Time delay to enhance the giant suppression in a bistable system

Abstract

Effects of time delay on the active rate of a bistable system was investigated. Using the steepest-descent approximation method, the analytical expression of the mean first passage time and the active rate of the bistable system with time delay was derived under the condition of small delay time. The numerical computations show that the time delay enhances the resonance suppression in the system.

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

“…Consider a bistable system with global delay and subjected to correlated multiplicative and additive noises: [38]…”

“…For a bistable system where the time delay exists in linear and cubic terms simultaneously, its stationary properties and rate process are given by a small delay expansion. [38] It is indicated that the transition rate and the mean first passage time both follow Arrhenius' law when the additive noise intensity is small, even if the delay is large. In order to fully understand the dynamical properties of the stochasticdelayed system, the correlation function of state variable should be further considered.…”