Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays (Advances in Applied Mathematics and Mechanics, 2013)
This paper is concerned with the Hopf bifurcation analysis oftumor-immune system competition model with two delays. First, wediscuss the stability of state points with different kinds ofdelays. Then, a sufficient condition to the existence of the Hopfbifurcation is derived with parameters at different points.Furthermore, under this condition, the stability and direction ofbifurcation are determined by applying the normal form method andthe center manifold theory. Finally, a kind of Runge-Kutta methodsis given out to simulate the periodic solutions numerically. Atlast, some numerical experiments are given to match well with themain conclusion of this paper.