Two different kinds of time delays in a stochastic system
School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu, 215006, P.R. China
Corresponding author: a email@example.com
Revised: 13 December 2006
Published online: 28 February 2007
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007