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Abstract: An approximate method for predicting the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump is proposed. By using the stochastic averaging method, the original system is reduced to one governed by a 1D averaged Itô equation for the total energy with the Markov jump process as parameter. A Fokker-Planck-Kolmogorov (FPK) equation is then deduced, from which the approximate stationary probability density of the response of the original system is obtained for different jump rules. To illustrate the effectiveness of the proposed method, a stochastically excited Markov jump Duffing system is worked out in detail.

The method of stochastic averaging is applied to predict the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump. The method itself has been validated with many nonlinear stochastic systems. The current work is yet another extension of the method to a new system with Markov jump.

随机激励下连续时间马尔科夫跳变非线性系统的平稳响应研究

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