TY - JOUR
T1 - Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays
AU - Zhao , Jing-Jun
AU - Xiao , Jing-Yu
AU - Xu , Yang
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 146
EP - 162
PY - 2013
DA - 2013/05
SN - 5
DO - http://doi.org/10.4208/aamm.12-m1224
UR - https://global-sci.org/intro/article_detail/aamm/62.html
KW - Hopf bifurcation, delay, tumor-immune, dynamical system, periodic solution.
AB - <p style="text-align: justify;">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.</p>