A numerical estimate of the regularity of a family of Strange non-chaotic Attractors

We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in C. Grebogy et al. (1984) (see also G. Keller (1996)). To estimate these regularities we use wavelet analysis in the spirit of R. de la Llave et al. (2002) together with so...

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Authors: Alsedà, Lluís|||0000-0001-9908-1063, Mondelo Gonzalez, Jose M.|||0000-0002-7135-0599, Romero i Sànchez, David|||0000-0002-2881-268X
Format: article
Publication Date:2017
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:199319
Online Access:https://ddd.uab.cat/record/199319
https://dx.doi.org/urn:doi:10.1016/j.physd.2016.12.006
Access Level:Open access
Keyword:Quasiperiodically forced system
Regularity
Wavelets
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spelling A numerical estimate of the regularity of a family of Strange non-chaotic AttractorsAlsedà, Lluís|||0000-0001-9908-1063Mondelo Gonzalez, Jose M.|||0000-0002-7135-0599Romero i Sànchez, David|||0000-0002-2881-268XQuasiperiodically forced systemRegularityWaveletsWe estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in C. Grebogy et al. (1984) (see also G. Keller (1996)). To estimate these regularities we use wavelet analysis in the spirit of R. de la Llave et al. (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done. 22017-01-0120172017-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/199319https://dx.doi.org/urn:doi:10.1016/j.physd.2016.12.006reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-26995-C02-01Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-01486open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1993192026-06-06T12:50:31Z
dc.title.none.fl_str_mv A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
title A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
spellingShingle A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
Alsedà, Lluís|||0000-0001-9908-1063
Quasiperiodically forced system
Regularity
Wavelets
title_short A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
title_full A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
title_fullStr A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
title_full_unstemmed A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
title_sort A numerical estimate of the regularity of a family of Strange non-chaotic Attractors
dc.creator.none.fl_str_mv Alsedà, Lluís|||0000-0001-9908-1063
Mondelo Gonzalez, Jose M.|||0000-0002-7135-0599
Romero i Sànchez, David|||0000-0002-2881-268X
author Alsedà, Lluís|||0000-0001-9908-1063
author_facet Alsedà, Lluís|||0000-0001-9908-1063
Mondelo Gonzalez, Jose M.|||0000-0002-7135-0599
Romero i Sànchez, David|||0000-0002-2881-268X
author_role author
author2 Mondelo Gonzalez, Jose M.|||0000-0002-7135-0599
Romero i Sànchez, David|||0000-0002-2881-268X
author2_role author
author
dc.subject.none.fl_str_mv Quasiperiodically forced system
Regularity
Wavelets
topic Quasiperiodically forced system
Regularity
Wavelets
description We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in C. Grebogy et al. (1984) (see also G. Keller (1996)). To estimate these regularities we use wavelet analysis in the spirit of R. de la Llave et al. (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.
publishDate 2017
dc.date.none.fl_str_mv 2
2017-01-01
2017
2017-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/199319
https://dx.doi.org/urn:doi:10.1016/j.physd.2016.12.006
url https://ddd.uab.cat/record/199319
https://dx.doi.org/urn:doi:10.1016/j.physd.2016.12.006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-26995-C02-01
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-01486
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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