时变参数系统的非完全分岔及其在Duffing方程中的应用

化存才; 陆启韶

时变参数系统的非完全分岔及其在Duffing方程中的应用

北京航空航天大学理学院, 北京100083

基金项目: 国家自然科学基金资助项目(19872010);航空科学基金资助项目(98B51125);育部博士点基金资助项目(98000619)

详细信息

作者简介:
化存才(1964- ),云南玉溪人,博士.

中图分类号: O175;O31513;O322
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- 被引次数: 0
出版历程
- 收稿日期: 1999-05-26
- 修回日期: 2000-05-25
- 刊出日期: 2000-09-15

Imperfect Bifurcation of Systems With Slowly Varying Parameters and Application to Duffing’s Equation

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P R China

摘要

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。
- 时变参数系统 /
- 分岔转迁 /
- 非完全分岔 /
- Duffing方程
Abstract: 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.
- time-dependent parametric system /
- bifurcation transition /
- imperfect bifurcation /
- Duffing’s equation

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参考文献(12)

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