Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method

Detalhes bibliográficos
Autor(a) principal: Rocha, Ronilson
Data de Publicação: 2020
Outros Autores: Medrano-T, Rene Orlando [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11071-020-06039-x
http://hdl.handle.net/11449/205388
Resumo: This work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations.
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spelling Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function methodChua circuitCubic nonlinearityDescribing functionsHidden oscillationsRoot locusStability analysisThis work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations.Federal University of Ouro Preto - UFOP/EM/DEMEC Campus Morro do CruzeiroFederal University of São Paulo - UNIFESP/DF Campus DiademaSão Paulo State University - UNESP/IGCE/DF Campus Rio ClaroSão Paulo State University - UNESP/IGCE/DF Campus Rio ClaroFederal University of Ouro Preto - UFOP/EM/DEMECUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Rocha, RonilsonMedrano-T, Rene Orlando [UNESP]2021-06-25T10:14:31Z2021-06-25T10:14:31Z2020-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2859-2874http://dx.doi.org/10.1007/s11071-020-06039-xNonlinear Dynamics, v. 102, n. 4, p. 2859-2874, 2020.1573-269X0924-090Xhttp://hdl.handle.net/11449/20538810.1007/s11071-020-06039-x2-s2.0-85094154232Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Dynamicsinfo:eu-repo/semantics/openAccess2021-10-23T12:40:00Zoai:repositorio.unesp.br:11449/205388Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:30:20.137717Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
title Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
spellingShingle Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
Rocha, Ronilson
Chua circuit
Cubic nonlinearity
Describing functions
Hidden oscillations
Root locus
Stability analysis
title_short Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
title_full Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
title_fullStr Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
title_full_unstemmed Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
title_sort Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
author Rocha, Ronilson
author_facet Rocha, Ronilson
Medrano-T, Rene Orlando [UNESP]
author_role author
author2 Medrano-T, Rene Orlando [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Federal University of Ouro Preto - UFOP/EM/DEMEC
Universidade de São Paulo (USP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Rocha, Ronilson
Medrano-T, Rene Orlando [UNESP]
dc.subject.por.fl_str_mv Chua circuit
Cubic nonlinearity
Describing functions
Hidden oscillations
Root locus
Stability analysis
topic Chua circuit
Cubic nonlinearity
Describing functions
Hidden oscillations
Root locus
Stability analysis
description This work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-01
2021-06-25T10:14:31Z
2021-06-25T10:14:31Z
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 http://dx.doi.org/10.1007/s11071-020-06039-x
Nonlinear Dynamics, v. 102, n. 4, p. 2859-2874, 2020.
1573-269X
0924-090X
http://hdl.handle.net/11449/205388
10.1007/s11071-020-06039-x
2-s2.0-85094154232
url http://dx.doi.org/10.1007/s11071-020-06039-x
http://hdl.handle.net/11449/205388
identifier_str_mv Nonlinear Dynamics, v. 102, n. 4, p. 2859-2874, 2020.
1573-269X
0924-090X
10.1007/s11071-020-06039-x
2-s2.0-85094154232
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Dynamics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2859-2874
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128523232083968

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