Noise-assisted estimation of attractor invariants

Autores
Restrepo Rinckoar, Juan Felipe; Schlotthauer, Gaston
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.
Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentina
Materia
CORRELATION DIMENSION
CORRELATION ENTROPY
CORRELATION INTEGRAL
NOISE-ASSISTED CORRELATION INTEGRAL
U CORRELATION INTEGRAL
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:11336/113842
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Noise-assisted estimation of attractor invariantsRestrepo Rinckoar, Juan FelipeSchlotthauer, GastonCORRELATION DIMENSIONCORRELATION ENTROPYCORRELATION INTEGRALNOISE-ASSISTED CORRELATION INTEGRALU CORRELATION INTEGRALhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; ArgentinaAmerican Physical Society2016-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/113842Restrepo Rinckoar, Juan Felipe; Schlotthauer, Gaston; Noise-assisted estimation of attractor invariants; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 1; 6-2016; 12212-122311539-3755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.94.012212info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.012212info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:59:10Zoai:ri.conicet.gov.ar:11336/113842instacron: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:34982025-10-15 14:59:10.992CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Noise-assisted estimation of attractor invariants
title Noise-assisted estimation of attractor invariants
spellingShingle Noise-assisted estimation of attractor invariants
Restrepo Rinckoar, Juan Felipe
CORRELATION DIMENSION
CORRELATION ENTROPY
CORRELATION INTEGRAL
NOISE-ASSISTED CORRELATION INTEGRAL
U CORRELATION INTEGRAL
title_short Noise-assisted estimation of attractor invariants
title_full Noise-assisted estimation of attractor invariants
title_fullStr Noise-assisted estimation of attractor invariants
title_full_unstemmed Noise-assisted estimation of attractor invariants
title_sort Noise-assisted estimation of attractor invariants
dc.creator.none.fl_str_mv Restrepo Rinckoar, Juan Felipe
Schlotthauer, Gaston
author Restrepo Rinckoar, Juan Felipe
author_facet Restrepo Rinckoar, Juan Felipe
Schlotthauer, Gaston
author_role author
author2 Schlotthauer, Gaston
author2_role author
dc.subject.none.fl_str_mv CORRELATION DIMENSION
CORRELATION ENTROPY
CORRELATION INTEGRAL
NOISE-ASSISTED CORRELATION INTEGRAL
U CORRELATION INTEGRAL
topic CORRELATION DIMENSION
CORRELATION ENTROPY
CORRELATION INTEGRAL
NOISE-ASSISTED CORRELATION INTEGRAL
U CORRELATION INTEGRAL
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.
Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentina
description In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DmU), the correlation entropy (KmU), and the noise level (σmU). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KmU outperforms its GCI-based counterpart. On the basis of the behavior of these estimators, we have proposed an automatic algorithm to find D,K2, and σ from a given time series. The results show that by using this approach, we are able to achieve statistically reliable estimations of those invariants.
publishDate 2016
dc.date.none.fl_str_mv 2016-06
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/11336/113842
Restrepo Rinckoar, Juan Felipe; Schlotthauer, Gaston; Noise-assisted estimation of attractor invariants; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 1; 6-2016; 12212-12231
1539-3755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/113842
identifier_str_mv Restrepo Rinckoar, Juan Felipe; Schlotthauer, Gaston; Noise-assisted estimation of attractor invariants; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 1; 6-2016; 12212-12231
1539-3755
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.94.012212
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.012212
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
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
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 13.22299

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