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几类非线性系统对白噪声参激与/或外激平稳响应的精确解*

朱位秋

朱位秋. 几类非线性系统对白噪声参激与/或外激平稳响应的精确解*[J]. 应用数学和力学, 1990, 11(2): 155-164.
引用本文: 朱位秋. 几类非线性系统对白噪声参激与/或外激平稳响应的精确解*[J]. 应用数学和力学, 1990, 11(2): 155-164.
Zhu Wei-qiu. Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations[J]. Applied Mathematics and Mechanics, 1990, 11(2): 155-164.
Citation: Zhu Wei-qiu. Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations[J]. Applied Mathematics and Mechanics, 1990, 11(2): 155-164.

几类非线性系统对白噪声参激与/或外激平稳响应的精确解*

基金项目: * 国家自然科学基金资助项目

Exact Solutions for Stationary Responses of Several Classes of Nonlinear Systems to Parametric and/or External White Noise Excitations

  • 摘要: 用福克-普朗克-柯尔莫哥洛夫方程方法构造了一类二阶、三类高阶非线性系统对白噪声参激与/或外激的平稳响应的精确解.讨论了解的存在与唯一性及解的性态.所考虑的系统的共同特点是非保守力依赖于相应保守系统的首次积分,因此可称为广义能量依赖系统.文中指出,对每个广义能量依赖系统,存在一族与之随机等价的非广义能量依赖系统,它们有相同的平稳概率密度.并指出对一给定广义能量依赖系统,如何找到其等价随机系统.作为例子,给出了二阶广义能量依赖随机系统的等价随机系统.最后指出并用例子说明,许多非广义能量依赖非线性随机系统的精确平稳解可通过寻求其等价广义能量依赖系统而找到.
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出版历程
  • 收稿日期:  1988-10-31
  • 刊出日期:  1990-02-15

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