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多频激励软弹簧型Duffing系统中的混沌

楼京俊 何其伟 朱石坚

楼京俊, 何其伟, 朱石坚. 多频激励软弹簧型Duffing系统中的混沌[J]. 应用数学和力学, 2004, 25(12): 1299-1304.
引用本文: 楼京俊, 何其伟, 朱石坚. 多频激励软弹簧型Duffing系统中的混沌[J]. 应用数学和力学, 2004, 25(12): 1299-1304.
LOU Jing-jun, HE Qi-wei, ZHU Shi-jian. Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1299-1304.
Citation: LOU Jing-jun, HE Qi-wei, ZHU Shi-jian. Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1299-1304.

多频激励软弹簧型Duffing系统中的混沌

详细信息
    作者简介:

    楼京俊(1976- ),男,浙江义乌人,博士研究生(E-mail:jingjun-lou@hotmail.com);朱石坚,教授,硕士(联系人.Tel:+86-27-83443991;Fax:+86-27-83443990;E-mail:zhushj@public.wh.hb.cn).

  • 中图分类号: O322

Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces

  • 摘要: 研究了多频激励下的软弹簧型Duffing系统的混沌动力学,发现混沌产生的根本原因是系统相空间中横截异宿环面的存在.建立了双频激励情况下二维环面上的Poincaré映射、稳定流形和不稳定流形,应用Melnikov方法给出了稳定流形和不稳定流形横截相交的条件,并将此方法推广到激励包含有限多个频率的情形.推广了Melnikov方法在高维系统中的应用,给出了Smale马蹄意义下混沌存在的判据.同时证明,激励频率数目的增加扩大了参数空间上的混沌区域.
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出版历程
  • 收稿日期:  2002-12-30
  • 修回日期:  2004-05-31
  • 刊出日期:  2004-12-15

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