二阶时滞微分方程的Hopf分歧分析及近似其周期解的一种约化方法(英文)  

A reduction method for the Hopf bifurcation and periodic solutions of a second-order delay differential equation

作　　者：胡万紫[1] 郭谦[1] 

机构地区：[1]上海师范大学数理学院

出　　处：《上海师范大学学报（自然科学版）》2010年第2期115-120,共6页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Supported by the NSF of China(10901106);the NSF of Shanghai(09ZR1423200);the Innovation Program of Shanghai Municipal Education Commission(09YZ150)

摘　　要：主要研究了一类二阶时滞微分方程的周期解.采用Lyapunov-Schmidt约化方法,找到了从Hopf点处平凡解枝上分支出来的周期解的近似表达式.We study the Hopf bifurcation and periodic solutions of a second-order nonlinear delay differential equation. Using the Lyapunov-Sehmidt reduction method, we investigate analytic approximate expressions of the periodic solutions bifurcated from the trivial solution on the Hopf bifurcation point.

关 键 词：时滞微分方程 周期解 投影方法 

分 类 号：O175[理学—数学]