subject.none.fl_str_mv chaos
sampling
Nyquist reconstruction
Takens reconstruction
topic chaos
sampling
Nyquist reconstruction
Takens reconstruction
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period T and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period T. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens´ one in a delay-time embedding, on one hand, and the exact Nyquist-Shannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens´ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension D2 between 2 and 3. One recent experiment confirms the analysis presented here.
Fil: de Micco, Luciana. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Fernandez, Juana Graciela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina
Fil: Larrondo, Hilda Angela. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rosso, Osvaldo Anibal. Universidade Federal de Minas Gerais; Brasil. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period T and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period T. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens´ one in a delay-time embedding, on one hand, and the exact Nyquist-Shannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens´ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension D2 between 2 and 3. One recent experiment confirms the analysis presented here.
publishDate 2012
dc.date.none.fl_str_mv 2012-04
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/11336/278249
de Micco, Luciana; Fernandez, Juana Graciela; Larrondo, Hilda Angela; Plastino, Ángel Luis; Rosso, Osvaldo Anibal; Sampling period, statistical complexity, and chaotic attractors; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 391; 8; 4-2012; 2564-2575
0378-4371
CONICET Digital
CONICET
url http://hdl.handle.net/11336/278249
identifier_str_mv de Micco, Luciana; Fernandez, Juana Graciela; Larrondo, Hilda Angela; Plastino, Ángel Luis; Rosso, Osvaldo Anibal; Sampling period, statistical complexity, and chaotic attractors; Elsevier Science; Physica A: Statistical Mechanics and its Applications; 391; 8; 4-2012; 2564-2575
0378-4371
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437111009782#
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2011.12.042
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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
_version_ 1852335707560869888
score 12.952241

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