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Stochastic stabilization of first-passage failure of Rayleigh oscillator under Gaussian White-Noise parametric excitations

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  • Li, Jiaorui
  • Xu, Wei

Abstract

Stochastic stabilization of first-passage failure of Rayleigh oscillator under Gaussian White-Noise parametric excitation is studied. The equation of motion of the system is first reduced to an averaged Itô stochastic differential equation by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function of first-passage failure is established. The conditional reliability function, and the conditional probability density are obtained by solving the backward Kolmogorov equation with boundary conditions. Finally, the cost function and optimal control forces are determined by the requirements of stabilizing the system by evaluating the maximal Lyapunov exponent. The numerical results show that the procedure is effective and efficiency.

Suggested Citation

  • Li, Jiaorui & Xu, Wei, 2005. "Stochastic stabilization of first-passage failure of Rayleigh oscillator under Gaussian White-Noise parametric excitations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1515-1521.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1515-1521
    DOI: 10.1016/j.chaos.2005.04.019
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    Cited by:

    1. Li, Jiaorui & Xu, Wei & Xie, Wenxian & Ren, Zhengzheng, 2008. "Research on nonlinear stochastic dynamical price model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1391-1396.

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