| 一类随机分叉系统概率1分叉研究 |
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| 引用本文： | 刘先斌. 一类随机分叉系统概率1分叉研究[J]. 固体力学学报, 2001, 22(3): 297-302. doi: 10.3969/j.issn.0254-7805.2001.03.013 |
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| 作者姓名： | 刘先斌 |
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| 作者单位： | 西南交通大学应用力学与工程系 |
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| 基金项目： | 国家自然科学基金 (196 0 2 0 16 )和 (195 72 0 5 1)资助项目 |
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| 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,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.
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| 关 键 词： | 实噪声 余维2分叉 FPK方程 扩散过程 奇异边界 最大Lyapunov指数 可解性条件 |
| 修稿时间： | 1999-11-17 |
ON THE BIFURCATION IN PROBABILITY 1 SENSE FOR A KIND OF STOCHASTIC BIFURCATION SYSTEM |
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| ON THE BIFURCATION IN PROBABILITY 1 SENSE FOR A KIND OF STOCHASTIC BIFURCATION SYSTEM[J]. Chinese Journal of Solid Mechanics, 2001, 22(3): 297-302. doi: 10.3969/j.issn.0254-7805.2001.03.013 |
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| Authors: | Liu Xianbin |
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| Abstract: | For a co dimension two bifurcation system on a three dimensional central manifold, which is parametrically excited by a real noise, 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 process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for relevant system are established by the use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum expansions of Fokker Planck operator. |
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| Keywords: | real noise co dimension two bifurcation FPK equation diffusion process singular boundary maximal Lyapunov exponent solvability condition |
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