以滞量为参数的二阶时滞微分方程的Hopf分支公式  

The Hopf bifurcation of the second order de lay differential equation parametered by the time lag

作　　者：唐风军[1] 周佐益 张伟 

机构地区：[1]复旦大学数学研究所,上海200433

出　　处：《复旦学报（自然科学版）》1997年第2期138-144,共7页Journal of Fudan University：Natural Science

摘　　要：本文考虑以滞量为参数的具有有限时滞的一般形式的二阶微分方程的Hopf分支问题，得到了该方程的Hopf分支值及分支方向，对有限时滞时r使方程有周期解所能取得的不同数值的个数作了估计．然后运用上述结果及Hassard“规范形”方法，对于具体的方程如Lienard方程进行讨论，给出其Hopf分支公式．利用该公式，能判断分支出的周期解的稳定性并且得到该周期解的近似估值．In this paper, the Hop f bifurcation question of the general second order delay differential equation with finite time lag. From the equation's linear part's characteristic equation is considered, got the bifurcation value and the direction of bifurcation. Also we estimated how many different values the delay r can take which made the equation have period solution. Then they used the aforementioned results and Hassard algorithm to analysis lienard equation, giving the Hopf bifurcation formula, from which they can judge the stability of the period solution of lienard equation and it's estimated form.

关 键 词：HOPF分支 周期解 稳定性 时滞微分方程 

分 类 号：O175.1[理学—数学]