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First-passage problem for strong nonlinear stochastic dynamical systems

Author

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  • Li, Wei
  • Xu, Wei
  • Zhao, Junfeng
  • Jin, Yanfei

Abstract

In this paper, the stochastic averaging method for stochastic and dissipative quasi-non-integrable Hamiltonian system is applied to study the first-passage problem of coupled Duffing–van der Pol system subject to Gaussian white noise excitation. First, a Backward Kolmogorov equation for the conditional reliability function and a Generalized Pontryagin equation for the conditional moment of the first-passage time are established. Then according to the classification of the boundary conditions and initial conditions of these two kinds of equations, the reliability of system response under external excitation and parametric excitation are analyzed, respectively, in detail. At last, numerical results for reliability function, the probability of first-passage time and mean first-passage time of system are given in virtue of figures.

Suggested Citation

  • Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2006. "First-passage problem for strong nonlinear stochastic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 414-421.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:414-421
    DOI: 10.1016/j.chaos.2005.05.054
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    References listed on IDEAS

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    1. Li, Wei & Xu, Wei & Zhao, Junfeng & Ma, Shaojuan, 2005. "Stochastic optimal control of first-passage failure for coupled Duffing–van der Pol system under Gaussian white noise excitations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1221-1228.
    2. Bekele, Mulugeta & Ananthakrishna, G & Kumar, N, 1999. "Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 149-158.
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    Cited by:

    1. Wei, Guoliang & Shu, Huisheng, 2007. "H∞ filtering on nonlinear stochastic systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 663-670.
    2. Wei, Wei & Xu, Wei & Liu, Jiankang, 2021. "Stochastic P-bifurcation analysis of a class of nonlinear Markov jump systems under combined harmonic and random excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    3. Hu, Rongchun & Zhang, Dongxu & Gu, Xudong, 2022. "Reliability analysis of a class of stochastically excited nonlinear Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Li, Wei & Li, Jiaorui & Chen, Weisheng, 2012. "The reliability of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3556-3565.

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    2. Li, Wei & Li, Jiaorui & Chen, Weisheng, 2012. "The reliability of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3556-3565.

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