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

Published online by Cambridge University Press:  03 June 2015

Jing-Jun Zhao ,
Jing-Yu Xiao  and
Yang Xu
Jing-Jun Zhao*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China
Jing-Yu Xiao
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China
Yang Xu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China
*
*Corresponding author. Email: hit_zjj@hit.edu.cn
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Abstract

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.

Keywords

34K1837G1037G1537N25Hopf bifurcationdelaytumor-immunedynamical systemperiodic solution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 2 , April 2013 , pp. 146 - 162
Copyright
Copyright © Global-Science Press 2013

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