具双时滞的生理模型的分支分析

Bifurcation Analysis for a Physiological Model with Two Delays

研究了一类简化的具有双时滞的生理模型.得到了该模型在正平衡点稳定的充分条件,通过选择两时滞的和τ为分支参数,得到了当时滞τ通过一系列的临界值时,Hopf分支产生,然后应用中心流形和正规型理论,得到了关于确定Hopf分支特性(例如Hopf分支方向和分支周期解的稳定性以及Hopf分支周期解的周期等)的计算公式.最后进行数值模拟验证了所得结果的正确性.

In this paper,a class of simplified physiological model with two delays is investigated.We get the sufficient condition of stability at the positive equilibrium.By choosing the sum τ of two delays as a bifurcation parameter,we show that Hopf bifurcation can occur when sum τ passes a sequence of critical values.Meanwhile,based on the center manifold theory and the normal form approach,we derive the formula determing the properties of Hopf bifurcating periodic orbit,such as the direction of Hopf bifurcation,the stability of Hopf bifurcating periodic solution and the periodic of Hopf bifurcating periodic solution.Finally,numerical simulations are carried out to illustrate the analytical results.