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• W4319304500 abstract "In this paper, we use stochastic averaging method and data-driven artificial neural network to study the response and reliability of a fractional stochastic dynamical system. Firstly, a generalized Harmonic transformation is introduced to get an approximate expression for the fractional derivative. Based on this procedure, stochastic averaging method is utilized to get Fokker–Planck Kolmogorov equation for the system response and Backward Kolmogorov equation for the system reliability. An exact stationary solution of amplitude response is obtained by solving Fokker–Planck Kolmogorov equation, in the meanwhile, numerical results regarding to the reliability by Crank–Nicolson difference method are derived too. We propose an algorithm of data-driven artificial neural network and apply it for solving these two equations simulatively, in order to verify the correction and accuracy of the analytical methods. All results illustrate that data-driven artificial neural network is highly effective to achieve the system response and reliability. The advantage of this deep learning algorithm mainly includes the meshless structure, boundary sample data collection, small amount of training data and unconstrained optimization. In addition, the increase of the fractional order can enhance the system response and leads to stochastic bifurcation." @default.
• W4319304500 created "2023-02-07" @default.
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• W4319304500 date "2023-06-01" @default.
• W4319304500 modified "2023-10-05" @default.
• W4319304500 title "Two methods for studying the response and the reliability of a fractional stochastic dynamical system" @default.
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• W4319304500 doi "https://doi.org/10.1016/j.cnsns.2023.107144" @default.
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