The European Physical Journal D

, Volume 42, Issue 3, pp 461–466

Two different kinds of time delays in a stochastic system

Authors

  • X. Gu
    • School of Physical Science and Technology, Suzhou University
    • School of Physical Science and Technology, Suzhou University
  • D. Wu
    • School of Physical Science and Technology, Suzhou University
Nonlinear Dynamics

DOI: 10.1140/epjd/e2007-00043-7

Cite this article as:
Gu, X., Zhu, S. & Wu, D. Eur. Phys. J. D (2007) 42: 461. doi:10.1140/epjd/e2007-00043-7

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 motion02.30.Ks Delay and functional equations02.50.Ey Stochastic processes
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Copyright information

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