具时滞物价瑞利方程的Hopf分支  

Hopf Bifurcation of Price Reyleigh Equation with Delay

作　　者：吕堂红[1] 刘振文[1] 

机构地区：[1]长春理工大学理学院,长春130022

出　　处：《吉林大学学报（理学版）》2009年第3期441-448,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10571073)

摘　　要：研究具时滞物价瑞利方程模型的动力学性质,利用指数多项式的-τD划分讨论平衡点的稳定性和Hopf分支的存在性,利用具有限时滞Liénard方程的Hopf分支公式获得了Hopf分支方向和周期解的稳定性计算公式,并给出了在r-γ参数平面上的Hopf分支图,得到了"时滞反映出价格对供给具有滞后作用"的结论,合理地解释了经济生活中的价格振荡现象.This paper deals with the dynamical properties of the Hopf bifurcation diagram of the price Reyleigh equation model with delay, and the stability of equilibrium point and the existence of Hopf bifurcation by the method of τ-D partitioning approach of exponential polynomial. Furthermore, we gained the computational forumla of the direction of the Hopf bifurcation and the stability of the periodic solutions with the Hopf bifurcation formula of Lirnard equation with finite delay and completely gave the Hopf bifurcation diagram in the parameter plane of r-γ. Finally we found an important conclusion that delay reflects that price has an hysteresis on supply , by which we can explain the shake phenomenon of price in economy life.

关 键 词：物价瑞利方程 时滞 HOPF分支 分支方向 稳定性 分支图 

分 类 号：O175[理学—数学]