On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data

Detalhes bibliográficos
Autor(a) principal: Erivelton Geraldo Nepomuceno
Data de Publicação: 2018
Outros Autores: Samir Martins, Márcio Lacerda, Eduardo Mazoni Andrade Marçal Mendes
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Institucional da UFMG
Texto Completo: https://doi.org/10.1155/2018/6909151
http://hdl.handle.net/1843/57005
https://orcid.org/0000-0002-5841-2193
https://orcid.org/0000-0003-1702-8504
https://orcid.org/0000-0001-8487-3535
https://orcid.org/0000-0002-3267-3862
Resumo: A method to estimate the (positive) largest Lyapunov exponent (LLE) from data using interval extensions is proposed. The method differs from the ones available in the literature in its simplicity since it is only based on three rather simple steps. Firstly, a polynomial NARMAX is used to identify a model from the data under investigation. Secondly, interval extensions, which can be easily extracted from the identified model, are used to calculate the lower bound error. Finally, a simple linear fit to the logarithm of lower bound error is obtained and then the LLE is retrieved from it as the third step. To illustrate the proposed method, the LLE is calculated for the following well-known benchmarks: sine map, Rössler Equations, and Mackey-Glass Equations from identified models given in the literature and also from two identified NARMAX models: a chaotic jerk circuit and the tent map. In the latter, a Gaussian noise has been added to show the robustness of the proposed method.
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repository_id_str
spelling On the use of interval extensions to estimate the largest lyapunov exponent from chaotic dataInterval extensionsLiapunovLiapunov, Funções deA method to estimate the (positive) largest Lyapunov exponent (LLE) from data using interval extensions is proposed. The method differs from the ones available in the literature in its simplicity since it is only based on three rather simple steps. Firstly, a polynomial NARMAX is used to identify a model from the data under investigation. Secondly, interval extensions, which can be easily extracted from the identified model, are used to calculate the lower bound error. Finally, a simple linear fit to the logarithm of lower bound error is obtained and then the LLE is retrieved from it as the third step. To illustrate the proposed method, the LLE is calculated for the following well-known benchmarks: sine map, Rössler Equations, and Mackey-Glass Equations from identified models given in the literature and also from two identified NARMAX models: a chaotic jerk circuit and the tent map. In the latter, a Gaussian noise has been added to show the robustness of the proposed method.Universidade Federal de Minas GeraisBrasilENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICAUFMG2023-07-26T17:03:32Z2023-07-26T17:03:32Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1155/2018/69091511024-123Xhttp://hdl.handle.net/1843/57005https://orcid.org/0000-0002-5841-2193https://orcid.org/0000-0003-1702-8504https://orcid.org/0000-0001-8487-3535https://orcid.org/0000-0002-3267-3862porMathematical problems in engineeringErivelton Geraldo NepomucenoSamir MartinsMárcio LacerdaEduardo Mazoni Andrade Marçal Mendesinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMG2023-07-26T17:03:32Zoai:repositorio.ufmg.br:1843/57005Repositório InstitucionalPUBhttps://repositorio.ufmg.br/oairepositorio@ufmg.bropendoar:2023-07-26T17:03:32Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.none.fl_str_mv On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
title On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
spellingShingle On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
Erivelton Geraldo Nepomuceno
Interval extensions
Liapunov
Liapunov, Funções de
title_short On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
title_full On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
title_fullStr On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
title_full_unstemmed On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
title_sort On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
author Erivelton Geraldo Nepomuceno
author_facet Erivelton Geraldo Nepomuceno
Samir Martins
Márcio Lacerda
Eduardo Mazoni Andrade Marçal Mendes
author_role author
author2 Samir Martins
Márcio Lacerda
Eduardo Mazoni Andrade Marçal Mendes
author2_role author
author
author
dc.contributor.author.fl_str_mv Erivelton Geraldo Nepomuceno
Samir Martins
Márcio Lacerda
Eduardo Mazoni Andrade Marçal Mendes
dc.subject.por.fl_str_mv Interval extensions
Liapunov
Liapunov, Funções de
topic Interval extensions
Liapunov
Liapunov, Funções de
description A method to estimate the (positive) largest Lyapunov exponent (LLE) from data using interval extensions is proposed. The method differs from the ones available in the literature in its simplicity since it is only based on three rather simple steps. Firstly, a polynomial NARMAX is used to identify a model from the data under investigation. Secondly, interval extensions, which can be easily extracted from the identified model, are used to calculate the lower bound error. Finally, a simple linear fit to the logarithm of lower bound error is obtained and then the LLE is retrieved from it as the third step. To illustrate the proposed method, the LLE is calculated for the following well-known benchmarks: sine map, Rössler Equations, and Mackey-Glass Equations from identified models given in the literature and also from two identified NARMAX models: a chaotic jerk circuit and the tent map. In the latter, a Gaussian noise has been added to show the robustness of the proposed method.
publishDate 2018
dc.date.none.fl_str_mv 2018
2023-07-26T17:03:32Z
2023-07-26T17:03:32Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://doi.org/10.1155/2018/6909151
1024-123X
http://hdl.handle.net/1843/57005
https://orcid.org/0000-0002-5841-2193
https://orcid.org/0000-0003-1702-8504
https://orcid.org/0000-0001-8487-3535
https://orcid.org/0000-0002-3267-3862
url https://doi.org/10.1155/2018/6909151
http://hdl.handle.net/1843/57005
https://orcid.org/0000-0002-5841-2193
https://orcid.org/0000-0003-1702-8504
https://orcid.org/0000-0001-8487-3535
https://orcid.org/0000-0002-3267-3862
identifier_str_mv 1024-123X
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv Mathematical problems in engineering
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
Brasil
ENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
UFMG
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
Brasil
ENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
UFMG
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
instacron_str UFMG
institution UFMG
reponame_str Repositório Institucional da UFMG
collection Repositório Institucional da UFMG
repository.name.fl_str_mv Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)
repository.mail.fl_str_mv repositorio@ufmg.br
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