Stability of Hahnfeldt Angiogenesis Models with Time Lags

Autores
Amster, Pablo Gustavo; Berezansky, L.; Idels, L.
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous delay differential systems with non-Lipschitz nonlinearities. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.
Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Berezansky, L.. Ben Gurion University Of The Negev; Israel
Fil: Idels, L.. Vancouver Island University; Canadá
Materia
Angiogenesis
Nonlinear nonautonomous delay differential equations
Global and local stability
Equilibria
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14869
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14869
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stability of Hahnfeldt Angiogenesis Models with Time LagsAmster, Pablo GustavoBerezansky, L.Idels, L.AngiogenesisNonlinear nonautonomous delay differential equationsGlobal and local stabilityEquilibriahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous delay differential systems with non-Lipschitz nonlinearities. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Berezansky, L.. Ben Gurion University Of The Negev; IsraelFil: Idels, L.. Vancouver Island University; CanadáElsevier2011-12-16info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14869Amster, Pablo Gustavo; Berezansky, L.; Idels, L.; Stability of Hahnfeldt Angiogenesis Models with Time Lags; Elsevier; Mathematical And Computer Modelling; 55; 9-10; 16-12-2011; 2052-20600895-7177enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S089571771100776Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2011.12.013info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:11Zoai:ri.conicet.gov.ar:11336/14869instacron: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 09:39:11.81CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stability of Hahnfeldt Angiogenesis Models with Time Lags
title Stability of Hahnfeldt Angiogenesis Models with Time Lags
spellingShingle Stability of Hahnfeldt Angiogenesis Models with Time Lags
Amster, Pablo Gustavo
Angiogenesis
Nonlinear nonautonomous delay differential equations
Global and local stability
Equilibria
title_short Stability of Hahnfeldt Angiogenesis Models with Time Lags
title_full Stability of Hahnfeldt Angiogenesis Models with Time Lags
title_fullStr Stability of Hahnfeldt Angiogenesis Models with Time Lags
title_full_unstemmed Stability of Hahnfeldt Angiogenesis Models with Time Lags
title_sort Stability of Hahnfeldt Angiogenesis Models with Time Lags
dc.creator.none.fl_str_mv Amster, Pablo Gustavo
Berezansky, L.
Idels, L.
author Amster, Pablo Gustavo
author_facet Amster, Pablo Gustavo
Berezansky, L.
Idels, L.
author_role author
author2 Berezansky, L.
Idels, L.
author2_role author
author
dc.subject.none.fl_str_mv Angiogenesis
Nonlinear nonautonomous delay differential equations
Global and local stability
Equilibria
topic Angiogenesis
Nonlinear nonautonomous delay differential equations
Global and local stability
Equilibria
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous delay differential systems with non-Lipschitz nonlinearities. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.
Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Berezansky, L.. Ben Gurion University Of The Negev; Israel
Fil: Idels, L.. Vancouver Island University; Canadá
description To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special class of nonlinear nonautonomous delay differential systems with non-Lipschitz nonlinearities. Explicit conditions for the existence of positive global solutions and the equilibria solutions were obtained. Based on a notion of an M-matrix, new results are presented for the global stability of the system and were used to prove local stability of one model. For a local stability of a second model, the recent result for a Lienard-type second-order differential equation with delays was used. It was shown that models with delays produce a complex and nontrivial dynamics. Some open problems are presented for further studies.
publishDate 2011
dc.date.none.fl_str_mv 2011-12-16
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/11336/14869
Amster, Pablo Gustavo; Berezansky, L.; Idels, L.; Stability of Hahnfeldt Angiogenesis Models with Time Lags; Elsevier; Mathematical And Computer Modelling; 55; 9-10; 16-12-2011; 2052-2060
0895-7177
url http://hdl.handle.net/11336/14869
identifier_str_mv Amster, Pablo Gustavo; Berezansky, L.; Idels, L.; Stability of Hahnfeldt Angiogenesis Models with Time Lags; Elsevier; Mathematical And Computer Modelling; 55; 9-10; 16-12-2011; 2052-2060
0895-7177
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S089571771100776X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2011.12.013
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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