Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays

被引：1

作者：

Zhao, Jing-Jun ^{[1
]}

Xiao, Jing-Yu ^{[1
]}

Xu, Yang ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2013年 / 5卷 / 02期

基金：

中国国家自然科学基金; 黑龙江省自然科学基金;

关键词：

Hopf bifurcation; delay; tumor-immune; dynamical system; periodic solution; DIFFERENTIAL-EQUATIONS; EFFICIENCY;

D O I：

10.4208/aamm.12-m1224

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the Hopf bifurcation analysis of tumor-immune system competition model with two delays. First, we discuss the stability of state points with different kinds of delays. Then, a sufficient condition to the existence of the Hopf bifurcation is derived with parameters at different points. Furthermore, under this condition, the stability and direction of bifurcation are determined by applying the normal form method and the center manifold theory. Finally, a kind of Runge-Kutta methods is given out to simulate the periodic solutions numerically At last, some numerical experiments are given to match well with the main conclusion of this paper.

引用

页码：146 / 162

页数：17

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