多频激励下Duffing vanderPol系统的两参数分岔分析

秦朝红; 陈予恕

doi:10.3879/j.issn.1000-0887.2010.08.009

多频激励下Duffing vanderPol系统的两参数分岔分析

doi: 10.3879/j.issn.1000-0887.2010.08.009

秦朝红¹,
陈予恕^1,2

基金项目: 国家自然科学基金(重点)资助项目(10632040)

详细信息

作者简介:
秦朝红(1979- ),女,山东人,博士生(联系人.E-mai:lzhh-qin@163.com).

中图分类号: O322
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- 文章访问数: 1665
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-29
- 刊出日期: 2010-08-15

Singularity Analysis of Duffing-van der Pol System With Two Bifurcation Parameters Under Multi-Frequency Excitations

QIN Zhao-hong¹,
CHEN Yu-shu^1,2

School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001, P. R. China;

摘要

摘要: 研究了含有两个分岔参数的多频激励下Duffing-van der Pol系统的分岔特性．分3种情况进行了讨论：情形1 将λ1看成分岔参数；情形2 将λ2看成分岔参数；情形3)将λ1和λ2都看成分岔参数．根据转迁集的定义，不同的情况下，整个参数空间都被分成了若干个不同的区域，得到了各个参数空间上系统的分岔图，从而为该类系统的参数优化控制奠定了基础．
- Duffing-van der Pol系统 /
- 两个分岔参数 /
- 奇异性分析
Abstract: Bifurcation properties of Duffing-van der Pol System with two parameters under multi-frequency excitations were studied. It was discussed for three cases 1 λ₁ was considered as bifurcation parameter, 2 λ₂ was considered as bifurcation parameter, 3 λ₁ and λ₂ were both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space was divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions were obtained, which could provide a theoretical basis for optmial design of the system.
- Duffing-van der Pol system /
- two bifurcation parameters /
- singularity analysis

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参考文献(18)

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