Stability analysis of the family of tumour angiogenesis models with distributed time delays

被引：15

作者：

Bodnar, Marek ^{[1
]}

Piotrowska, Monika Joanna ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Inst Appl Math & Mech, Banacha 2, PL-02097 Warsaw, Poland

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2016年 / 31卷 / 1-3期

关键词：

Delay differential equations; Distributed delay; Stability analysis; Hopf bifurcation; Angiogenesis; CONTINUUM MATHEMATICAL-MODEL; HOPF-BIFURCATION; DIFFERENTIAL EQUATIONS; ANTIANGIOGENIC THERAPY; IN-VIVO; GROWTH; DYNAMICS; SYSTEMS; CANCER; HES1;

D O I：

10.1016/j.cnsns.2015.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper a family of angiogenesis models that is a generalisation of the Hahnfeldt et al. model is proposed. Considered family of models consists of two differential equations with distributed time delays. The global existence and the uniqueness of the solutions are proved. Moreover, the stability of the unique positive steady state is examined in the case of Erlang and piecewise linear delay distributions. Theorems guaranteeing the existence of stability switches and occurrence of Hopf bifurcations are proved. Theoretical results are illustrated by numerical analysis performed for parameters estimated by Hahnfeldt et al. (1999) [47]. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：124 / 142

页数：19

共 72 条

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