New Insights on the Application of Moment Closure Methods to Nonlinear Stochastic Systems
The cumulant-neglect closure method is briefly outlined and subsequently applied to two Duffing systems, one exhibiting a unimodal and the other a bimodal response probability density function. The closure results are compared at stationarity to the exact solution over a broad range of parameters, and some connections are drawn between the accuracy of cumulant-neglect closure and the choice of system parameters. Finally, characteristic equations governing all stationary solutions of the closed system of moments equations are obtained, and the stability of the resulting solutions is ascertained. From this analysis, it is determined whether the closure results are physically consistent; that is, if the stationary closure results can be reached by letting the system evolve from arbitrary initial conditions.
KeywordsMoment Equation Random Vibration Closure Result Closure Scheme Duffing Oscillator
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