双时滞物价瑞利方程的Neimark-Sacker分支  

Neimark-Sacker Hopf Bifurcation for Price Reyleigh Equation with Two Delays

作　　者：吕堂红[1] 

机构地区：[1]长春理工大学理学院,吉林长春130022

出　　处：《中北大学学报（自然科学版）》2012年第5期490-494,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10726062)

摘　　要：研究了以滞量为参数的双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,在物价瑞利方程具有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Euler离散使得方程的Hopf分支性质得以保持的结论.The numerical Hopf bifurcation for Price Reyleigh equation with two delays was investigated,through using a delay as a parameter.First,the delay difference equation obtained by using Euler method was written as a map.And then according to the theories of bifurcation for discrete dynamical systems,on condition that Price Reyleigh equation had bifurcations,the conditions of Hopf bifurcation difference equations as well as the relations between successive system and numerical approximation were discussed.Finally,it is proved that when successive system produces Hopf bifurcation,the Euler discretion produces a Neimark-Sacker bifurcation.Further,it draws the conclusion that the Euler discretion preserves the features of the Hopf bifurcation.

关 键 词：物价瑞利方程 双时滞 EULER方法 HOPF分支 Neimark-Sacker分支 数值逼近 

分 类 号：O175[理学—数学]