Moments and Mean First—Passage Time of Parabolic—Bistable Potential System Driven by Colored Noise

A parabolic-bistable potential system driven by colored noise is studied.The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived.Furthermore,the mean first-passage time is calculated by the use of two approximate methods,respectively.It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity;(ii) a minimum occurs on the curve of the second-order moment of the system vs.noise intensity at the point DΓ=0.025;(iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time τ,while the conventional steepest descent approximation leads to poor results.     

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises： Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.