具时滞物价瑞利方程的Neimark-Sacker分支

Neimark-Sacker Hopf Bifurcation for Price Reyleigh Equation with Delays

研究了以滞量为参数的具时滞物价瑞利方程的数值Hopf分支问题。首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其数值逼近间的关系,最后证明了当连续系统产生Hopf分支时,其Euler离散将产生Neimark-Sacker分支,进而得到结论:Euler离散使得方程的Hopf分支性质得以保持。

The numerical Hopf bifurcation for Price Reyleigh equation with delays is investigated,through using a delay as a parameter. At first, the delay deference equation obtained by using Euler method is written as a map. And then according to the theories of bifurcation for discrete dynamical systems,under the condition that Price Reyleigh equation has bifurcations,the conditions of Hopf bifurcation difference equations as well as the relations between successive sys-tem and numerical approximation are discussed. Finally,it is proved that when successive system produces Hopf bifurca-tion,the Euler discretion produces a Neimark-Sacker bifurcation. Further,it draws the conclusion that the Euler discre-tion preserves the features of the Hopf bifurcation.