CLC number: O324
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2017-01-05
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Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan. Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump[J]. Journal of Zhejiang University Science A, 2017, 18(2): 83-91.
@article{title="Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump",
author="Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan",
journal="Journal of Zhejiang University Science A",
volume="18",
number="2",
pages="83-91",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1600176"
}
%0 Journal Article
%T Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump
%A Shan-shan Pan
%A Wei-qiu Zhu
%A Rong-chun Hu
%A Rong-hua Huan
%J Journal of Zhejiang University SCIENCE A
%V 18
%N 2
%P 83-91
%@ 1673-565X
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1600176
TY - JOUR
T1 - Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump
A1 - Shan-shan Pan
A1 - Wei-qiu Zhu
A1 - Rong-chun Hu
A1 - Rong-hua Huan
J0 - Journal of Zhejiang University Science A
VL - 18
IS - 2
SP - 83
EP - 91
%@ 1673-565X
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1600176
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.
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