实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅱ)

基金项目: 国家自然科学基金资助项目(19602016)

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

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

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,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: Foraco-dimension two bifurcation system on a three-dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system-a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker-Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.
- real noise /
- parametric excitation /
- co-dimension two bifurcation /
- detailed balance /
- FPK equation /
- singular boundary /
- maximal Lyapunov exponent /
- solvability condition

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