The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis

被引：5

作者：

Zhou, Haihua ^{[1
]}

Song, Huijuan ^{[1
]}

Wang, Zejia ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2022年 / 160卷

基金：

中国国家自然科学基金;

关键词：

Tumor model; Free boundary problem; Angiogenesis; Time delay; Hopf bifurcation; GROWTH MODEL; DYNAMICS;

D O I：

10.1016/j.chaos.2022.112219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a free boundary problem modeling tumor growth with angiogenesis and time delay in regulatory apoptosis. Two factors are introduced to cause tumor cell death: one is the apoptosis because of ex-ceeding the natural lifespan, the other is the regulatory apoptosis with time delay. The existence, uniqueness and asymptotic behavior of solutions are investigated. The results show that the stabilities of stationary solutions are dramatically affected by such time delay in certain cases, and Hopf bifurcation occurs at some threshold values of time delay. Some numerical simulation results are incorporated supporting the analytical results. The impact of angiogenesis on the Hopf bifurcation is also numerically discussed. 2020 Mathematics subject classification: 35R35, 35B35, 35K57.(c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：7

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