Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays
Year: 2013
Author: Jing-Jun Zhao, Jing-Yu Xiao, Yang Xu
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 2 : pp. 146–162
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.12-m1224
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 2 : pp. 146–162
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Hopf bifurcation delay tumor-immune dynamical system periodic solution.