| 一类时变动力系统的高余维分岔及其控制 |
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| 引用本文： | 化存才,陆启韶.一类时变动力系统的高余维分岔及其控制[J].高校应用数学学报(A辑),2001,16(2):154-162. |
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| 作者姓名： | 化存才 陆启韶 |
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| 作者单位： | 北京航空航天大学 理学院, |
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| 基金项目： | 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) |
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| 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蚀控制问题，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，研究揭示出脉冲振动产生的机理是分岔参数随时间周期变化经过定常分岔值时所发生的分岔转迁的滞后和跃迁现象。
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| 关 键 词： | 时变动力系统 分岔 反馈控制 脉冲振动 Hopf分岔 动态滞后环 分岔转迁值 |
| 文章编号： | 1000-4424(2001)02-0154-09 |
| 修稿时间： | 2000年4月13日 |
A CLASS OF HIGH CODIMENSIONAL BIFURCATION OFTIME-DEPENDENT DYNAMICAL SYSTEMAND ITS CONTROL |
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| Hua Cuncai,Lu Qishao.A CLASS OF HIGH CODIMENSIONAL BIFURCATION OFTIME-DEPENDENT DYNAMICAL SYSTEMAND ITS CONTROL[J].Applied Mathematics A Journal of Chinese Universities,2001,16(2):154-162. |
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| Authors: | Hua Cuncai Lu Qishao |
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| Abstract: | 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. |
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| Keywords: | Time-dependent Dynamical System Bifurcation Feedback Control Pulse |
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