Insight into Resonant Activation in Discrete Systems

TL;DR

This paper investigates the resonant activation phenomenon in discrete systems using master equations, providing analytical and numerical insights into the conditions and behaviors of RAP, including boundary effects and biological system implications.

Contribution

It introduces an analytical expression for the resonant frequency and explores RAP behavior across different boundary conditions in discrete systems.

Findings

RAP shows non-monotonic behavior in first passage time density.

Resonant frequency derived analytically and supported numerically.

Minimum and maximum MFPT observed with absorbing boundaries.

Abstract

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density function (pdf). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time (MFPT) can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.