Chaos prediction and bifurcation analysis in control engineering

Autores
Alonso, Diego; Calandrini, Guillermo Luis; Berns, Daniel Walther; Paolini, Eduardo Emilio; Moiola, Jorge Luis
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, two different methods to compute the period-doubling route to chaos (or Feigenbaum chaos) in nonlinear systems are presented. The first one is a semi-analytical procedure, based on a symbolic calculation of an approximate monodromy matrix. The second one takes advantage of software packages for continuation of periodic solutions. Both procedures are used to analyze Chua´s circuit. The second method is also applied to the Rössler system and one of the chaotic systems of Sprott. In all three cases, several period-doubling bifurcation points in the parameter space are detected, allowing to compute a sequence of values supposedly converging to Feigenbaum´s constant. This "experimental´´ computer verification agrees with experiments performed by other researchers in real systems. This material has been used in final projects in a graduate course in dynamical systems.
Fil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Fil: Calandrini, Guillermo Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; Argentina
Fil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Materia
PERIOD-DOUBLING BIFURCATIONS
FEIGENBAUM´S CONSTANT
CHAOTIC SYSTEMS
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:11336/104064
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Chaos prediction and bifurcation analysis in control engineeringAlonso, DiegoCalandrini, Guillermo LuisBerns, Daniel WaltherPaolini, Eduardo EmilioMoiola, Jorge LuisPERIOD-DOUBLING BIFURCATIONSFEIGENBAUM´S CONSTANTCHAOTIC SYSTEMShttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this paper, two different methods to compute the period-doubling route to chaos (or Feigenbaum chaos) in nonlinear systems are presented. The first one is a semi-analytical procedure, based on a symbolic calculation of an approximate monodromy matrix. The second one takes advantage of software packages for continuation of periodic solutions. Both procedures are used to analyze Chua´s circuit. The second method is also applied to the Rössler system and one of the chaotic systems of Sprott. In all three cases, several period-doubling bifurcation points in the parameter space are detected, allowing to compute a sequence of values supposedly converging to Feigenbaum´s constant. This "experimental´´ computer verification agrees with experiments performed by other researchers in real systems. This material has been used in final projects in a graduate course in dynamical systems.Fil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaFil: Calandrini, Guillermo Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; ArgentinaFil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; ArgentinaPlanta Piloto de Ingeniería Química2001-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/104064Alonso, Diego; Calandrini, Guillermo Luis; Berns, Daniel Walther; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chaos prediction and bifurcation analysis in control engineering; Planta Piloto de Ingeniería Química; Latin American Applied Research; 31; 3; 12-2001; 185-1920327-07931851-8796CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.laar.plapiqui.edu.ar/OJS/public/site/volumens/indexes/i31_03.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:00Zoai:ri.conicet.gov.ar:11336/104064instacron: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:34982025-09-29 09:38:01.04CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Chaos prediction and bifurcation analysis in control engineering
title Chaos prediction and bifurcation analysis in control engineering
spellingShingle Chaos prediction and bifurcation analysis in control engineering
Alonso, Diego
PERIOD-DOUBLING BIFURCATIONS
FEIGENBAUM´S CONSTANT
CHAOTIC SYSTEMS
title_short Chaos prediction and bifurcation analysis in control engineering
title_full Chaos prediction and bifurcation analysis in control engineering
title_fullStr Chaos prediction and bifurcation analysis in control engineering
title_full_unstemmed Chaos prediction and bifurcation analysis in control engineering
title_sort Chaos prediction and bifurcation analysis in control engineering
dc.creator.none.fl_str_mv Alonso, Diego
Calandrini, Guillermo Luis
Berns, Daniel Walther
Paolini, Eduardo Emilio
Moiola, Jorge Luis
author Alonso, Diego
author_facet Alonso, Diego
Calandrini, Guillermo Luis
Berns, Daniel Walther
Paolini, Eduardo Emilio
Moiola, Jorge Luis
author_role author
author2 Calandrini, Guillermo Luis
Berns, Daniel Walther
Paolini, Eduardo Emilio
Moiola, Jorge Luis
author2_role author
author
author
author
dc.subject.none.fl_str_mv PERIOD-DOUBLING BIFURCATIONS
FEIGENBAUM´S CONSTANT
CHAOTIC SYSTEMS
topic PERIOD-DOUBLING BIFURCATIONS
FEIGENBAUM´S CONSTANT
CHAOTIC SYSTEMS
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 paper, two different methods to compute the period-doubling route to chaos (or Feigenbaum chaos) in nonlinear systems are presented. The first one is a semi-analytical procedure, based on a symbolic calculation of an approximate monodromy matrix. The second one takes advantage of software packages for continuation of periodic solutions. Both procedures are used to analyze Chua´s circuit. The second method is also applied to the Rössler system and one of the chaotic systems of Sprott. In all three cases, several period-doubling bifurcation points in the parameter space are detected, allowing to compute a sequence of values supposedly converging to Feigenbaum´s constant. This "experimental´´ computer verification agrees with experiments performed by other researchers in real systems. This material has been used in final projects in a graduate course in dynamical systems.
Fil: Alonso, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
Fil: Calandrini, Guillermo Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Berns, Daniel Walther. Universidad Nacional de la Patagonia "San Juan Bosco"; Argentina
Fil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages". Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages"; Argentina
description In this paper, two different methods to compute the period-doubling route to chaos (or Feigenbaum chaos) in nonlinear systems are presented. The first one is a semi-analytical procedure, based on a symbolic calculation of an approximate monodromy matrix. The second one takes advantage of software packages for continuation of periodic solutions. Both procedures are used to analyze Chua´s circuit. The second method is also applied to the Rössler system and one of the chaotic systems of Sprott. In all three cases, several period-doubling bifurcation points in the parameter space are detected, allowing to compute a sequence of values supposedly converging to Feigenbaum´s constant. This "experimental´´ computer verification agrees with experiments performed by other researchers in real systems. This material has been used in final projects in a graduate course in dynamical systems.
publishDate 2001
dc.date.none.fl_str_mv 2001-12
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/11336/104064
Alonso, Diego; Calandrini, Guillermo Luis; Berns, Daniel Walther; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chaos prediction and bifurcation analysis in control engineering; Planta Piloto de Ingeniería Química; Latin American Applied Research; 31; 3; 12-2001; 185-192
0327-0793
1851-8796
CONICET Digital
CONICET
url http://hdl.handle.net/11336/104064
identifier_str_mv Alonso, Diego; Calandrini, Guillermo Luis; Berns, Daniel Walther; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chaos prediction and bifurcation analysis in control engineering; Planta Piloto de Ingeniería Química; Latin American Applied Research; 31; 3; 12-2001; 185-192
0327-0793
1851-8796
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.laar.plapiqui.edu.ar/OJS/public/site/volumens/indexes/i31_03.htm
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
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
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 13.070432

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