THE RELAXATION TIME OF A BISTABLE SYSTEM WITH TWO DIFFERENT KINDS OF TIME DELAYS

Abstract

In this paper, we study the relaxation time of a bistable system driven by correlated noises when there are two different kinds of time delays in the deterministic (τ) and random (θ) forces, respectively. The expression for the relaxation time Tc is derived by the projection operator method, in which the effects of the memory kernels are taken into account. After introducing a dimensionless parameter R (R = D/α, where D is the strength of multiplicative noise and α is the strength of additive noise), and then performing numerical computations, we find the following: (1) for the case of R ≤ 1, the relaxation time Tc increases as τ increases, i.e. τ slows down the fluctuation decay of the dynamical variable for the case of R ≤ 1; (2) however, for the case of R > 1, Tc decreases as τ increases, i.e. τ enhances the fluctuation decay of the dynamical variable for the case of R > 1; (3) Tc decreases as θ increases, i.e. θ enhances the fluctuation decay of the dynamical variable for the three cases of R (R > 1, R=1, and R < 1).