Chua’s oscillator: an introductory approach to chaos theory

Detalhes bibliográficos
Autor(a) principal: Sordi,Alexandre
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100406
Resumo: The purpose of this article is to build an introductory approach to chaos theory from the Chua’ oscillator for students of mathematics, physics and engineering. The Chua’ circuit is one of the simplest dynamic systems that produce irregular behavior. Despite its simplicity, this oscillating circuit is a very useful device for studying basic principles of chaos theory. This study begins with the definition of equilibrium points, this is done in a graphic and analytical way. The analysis of the stationary solution of differential equations system allows to show the occurrence of pitchfork bifurcation. The eigenvalues are calculated and the trajectories of the Chua’ oscillator are analyzed, then the occurrence of Hopf bifurcation is demonstrated. Period-doubling cascade are observed using phase portrait and orbit diagram. Finally, sensitivity to initial conditions is studied by calculating Lyapunov exponents.
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spelling Chua’s oscillator: an introductory approach to chaos theoryNon-linear oscillatorchaos theoryattractorsThe purpose of this article is to build an introductory approach to chaos theory from the Chua’ oscillator for students of mathematics, physics and engineering. The Chua’ circuit is one of the simplest dynamic systems that produce irregular behavior. Despite its simplicity, this oscillating circuit is a very useful device for studying basic principles of chaos theory. This study begins with the definition of equilibrium points, this is done in a graphic and analytical way. The analysis of the stationary solution of differential equations system allows to show the occurrence of pitchfork bifurcation. The eigenvalues are calculated and the trajectories of the Chua’ oscillator are analyzed, then the occurrence of Hopf bifurcation is demonstrated. Period-doubling cascade are observed using phase portrait and orbit diagram. Finally, sensitivity to initial conditions is studied by calculating Lyapunov exponents.Sociedade Brasileira de Física2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100406Revista Brasileira de Ensino de Física v.43 2021reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-rbef-2020-0437info:eu-repo/semantics/openAccessSordi,Alexandreeng2020-12-17T00:00:00Zoai:scielo:S1806-11172021000100406Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2020-12-17T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Chua’s oscillator: an introductory approach to chaos theory
title Chua’s oscillator: an introductory approach to chaos theory
spellingShingle Chua’s oscillator: an introductory approach to chaos theory
Sordi,Alexandre
Non-linear oscillator
chaos theory
attractors
title_short Chua’s oscillator: an introductory approach to chaos theory
title_full Chua’s oscillator: an introductory approach to chaos theory
title_fullStr Chua’s oscillator: an introductory approach to chaos theory
title_full_unstemmed Chua’s oscillator: an introductory approach to chaos theory
title_sort Chua’s oscillator: an introductory approach to chaos theory
author Sordi,Alexandre
author_facet Sordi,Alexandre
author_role author
dc.contributor.author.fl_str_mv Sordi,Alexandre
dc.subject.por.fl_str_mv Non-linear oscillator
chaos theory
attractors
topic Non-linear oscillator
chaos theory
attractors
description The purpose of this article is to build an introductory approach to chaos theory from the Chua’ oscillator for students of mathematics, physics and engineering. The Chua’ circuit is one of the simplest dynamic systems that produce irregular behavior. Despite its simplicity, this oscillating circuit is a very useful device for studying basic principles of chaos theory. This study begins with the definition of equilibrium points, this is done in a graphic and analytical way. The analysis of the stationary solution of differential equations system allows to show the occurrence of pitchfork bifurcation. The eigenvalues are calculated and the trajectories of the Chua’ oscillator are analyzed, then the occurrence of Hopf bifurcation is demonstrated. Period-doubling cascade are observed using phase portrait and orbit diagram. Finally, sensitivity to initial conditions is studied by calculating Lyapunov exponents.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100406
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100406
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1806-9126-rbef-2020-0437
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.43 2021
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
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instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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