Stability analysis of the singular points and Hopf bifurcations of a tumor growth control model

被引：1

作者：

Drexler, Daniel Andras ^{[1
]}

Nagy, Ilona ^{[2
,6
]}

Romanovski, Valery G. ^{[3
,4
,5
]}

机构：

[1] Obuda Univ, Physiol Controls Res Ctr, Budapest, Hungary

[2] Budapest Univ Technol & Econ, Inst Math, Dept Anal & Operat Res, Budapest, Hungary

[3] Univ Maribor, Fac Elect Engn & Comp Sci, Maribor, Slovenia

[4] Univ Maribor, Ctr Appl Math & Theoret Phys, Maribor, Slovenia

[5] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

[6] Budapest Univ Technol & Econ, Inst Math, Dept Anal & Operat Res, Muegyetem Rkp 3, H-1111 Budapest, Hungary

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 07期

基金：

欧盟地平线“2020”;

关键词：

bifurcation; cancer therapy; limit cycle; singular point; tumor control; tumor therapy;

D O I：

10.1002/mma.9885

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We carry out qualitative analysis of a fourth-order tumor growth control model using ordinary differential equations. We show that the system has one positive equilibrium point, and its stability is independent of the feedback gain. Using a Lyapunov function method, we prove that there exist realistic parameter values for which the systems admit limit cycle oscillations due to a supercritical Hopf bifurcation. The time evolution of the state variables is also represented.

引用

页码：5677 / 5691

页数：15

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