具时滞物价瑞利方程的Hopf及共振余维2分支  

Hopf and resonant codimension two bifurcation in price rayleigh equation with delays

作　　者：吕堂红[1] 周林华[1] 

机构地区：[1]长春理工大学理学院,吉林长春130022

出　　处：《东北师大学报（自然科学版）》2012年第4期43-49,共7页Journal of Northeast Normal University(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r为参数的具时滞物价瑞利方程的Hopf分支问题,得到了Hopf分支值及分支方向,估计出时滞r可取多少个不同的值使方程有周期解,并利用规范型理论和中心流形定理给出了确定分支方向及分支周期解稳定性的计算公式.证明了模型中可以出现共振余维2分支,给出了参数空间中点位置的描述,指出参数空间中超越特征方程有两对纯虚根±iω1,±iω2,并且ω1∶ω2=m∶n,(m,n∈Z+),最后通过数值模拟验证了理论分析结果.This paper studied Hopf bifurcation of Price Rayleigh equation with delay r as parameter and obtained the branch value and the direction of Hopf bifurcation.The values of delay r was estimated,which can lead to periodic solution.Moreover,used theories of normal form and center manifold to obtain the calculation formula of the direction of the bifurcation and the stability of the periodic solution.It was found that resonant codimension two bifurcation occur in this model.A complete description of the location of points in parameter space where the transcendental characteristic equation possesses two pairs of pure imaginary roots,±iω1,±iω2 with ω1∶ω2=m∶n（m,n∈Z＋,Z＋ is the set of positive integers） is given.Some numerical simulation examples for justifying the theoretical results are also illustrated.

关 键 词：物价瑞利方程 HOPF分支 余维2分支 分支方向 稳定性 周期解 

分 类 号：O175[理学—数学]