Stability of Hahnfeldt angiogenesis models with time lags

Mathematical models of angiogenesis, pioneered by Hahnfeldt, are under study. 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 no...

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Detalles Bibliográficos
Autor principal: Amster, Pablo Gustavo
Publicado: 2012
Materias:
Angiogenesis
Equilibria
Global and local stability
Lienard equations
M-matrix
Non-Lipschitz nonlinearities
Nonlinear nonautonomous delay differential equations
Local stability
Nonautonomous
Differential equations
Dynamics
Mathematical models
Stability
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08957177_v55_n9-10_p2052_Amster
http://hdl.handle.net/20.500.12110/paper_08957177_v55_n9-10_p2052_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_08957177_v55_n9-10_p2052_Amster
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spelling paper:paper_08957177_v55_n9-10_p2052_Amster2025-07-30T18:24:25Z Stability of Hahnfeldt angiogenesis models with time lags Amster, Pablo Gustavo Angiogenesis Equilibria Global and local stability Lienard equations M-matrix Non-Lipschitz nonlinearities Nonlinear nonautonomous delay differential equations Angiogenesis Equilibria Lienard equations Local stability M-matrix Non-Lipschitz nonlinearities Nonautonomous Differential equations Dynamics Mathematical models Stability Mathematical models of angiogenesis, pioneered by Hahnfeldt, are under study. 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. © 2011 Elsevier Ltd. Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08957177_v55_n9-10_p2052_Amster http://hdl.handle.net/20.500.12110/paper_08957177_v55_n9-10_p2052_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Angiogenesis
Equilibria
Global and local stability
Lienard equations
M-matrix
Non-Lipschitz nonlinearities
Nonlinear nonautonomous delay differential equations
Angiogenesis
Equilibria
Lienard equations
Local stability
M-matrix
Non-Lipschitz nonlinearities
Nonautonomous
Differential equations
Dynamics
Mathematical models
Stability
spellingShingle Angiogenesis
Equilibria
Global and local stability
Lienard equations
M-matrix
Non-Lipschitz nonlinearities
Nonlinear nonautonomous delay differential equations
Angiogenesis
Equilibria
Lienard equations
Local stability
M-matrix
Non-Lipschitz nonlinearities
Nonautonomous
Differential equations
Dynamics
Mathematical models
Stability
Amster, Pablo Gustavo
Stability of Hahnfeldt angiogenesis models with time lags
topic_facet Angiogenesis
Equilibria
Global and local stability
Lienard equations
M-matrix
Non-Lipschitz nonlinearities
Nonlinear nonautonomous delay differential equations
Angiogenesis
Equilibria
Lienard equations
Local stability
M-matrix
Non-Lipschitz nonlinearities
Nonautonomous
Differential equations
Dynamics
Mathematical models
Stability
description Mathematical models of angiogenesis, pioneered by Hahnfeldt, are under study. 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. © 2011 Elsevier Ltd.
author Amster, Pablo Gustavo
author_facet Amster, Pablo Gustavo
author_sort Amster, Pablo Gustavo
title Stability of Hahnfeldt angiogenesis models with time lags
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
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08957177_v55_n9-10_p2052_Amster
http://hdl.handle.net/20.500.12110/paper_08957177_v55_n9-10_p2052_Amster
work_keys_str_mv AT amsterpablogustavo stabilityofhahnfeldtangiogenesismodelswithtimelags
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