IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i2p414-421.html
   My bibliography  Save this article

First-passage problem for strong nonlinear stochastic dynamical systems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905005503
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.05.054?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Wei, Guoliang & Shu, Huisheng, 2007. "H∞ filtering on nonlinear stochastic systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 663-670.
    3. 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).
    4. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jing, Zhujun & Huang, Jicai & Deng, Jin, 2007. "Complex dynamics in three-well duffing system with two external forcings," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 795-812.
    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:414-421. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.