On the use of interval extensions to estimate the largest lyapunov exponent from chaotic data
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
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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Repositório Institucional da UFMG |
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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 |
_version_ |
1823248142290649088 |