摘要
提出新的方法从本质上研究时变参数系统的非完全分岔问题· 通过建立时变参数系统的解的线性近似定理去分析时变分岔方程运动的分岔转迁滞后和跃迁现象· 利用 V函数预测分岔转迁值 ,将新方法应用于Duffing方程 ,获得一些新的分岔结果和关于解对初值和参数的敏感性结论·
A new method a proposed for essentially studying the imperfect bifurcation problem of nonlinear systems with a slowly varying parameter. By establishing some theorems on the solution approximated by that of the linearized system, the delayed bifurcation transition and jump phenomena of the time_dependent equation were analyzed. V_function was used to predict the bifurcation transition value. Applying the new method to analyze the Duffing's equation, some new results about bifurcation as well as that about the sensitivity of the solutions with respect to initial values and parameters are obtained.
出处
《应用数学和力学》
CSCD
北大核心
2000年第9期925-932,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目!(19872 0 10 )
航空科学基金资助项目!(98B5112 5)
育部博士点基金资助项目 !(980 0 0 6 19)
关键词
时变参数系统
分岔转迁
非完全分岔
DUFFING方程
time_dependent parametric system
bifurcation transition
imperfect bifurcation
Duffing's equation
