以滞量为参数的向日葵方程Hopf分支的数值逼近

Hopf bifurcation in numerical approximation for sunflower equation using delay as parameter

研究了欧拉方法对以滞量为参数的具有Hopf分支的向日葵方程的数值逼近问题。首先,将利用欧拉方法得到的时滞差分方程表示为映射,然后以时滞r为分支参数,利用离散动力系统的分支理论,在向日葵方程具有Hopf分支的条件下,给出了差分方程Hopf分支存在的条件。给出了连续模型与其数值逼近间的关系,证明了当该方程在r=ro产生Hopf分支时,其数值逼近也在相应的参数r_h处具有Hopf分支,并且r_h=r_0+O(h)。

The numerical approximation of sunflower equation is considered using delay as parameter. First, the delay deference equation obtained by using Euler method is written as a map. According to 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. That when the sunflower equation has Hopf bifurcations at r=r0,the numerical approximation also has Hopf bifurcations at rh=r0+O(h) is proved.