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First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation

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  • Li, Jiaorui
  • Feng, C.S.

Abstract

First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system.

Suggested Citation

  • Li, Jiaorui & Feng, C.S., 2010. "First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5557-5562.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5557-5562
    DOI: 10.1016/j.physa.2010.08.028
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    References listed on IDEAS

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    1. A. C. -L. Chian & E. L. Rempel & C. Rogers, 2007. "Crisis-induced intermittency in non-linear economic cycles," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 211-218.
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    5. Li, Jiaorui & Ren, Zhengzheng & Wang, Zuoren, 2008. "Response of nonlinear random business cycle model with time delay state feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5844-5851.
    6. Adam Krawiec & Marek Szydłowski & Janusz Toboła, 2000. "Nonlinear Oscillations In Business Cycle Model With Time Lags," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 603-604.
    7. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
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    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. Jochen Jungeilges & Tatyana Ryazanova, 2018. "Output volatility and savings in a stochastic Goodwin economy," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 8(3), pages 355-380, December.

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