一类具时滞的生理模型的Hopf分支

本文研究了一类简化的具时滞的生理模型的稳定性和Ｈｏｐｆ分支．首先，以滞量为参数，应用Ｃｏｏｋｅ的方法，把Ｒ＾＋分为两个区间，使当滞量属于相应区间时，所考虑的模型的平凡解是稳定或不稳定的，同时得到了Ｈｏｐｆ分支值．然后，应用中心流形和规范型理论，得到了关于确定Ｈｏｐｆ分支方向和分支周期解的稳定性的计算公式．最后，应用Ｍａｔｈｅｍａｔｉｃａ软件进行了数值模拟。

HOPF BIFURCATION FOR A PHYSIOLOGICAL MODEL WITH DELAY

In this paper, we investigate the stability and Hopf bifurcation for a simplified physiological model with delay. Firstly, regarding the delay as a parameter and employing the method of Cooke, we divide R into two intervals such that the trivial solution of this model is stable or unstable when the delay belongs to each interval respectively. Meanwhile, the model undergoes Hopf bifurcation at some values of the delay. Then, based on center manifold and normal form, we get the formulas for determining the direct of Hopf bifurcation and the stability of bifurcating periodic solutions. Finaly, we use the Mathematica program to carry out some numerical simulations.