Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks

Autores
Gentile, Franco Sebastián; Moiola, Jorge Luis
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study how to capture smooth oscillations arising from delay-differential equations with distributed delays. For this purpose, we introduce a modified version of the frequency-domain method based on the Graphical Hopf Bifurcation Theorem. Our approach takes advantage of a simple interpretation of the distributed delay effect by means of some Laplace-transformed properties. Our theoretical results are illustrated through an example of two coupled neurons with distributed delay in their communication channel. For this system, we compute several bifurcation diagrams and approximations of the amplitudes of periodic solutions. In addition, we establish analytical conditions for the appearance of a double zero bifurcation and investigate the unfolding by the proposed methodology.
Fil: Gentile, Franco Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
Materia
Delay-Differential Equation
Distributed Delay
Hopf Bifurcation
Frequency-Domain Method
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:11336/11840
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/11840
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural NetworksGentile, Franco SebastiánMoiola, Jorge LuisDelay-Differential EquationDistributed DelayHopf BifurcationFrequency-Domain Methodhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2In this paper, we study how to capture smooth oscillations arising from delay-differential equations with distributed delays. For this purpose, we introduce a modified version of the frequency-domain method based on the Graphical Hopf Bifurcation Theorem. Our approach takes advantage of a simple interpretation of the distributed delay effect by means of some Laplace-transformed properties. Our theoretical results are illustrated through an example of two coupled neurons with distributed delay in their communication channel. For this system, we compute several bifurcation diagrams and approximations of the amplitudes of periodic solutions. In addition, we establish analytical conditions for the appearance of a double zero bifurcation and investigate the unfolding by the proposed methodology.Fil: Gentile, Franco Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; ArgentinaWorld Scientific2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11840Gentile, Franco Sebastián; Moiola, Jorge Luis; Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks; World Scientific; International Journal Of Bifurcation And Chaos; 25; 11; 11-2015; 1-150218-12741793-6551enginfo:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0218127415501564info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127415501564info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:53Zoai:ri.conicet.gov.ar:11336/11840instacron: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 09:38:54.208CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
title Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
spellingShingle Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
Gentile, Franco Sebastián
Delay-Differential Equation
Distributed Delay
Hopf Bifurcation
Frequency-Domain Method
title_short Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
title_full Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
title_fullStr Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
title_full_unstemmed Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
title_sort Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks
dc.creator.none.fl_str_mv Gentile, Franco Sebastián
Moiola, Jorge Luis
author Gentile, Franco Sebastián
author_facet Gentile, Franco Sebastián
Moiola, Jorge Luis
author_role author
author2 Moiola, Jorge Luis
author2_role author
dc.subject.none.fl_str_mv Delay-Differential Equation
Distributed Delay
Hopf Bifurcation
Frequency-Domain Method
topic Delay-Differential Equation
Distributed Delay
Hopf Bifurcation
Frequency-Domain Method
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, we study how to capture smooth oscillations arising from delay-differential equations with distributed delays. For this purpose, we introduce a modified version of the frequency-domain method based on the Graphical Hopf Bifurcation Theorem. Our approach takes advantage of a simple interpretation of the distributed delay effect by means of some Laplace-transformed properties. Our theoretical results are illustrated through an example of two coupled neurons with distributed delay in their communication channel. For this system, we compute several bifurcation diagrams and approximations of the amplitudes of periodic solutions. In addition, we establish analytical conditions for the appearance of a double zero bifurcation and investigate the unfolding by the proposed methodology.
Fil: Gentile, Franco Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; Argentina
description In this paper, we study how to capture smooth oscillations arising from delay-differential equations with distributed delays. For this purpose, we introduce a modified version of the frequency-domain method based on the Graphical Hopf Bifurcation Theorem. Our approach takes advantage of a simple interpretation of the distributed delay effect by means of some Laplace-transformed properties. Our theoretical results are illustrated through an example of two coupled neurons with distributed delay in their communication channel. For this system, we compute several bifurcation diagrams and approximations of the amplitudes of periodic solutions. In addition, we establish analytical conditions for the appearance of a double zero bifurcation and investigate the unfolding by the proposed methodology.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
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/11336/11840
Gentile, Franco Sebastián; Moiola, Jorge Luis; Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks; World Scientific; International Journal Of Bifurcation And Chaos; 25; 11; 11-2015; 1-15
0218-1274
1793-6551
url http://hdl.handle.net/11336/11840
identifier_str_mv Gentile, Franco Sebastián; Moiola, Jorge Luis; Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks; World Scientific; International Journal Of Bifurcation And Chaos; 25; 11; 11-2015; 1-15
0218-1274
1793-6551
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0218127415501564
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127415501564
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 World Scientific
publisher.none.fl_str_mv World Scientific
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_ 1844613229930610688
score 13.070432

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