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Abstract:

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.

Registro:

Documento: Artículo
Título:Stability of Hahnfeldt angiogenesis models with time lags
Autor:Amster, P.; Berezansky, L.; Idels, L.
Filiación:FCEyN, Departamento de Matematica, Universidad de Buenos Aires, Argentina
Department of Mathematics, Ben-Gurion University of Negev Beer-Sheva, 84105, Israel
Department of Mathematics, Vancouver Island University, 900 Fifth St., Nanaimo, BC V9S5S5, Canada
Palabras clave: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
Año:2012
Volumen:55
Número:9-10
Página de inicio:2052
Página de fin:2060
DOI: http://dx.doi.org/10.1016/j.mcm.2011.12.013
Título revista:Mathematical and Computer Modelling
Título revista abreviado:Math. Comput. Model.
ISSN:08957177
CODEN:MCMOE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08957177_v55_n9-10_p2052_Amster

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Citas:

---------- APA ----------
Amster, P., Berezansky, L. & Idels, L. (2012) . Stability of Hahnfeldt angiogenesis models with time lags. Mathematical and Computer Modelling, 55(9-10), 2052-2060.
http://dx.doi.org/10.1016/j.mcm.2011.12.013
---------- CHICAGO ----------
Amster, P., Berezansky, L., Idels, L. "Stability of Hahnfeldt angiogenesis models with time lags" . Mathematical and Computer Modelling 55, no. 9-10 (2012) : 2052-2060.
http://dx.doi.org/10.1016/j.mcm.2011.12.013
---------- MLA ----------
Amster, P., Berezansky, L., Idels, L. "Stability of Hahnfeldt angiogenesis models with time lags" . Mathematical and Computer Modelling, vol. 55, no. 9-10, 2012, pp. 2052-2060.
http://dx.doi.org/10.1016/j.mcm.2011.12.013
---------- VANCOUVER ----------
Amster, P., Berezansky, L., Idels, L. Stability of Hahnfeldt angiogenesis models with time lags. Math. Comput. Model. 2012;55(9-10):2052-2060.
http://dx.doi.org/10.1016/j.mcm.2011.12.013