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The numerical path integration based on GaussLegendre 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 MonteCarlo 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.
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Keywords:
- path integration /
- P bifurcation /
- stochastic parametric excitation /
- stochastic external excitation
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