Stability of equilibrium and bifurcation analysis in delay differential equations

Autores
Itovich, Griselda Rut; Gentile, Franco Sebastián; Moiola, Jorge Luis
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión aceptada
Descripción
Fil: Itovich, Griselda Rut. Universidad Nacional de Río Negro. Escuela de Producción, Tecnología y Medio Ambiente. Río Negro, Argentina.
Fil: Gentile, Franco Sebastián. Universidad Nacional del Sur. Departamento de Matemática. Buenos Aires, Argentina.
Fil: Gentile, Franco Sebastián. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.
Fil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Buenos Aires. Argentina.
Fil: Moiola, Jorge Luis. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.
When delay differential equations are considered, the determination of the stability of an equilibrium is connected with the location of the roots of an exponential polynomial. Applying some results of Pontryagin (1955), Danskin, Bellman and Cooke (1954, 1963), some theorems have been set. They give necessary and sufficient conditions to guarantee the asymptotic stability of the equilibrium points. The models are written as retarded and neutral delay differential equations. So, these results, expressed as inequalities in terms of the involved parameters, allow to find areas of stability as well as its frontiers: the Hopf bifurcation curves. These results together with those coming from the frequency domain methodology (Moiola and Chen, 1996), this last to study limit cycles and its bifurcations, complete the description of the dynamic behavior.
Materia
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
Delay Differential Equations
Stability
Bifurcation
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
RID-UNRN (UNRN)
Institución
Universidad Nacional de Río Negro
OAI Identificador
oai:rid.unrn.edu.ar:20.500.12049/6064
Acceder
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network_name_str RID-UNRN (UNRN)
spelling Stability of equilibrium and bifurcation analysis in delay differential equationsItovich, Griselda RutGentile, Franco SebastiánMoiola, Jorge LuisCiencias Exactas y NaturalesIngeniería, Ciencia y TecnologíaDelay Differential EquationsStabilityBifurcationCiencias Exactas y NaturalesIngeniería, Ciencia y TecnologíaFil: Itovich, Griselda Rut. Universidad Nacional de Río Negro. Escuela de Producción, Tecnología y Medio Ambiente. Río Negro, Argentina.Fil: Gentile, Franco Sebastián. Universidad Nacional del Sur. Departamento de Matemática. Buenos Aires, Argentina.Fil: Gentile, Franco Sebastián. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.Fil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Buenos Aires. Argentina.Fil: Moiola, Jorge Luis. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.When delay differential equations are considered, the determination of the stability of an equilibrium is connected with the location of the roots of an exponential polynomial. Applying some results of Pontryagin (1955), Danskin, Bellman and Cooke (1954, 1963), some theorems have been set. They give necessary and sufficient conditions to guarantee the asymptotic stability of the equilibrium points. The models are written as retarded and neutral delay differential equations. So, these results, expressed as inequalities in terms of the involved parameters, allow to find areas of stability as well as its frontiers: the Hopf bifurcation curves. These results together with those coming from the frequency domain methodology (Moiola and Chen, 1996), this last to study limit cycles and its bifurcations, complete the description of the dynamic behavior.2019-06-06info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfhttps://www.matematica.uns.edu.ar/xvcm/comunicaciones/Aplicada/Itovich_presentacion_Monteiro_Junio_2019.pdfhttp://rid.unrn.edu.ar/handle/20.500.12049/6064engXV Congreso Dr. Antonio Monteirohttps://www.matematica.uns.edu.ar/xvcm/Comunic.phpinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/4.0/reponame:RID-UNRN (UNRN)instname:Universidad Nacional de Río Negro2025-09-11T10:49:25Zoai:rid.unrn.edu.ar:20.500.12049/6064instacron:UNRNInstitucionalhttps://rid.unrn.edu.ar/jspui/Universidad públicaNo correspondehttps://rid.unrn.edu.ar/oai/snrdrid@unrn.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:43692025-09-11 10:49:25.279RID-UNRN (UNRN) - Universidad Nacional de Río Negrofalse
dc.title.none.fl_str_mv Stability of equilibrium and bifurcation analysis in delay differential equations
title Stability of equilibrium and bifurcation analysis in delay differential equations
spellingShingle Stability of equilibrium and bifurcation analysis in delay differential equations
Itovich, Griselda Rut
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
Delay Differential Equations
Stability
Bifurcation
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
title_short Stability of equilibrium and bifurcation analysis in delay differential equations
title_full Stability of equilibrium and bifurcation analysis in delay differential equations
title_fullStr Stability of equilibrium and bifurcation analysis in delay differential equations
title_full_unstemmed Stability of equilibrium and bifurcation analysis in delay differential equations
title_sort Stability of equilibrium and bifurcation analysis in delay differential equations
dc.creator.none.fl_str_mv Itovich, Griselda Rut
Gentile, Franco Sebastián
Moiola, Jorge Luis
author Itovich, Griselda Rut
author_facet Itovich, Griselda Rut
Gentile, Franco Sebastián
Moiola, Jorge Luis
author_role author
author2 Gentile, Franco Sebastián
Moiola, Jorge Luis
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
Delay Differential Equations
Stability
Bifurcation
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
topic Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
Delay Differential Equations
Stability
Bifurcation
Ciencias Exactas y Naturales
Ingeniería, Ciencia y Tecnología
dc.description.none.fl_txt_mv Fil: Itovich, Griselda Rut. Universidad Nacional de Río Negro. Escuela de Producción, Tecnología y Medio Ambiente. Río Negro, Argentina.
Fil: Gentile, Franco Sebastián. Universidad Nacional del Sur. Departamento de Matemática. Buenos Aires, Argentina.
Fil: Gentile, Franco Sebastián. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.
Fil: Moiola, Jorge Luis. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras. Buenos Aires. Argentina.
Fil: Moiola, Jorge Luis. Instituto de Investigaciones en Ingeniería Eléctrica (IIIE - CONICET). Buenos Aires. Argentina.
When delay differential equations are considered, the determination of the stability of an equilibrium is connected with the location of the roots of an exponential polynomial. Applying some results of Pontryagin (1955), Danskin, Bellman and Cooke (1954, 1963), some theorems have been set. They give necessary and sufficient conditions to guarantee the asymptotic stability of the equilibrium points. The models are written as retarded and neutral delay differential equations. So, these results, expressed as inequalities in terms of the involved parameters, allow to find areas of stability as well as its frontiers: the Hopf bifurcation curves. These results together with those coming from the frequency domain methodology (Moiola and Chen, 1996), this last to study limit cycles and its bifurcations, complete the description of the dynamic behavior.
description Fil: Itovich, Griselda Rut. Universidad Nacional de Río Negro. Escuela de Producción, Tecnología y Medio Ambiente. Río Negro, Argentina.
publishDate 2019
dc.date.none.fl_str_mv 2019-06-06
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/acceptedVersion
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
format conferenceObject
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://www.matematica.uns.edu.ar/xvcm/comunicaciones/Aplicada/Itovich_presentacion_Monteiro_Junio_2019.pdf
http://rid.unrn.edu.ar/handle/20.500.12049/6064
url https://www.matematica.uns.edu.ar/xvcm/comunicaciones/Aplicada/Itovich_presentacion_Monteiro_Junio_2019.pdf
http://rid.unrn.edu.ar/handle/20.500.12049/6064
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv XV Congreso Dr. Antonio Monteiro
https://www.matematica.uns.edu.ar/xvcm/Comunic.php
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:RID-UNRN (UNRN)
instname:Universidad Nacional de Río Negro
reponame_str RID-UNRN (UNRN)
collection RID-UNRN (UNRN)
instname_str Universidad Nacional de Río Negro
repository.name.fl_str_mv RID-UNRN (UNRN) - Universidad Nacional de Río Negro
repository.mail.fl_str_mv rid@unrn.edu.ar
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score 12.993085

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