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有界噪声参激一类三维系统的矩Liapunov指数

方次军 杨建华 刘先斌

方次军, 杨建华, 刘先斌. 有界噪声参激一类三维系统的矩Liapunov指数[J]. 应用数学和力学, 2012, 33(5): 526-538. doi: 10.3879/j.issn.1000-0887.2012.05.002
引用本文: 方次军, 杨建华, 刘先斌. 有界噪声参激一类三维系统的矩Liapunov指数[J]. 应用数学和力学, 2012, 33(5): 526-538. doi: 10.3879/j.issn.1000-0887.2012.05.002
FANG Ci-jun, YANG Jian-hua, LIU Xian-bin. Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation[J]. Applied Mathematics and Mechanics, 2012, 33(5): 526-538. doi: 10.3879/j.issn.1000-0887.2012.05.002
Citation: FANG Ci-jun, YANG Jian-hua, LIU Xian-bin. Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation[J]. Applied Mathematics and Mechanics, 2012, 33(5): 526-538. doi: 10.3879/j.issn.1000-0887.2012.05.002

有界噪声参激一类三维系统的矩Liapunov指数

doi: 10.3879/j.issn.1000-0887.2012.05.002
基金项目: 国家自然科学基金资助项目(10672074;11072107);高等学校博士学科点专项科研基金资助项目(20093218110003)
详细信息
    通讯作者:

    方次军(1975—),男,湖北孝感人,讲师,博士生(E-mail :cjfang68@163.com);刘先斌(1964—),男,教授,博士生导师(联系人.Tel: +86-25-84892106; E-mail: xbliu@nuaa.edu.cn).

  • 中图分类号: O324

Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation

  • 摘要: 对于一类三维中心流形上受有界噪声参激的余维2分岔系统,计算了它的矩Liapunov指数.根据随机动力系统理论,首先建立了系统矩Liapunov指数求解的特征值问题,然后由奇异摄动法,得到了弱噪声展开的矩Liapunov指数的二阶渐近解析表达式和数值结果.接着进一步研究了有界噪声和系统参数对矩Liapunov指数和稳定指标的影响.结果表明:系统的随机稳定性有被有界噪声加强的可能性.
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出版历程
  • 收稿日期:  2011-09-06
  • 修回日期:  2012-02-16
  • 刊出日期:  2012-05-15

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