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The European Physical Journal D

, Volume 42, Issue 3, pp 461–466 | Cite as

Two different kinds of time delays in a stochastic system

  • X. Gu
  • S. ZhuEmail author
  • D. Wu
Nonlinear Dynamics

Abstract.

The steady state properties of a noise-driven bistable system are investigated when there are two different kinds of time delays existed in the deterministic and fluctuating forces respectively. Using the approximation of the probability density approach, the delayed Fokker-Planck equation is obtained. The stationary probability distribution (SPD) and the variance of the system are derived. It is found that the time delay τ in the deterministic force can reduce the fluctuations while the time delay β in the fluctuating force can enhance the fluctuations. Numerical simulations are presented and are in good agreement with the approximate theoretical results.

PACS.

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 02.30.Ks Delay and functional equations 02.50.Ey Stochastic processes 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Physical Science and Technology, Suzhou UniversityJiangsuP.R. China

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