余维4的Duffing-Van der Pol方程全局分岔分析

刘延彬;陈予恕

振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 69-72,1.

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (1) : 69-72,1.
论文

余维4的Duffing-Van der Pol方程全局分岔分析

  • 刘延彬1; 陈予恕1
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Global bifurcations for the generalized codimension-4 Duffing-Van der Pol equation

  • Yanbin Liu and Yushu Chen
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摘要

本文采用级数展开形式的Melnikov函数解决高余维分岔问题。通过研究一类5次项和3次项共存,具有异宿轨的Duffing-Van der Pol方程的余维4全局分岔问题,得到了该系统的分岔方程及全局拓扑结构,说明了该方法的可行性。研究结果表明,该系统有单个极限环、单个异宿轨、异宿轨和极限环共存、两个极限环共存等情况。最后通过数值模拟验正了理论分析结果的正确性。



Abstract

The Taylor series of Melnikov function is used to study the bifurcation of nonlinear systems with high codimension in this paper. The method is approved feasible by analyzing the generalized codimension-4 Duffing-Van der Pol equation. The results shown that there is the phenomena of multiple limit cycles, limit cycle and heteroclinic loop, heteroclinic loop are possible. Finally the numerical solutions are given to show that the analysis results are correct.

关键词

全局分岔 / 余维 / Melnikov函数 / 异宿轨

Key words

global bifurcation / codimension / Melnikov function / heteroclinic loop

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导出引用
刘延彬;陈予恕 . 余维4的Duffing-Van der Pol方程全局分岔分析[J]. 振动与冲击, 2011, 30(1): 69-72,1
Yanbin Liu and Yushu Chen. Global bifurcations for the generalized codimension-4 Duffing-Van der Pol equation [J]. Journal of Vibration and Shock, 2011, 30(1): 69-72,1

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