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Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing–Rayleigh–Mathieu system

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Abstract

The first-passage statistics of Duffing–Rayleigh–Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.

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Authors and Affiliations

  1. Institute of Automation, School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China

    Yongjun Wu

  2. Hangzhou Yiheng Technologies Co., Ltd, 2F, 28 Wantang Road, Hangzhou, 310013, China

    Wang Fang

Authors
  1. Yongjun Wu
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  2. Wang Fang
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Correspondence to Yongjun Wu.

Additional information

The work reported in this paper was supported by the Foundation of ECUST (East China University of Science and Technology) for Outstanding Young Teachers (YH0157105).

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Wu, Y., Fang, W. Stochastic averaging method for estimating first-passage statistics of stochastically excited Duffing–Rayleigh–Mathieu system. Acta Mech Sin 24, 575–582 (2008). https://doi.org/10.1007/s10409-008-0140-7

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  • DOI: https://doi.org/10.1007/s10409-008-0140-7

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