摘要
研究了一类时变动力系统的高余维分岔及其控制问题 .首先利用新方法对时变分岔方程的两个方向的分岔转迁和跃迁现象进行分析 ,分别通过慢变解的线性化近似和量级平衡估计分岔转迁值 .然后研究这类时变分岔方程的线性反馈控制问题 ,通过分析相应的二维高次自治系统的 Hopf分岔 ,在适当的条件下得到了稳定的动态滞后环 .
A class of high codimensional bifurcations of time-dependent dynamical systems and its control problem are studied.Firstly,delayed bifurcation transitions and jumps in two directions are analyzed by new methods.The bifurcation transition values are estimated through the solutions of the linearilized system and the scaling balance respectively.Then the linear-feedback control problem of the time-dependent bifurcation equation is investigated.By analyzing the Hopf bifurcation of the corresponding two- dimensional autonomous system with higher-order terms,stable dynamical hysteresis cycles are obtained under appropriate conditions.The mechanism of pulses is found to be the delayed bifurcation transitions and jumps when the bifurcation parameter varies with time periodically passing through the steady bifurcation value.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2001年第2期154-162,共9页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金!(1 9872 0 1 0 )
教育部博士点基金!(980 0 0 61 9)
