| 余维4的Duffing-Van der Pol方程全局分岔分析 |
| |
| 引用本文： | 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. DOI: |
| |
| 作者姓名： | 刘延彬 陈予恕 |
| |
| 作者单位： | 1.哈尔滨工业大学 航天学院 哈尔滨 150001 |
| |
| 基金项目： | 国家自然科学基金重点资助项目 |
| |
| 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。
|
| 关 键 词： | 全局分岔 余维 Melnikov函数 异宿轨 |
| 收稿时间： | 2009-07-24 |
| 修稿时间： | 2009-11-03 |
Global bifurcations for a generalized codimension-4 Duffing-Van der Pol equation |
| |
| LIU Yan-bin,CHEN Yu-shu. Global bifurcations for a generalized codimension-4 Duffing-Van der Pol equation[J]. Journal of Vibration and Shock, 2011, 30(1): 69. DOI: |
| |
| Authors: | LIU Yan-bin CHEN Yu-shu |
| |
| Affiliation: | The School of Astronautics, Harbin Institute of Technology, China PO Box 137, Harbin 150001, China |
| |
| Abstract: | A Taylor series of Melnikov function was used to study bifurcation of nonlinear systems with high codimension here.The method was approved to be feasible by analyzing a generalized codimension-4 Duffing-Van der Pol equation.The results showed that there are phenomena of multiple limit cycles,single limit cycle and heteroclinic loop. Finally,numerical simulations verified the correctness of the theorectical analysis results. |
| |
| Keywords: | global bifurcation codimension Melnikov function heteroclinic loop |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《振动与冲击》浏览原始摘要信息 |
|
点击此处可从《振动与冲击》下载免费的PDF全文 |
