一个生理模型的Hopf分支的数值逼近

HOPF BIFURCATION IN NUMERICAL APPROXIMATION FOR A PHYSIOLOGICAL MODEL WITH DELAY

本文研究了欧拉方法对一类简化的生理模型的数值逼近问题 .首先 ,将时滞差分方程表示为映射 .然后以时滞 τ为分支参数 ,利用离散动力系统的分支理论 ,在该模型具有 Hopf分支的条件下 ,给出了差分方程 Hopf分支存在的条件 .证明了当该模型在 τ=τ0 产生 Hopf分支时 ,其数值解也在相应的参数值 τh 处具有 Hopf分支 ,并且 τh=τ0 + O( h) .

In this paper, the numerical approximation of a physological model with delay is considered. First, the delay deference equation is written as a map, employing the theories of bifurcation for discrete dynamical systems, the conditions to guarantee the existence of Hopf bifurcations for numerical approximation are given. The relations of Hopf bifurcation between the continuous and the discrete are discussed. We prove that when the continuous model has Hopf bifurcations at τ=τ 0, the numerical approximation also has Hopf bifurcations at τ h=τ 0+O(h).