加性和乘性泊松白噪声联合激励下光滑非连续振子的随机响应

摘要

The stochastic response of the smooth and discontinuous (SD) oscillator under additive and multiplicative Poisson white noise excitation is studied by the generalized cell mapping method. Based on the digraph analysis algorithm, the attractors, basins of attraction, basin boundaries, saddles and invariant manifolds of the SD oscillator can be obtained. The transient and stationary responses of the SD oscillator under Poisson white noise excitation are computed based on the matrix analysis algorithm. It can be found that there is a close relationship between the evolution direction of probability density and the unstable manifold. Monte Carlo results are used to verify the efficiency and accuracy of the matrix analysis algorithm.%利用广义胞映射方法，研究了加性和乘性泊松白噪声联合作用下SD振子(smooth and discontinuous oscillator)的随机响应问题。基于图分析算法，获得确定SD振子的吸引子、吸引域、域边界、鞍和不变流形等全局特性。基于矩阵分析算法，计算了SD振子在泊松白噪声激励下的瞬态和稳态响应。结果表明：随机响应的概率密度函数演化方向和确定情况下的不稳定流形形状之间存在密切联系。蒙特卡罗模拟结果表明，所使用的方法是有效且准确的。