实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅰ)

刘先斌; 陈大鹏; 陈虬

实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅰ)

1.
西南交通大学应用力学与工程系, 成都 610031;
2.
西南交通大学工程科学研究院, 成都 610031

基金项目: 国家自然科学基金资助项目(19602016)

详细信息

作者简介:
刘先斌(1965~ ),男,博士,副教授,已发表论文30余篇.

中图分类号: O211.63
计量
- 文章访问数: 2781
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- 被引次数: 0
出版历程
- 收稿日期: 1998-05-29
- 修回日期: 1999-04-15
- 刊出日期: 1999-09-15

On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅰ)

1.
Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
2.
Institute of Engineering Science, Southwest Jiaotong University, Chengdu 610031, P. R. China

摘要

摘要: 对于三维中心流形上实噪声参激的一类余维2分叉系统,为使模型更具有一般性,取系统的参激实噪声为一线性滤波系统的输出-零均值的平稳高斯扩散过程,并满足细致平衡条件.并在此基础上首次使用Arnold的渐近方法以及Fokker-Planck算子的特征谱展式,求解不变测度以及最大的Lyapunov指数的e_max的渐近展式.
- 实噪声 /
- 参数激励 /
- 余维2分叉 /
- 细致平衡 /
- FPK方程 /
- 奇异边界 /
- 最大Lyapunov指数 /
- 可解性条件
Abstract: For a real noise parametrically excited co-dimension two bifurcation system on a three-dimensional central manifold,a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system,namely,a zero-mean stationary Gaussian diffusion process that satisfies the detailed balance condition.On such basis,asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker-Planck operator.
- real noise /
- parametric excitation /
- co-dimension two bifurcation /
- detailed balance condition /
- FPK equation /
- singular boundary /
- maximal Lyapunov exponent /
- solvability condition

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参考文献(24)

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