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Stochastic time-delayed systems driven by correlated noises: Steady-state analysis

Author

Listed:
  • Zhang, Huiqing
  • Xu, Wei
  • Xu, Yong
  • Li, Dongxi

Abstract

In the present paper, a class of stochastic time-delayed systems driven by correlated Gaussian white noises are considered. Novikov’s theorem is used to derive delay Fokker–Planck equations. In the case of small time delays, approximate stationary solutions are obtained. As a special case, the delay Fokker–Planck equation and the approximate stationary probability density function is obtained for a bistable system. Numerical simulations show that the small-delay approximation is a good approximation in the case of small delay. Furthermore, the effects of the correlated noises and the feedback are investigated. The critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by λ (the degree of the correlation of the noises) and ε (the strength of the feedback). Both λ and ε can change the curve of the stationary probability density function from a bimodal to a unimodal structure.

Suggested Citation

  • Zhang, Huiqing & Xu, Wei & Xu, Yong & Li, Dongxi, 2009. "Stochastic time-delayed systems driven by correlated noises: Steady-state analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3017-3023.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:15:p:3017-3023
    DOI: 10.1016/j.physa.2009.04.032
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    Cited by:

    1. Li, Chao & Xu, Wei & Feng, Jinqian & Wang, Liang, 2013. "Response probability density functions of Duffing–Van der Pol vibro-impact system under correlated Gaussian white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1269-1279.

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