随机参激和外激联合作用下非线性动力系统的路径积分解

将基于Gauss Legendre公式的路径积分法推广到随机参激和外激联合作用的非线性动力系统.研究了受高斯白噪声参激和外激联合作用的非线性振子，将所得路径积分解与其精确解（满足一定条件时该系统存在精确解）或Monte Carlo随机模拟结果相比较，充分验证了路径积分的准确性.并借助路径积分数值解，捕捉到该随机系统的一维P分岔.关键词：路径积分P分岔随机参激随机外激

Solutions of path integration for nonlinear dynamical system under stochastic parametric and external excitations

The numerical path integration based on Gauss Legendre scheme is extended to the case of nonlinear dynamical system under stochastic parametric and external excitations. For the purpose of comparison between the numerical solutions and the analytic solution(if the system has) or Monte Carlo simulation, we discuss the system under parametric and external Gaussian white noise excitations. The numerical method is shown to give accurate results. Via the numerical solutions of path integration, we have studied the P bifurcation of the stochastic system.