具时滞物价瑞利方程的动力学性质  

Dynamics of Price Reyleigh Equation with Time Delay

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：《山西大学学报（自然科学版）》2013年第2期143-148,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(10726062)

摘　　要：以滞量r为分支参数,研究了具时滞的物价瑞利模型的动力学行为,这些行为包括:系统在平衡点附近的稳定性,局部Hopf分支的存在性,发生条件、Hopf分支的方向,分支周期解的稳定性以及分支随参数变化其周期解的周期变化.最后通过数值模拟验证了理论分析结果,并用分支理论解释了物价瑞利模型产生且维持周期振荡的原因.The dynamic behaviors of delay Price Reyleigh Model with the time delay were studied by using delay r as bifurcation parameter. These behaviors include the stability near the equilibrium point,the exist- ence of the local Hopf bifurcation,the condition of occurrence, the direction of the Hopf bifurcation, the stability of the periodic solution, and the cycle of the periodic solution of the bifurcation changing with the parameter change. Moreover, the theory findings were supported by some simulations we carried out, and the reason of the Price Reyleigh Model to generate and maintain the periodic oscillations was explained by the bifurcation theory.

关 键 词：平衡点 稳定性 周期解 HOPF分支 

分 类 号：O175[理学—数学]