Effects of time delay on transition rate of state in an increasing process of Logistic system

Abstract

The effects of time delay on transition rate from metastable state to stable state in a Logistic system are investigated. On the assumption that there is a delay time in the decay process of cell evolution, the expression of the transition rate is derived in the first order approximation under the condition of the small delay time and the steepest-descent approximation. The numerically calculated results indicate that the additive noise, the multiplicative noise and the correlations between additive and multiplicative noises enhance the system transition from metastable state to stable state. However, such a transition is restrained by the time delay, i.e., the time delay enhances the stability of the system.