Bifurcation theory and harmonic content of oscillations

Autores
Itovich, Griselda Rut; Robbio, Federico I.; Moiola, Jorge Luis
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The harmonic content of periodic solutions in ODEs is obtained using standard techniques of harmonic balance and the fast Fourier transform (FFT). For the first method, the harmonic content is attained in the vicinity of the Hopf bifurcation condition where a smooth branch of oscilations is born under the variation of a distinguished parameter. The second technique is applied directly to numerical simulation, which is assumed to be the correct solution. Although the first method is local, it provides an excellent tool to characterize the periodic behavior in the unfoldings of other more complex singularities, such as the double Hopf bifurcation (DHB). An example with a DBH is analyzed with this methodology and the FFT algorithm.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; Argentina
Fil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
Materia
Harmonic
Content
Oscillations
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:11336/105853
Acceder
id CONICETDig_0b8a60797829c697eafc610999f5d26e
oai_identifier_str oai:ri.conicet.gov.ar:11336/105853
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Bifurcation theory and harmonic content of oscillationsItovich, Griselda RutRobbio, Federico I.Moiola, Jorge LuisHarmonicContentOscillationshttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2The harmonic content of periodic solutions in ODEs is obtained using standard techniques of harmonic balance and the fast Fourier transform (FFT). For the first method, the harmonic content is attained in the vicinity of the Hopf bifurcation condition where a smooth branch of oscilations is born under the variation of a distinguished parameter. The second technique is applied directly to numerical simulation, which is assumed to be the correct solution. Although the first method is local, it provides an excellent tool to characterize the periodic behavior in the unfoldings of other more complex singularities, such as the double Hopf bifurcation (DHB). An example with a DBH is analyzed with this methodology and the FFT algorithm.Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; ArgentinaFil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; ArgentinaUnión Matemática Argentina2006-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105853Itovich, Griselda Rut; Robbio, Federico I.; Moiola, Jorge Luis; Bifurcation theory and harmonic content of oscillations; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 47; 02; 12-2006; 137-1500041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol47info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:54Zoai:ri.conicet.gov.ar:11336/105853instacron: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 09:38:54.368CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bifurcation theory and harmonic content of oscillations
title Bifurcation theory and harmonic content of oscillations
spellingShingle Bifurcation theory and harmonic content of oscillations
Itovich, Griselda Rut
Harmonic
Content
Oscillations
title_short Bifurcation theory and harmonic content of oscillations
title_full Bifurcation theory and harmonic content of oscillations
title_fullStr Bifurcation theory and harmonic content of oscillations
title_full_unstemmed Bifurcation theory and harmonic content of oscillations
title_sort Bifurcation theory and harmonic content of oscillations
dc.creator.none.fl_str_mv Itovich, Griselda Rut
Robbio, Federico I.
Moiola, Jorge Luis
author Itovich, Griselda Rut
author_facet Itovich, Griselda Rut
Robbio, Federico I.
Moiola, Jorge Luis
author_role author
author2 Robbio, Federico I.
Moiola, Jorge Luis
author2_role author
author
dc.subject.none.fl_str_mv Harmonic
Content
Oscillations
topic Harmonic
Content
Oscillations
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The harmonic content of periodic solutions in ODEs is obtained using standard techniques of harmonic balance and the fast Fourier transform (FFT). For the first method, the harmonic content is attained in the vicinity of the Hopf bifurcation condition where a smooth branch of oscilations is born under the variation of a distinguished parameter. The second technique is applied directly to numerical simulation, which is assumed to be the correct solution. Although the first method is local, it provides an excellent tool to characterize the periodic behavior in the unfoldings of other more complex singularities, such as the double Hopf bifurcation (DHB). An example with a DBH is analyzed with this methodology and the FFT algorithm.
Fil: Itovich, Griselda Rut. Universidad Nacional del Comahue; Argentina
Fil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur; Argentina
description The harmonic content of periodic solutions in ODEs is obtained using standard techniques of harmonic balance and the fast Fourier transform (FFT). For the first method, the harmonic content is attained in the vicinity of the Hopf bifurcation condition where a smooth branch of oscilations is born under the variation of a distinguished parameter. The second technique is applied directly to numerical simulation, which is assumed to be the correct solution. Although the first method is local, it provides an excellent tool to characterize the periodic behavior in the unfoldings of other more complex singularities, such as the double Hopf bifurcation (DHB). An example with a DBH is analyzed with this methodology and the FFT algorithm.
publishDate 2006
dc.date.none.fl_str_mv 2006-12
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/11336/105853
Itovich, Griselda Rut; Robbio, Federico I.; Moiola, Jorge Luis; Bifurcation theory and harmonic content of oscillations; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 47; 02; 12-2006; 137-150
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105853
identifier_str_mv Itovich, Griselda Rut; Robbio, Federico I.; Moiola, Jorge Luis; Bifurcation theory and harmonic content of oscillations; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 47; 02; 12-2006; 137-150
0041-6932
1669-9637
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol47
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
dc.publisher.none.fl_str_mv Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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
_version_ 1844613230023933952
score 13.070432

Publicaciones similares