First passage time and stochastic resonance of excitable systems

TL;DR

This paper investigates how temperature-dependent viscous friction influences the first passage time and stochastic resonance in an excitable Brownian system with a periodic potential, revealing lower passage times and conditions for resonance.

Contribution

It introduces a model where viscous friction decreases exponentially with temperature and analyzes its effects on barrier crossing and stochastic resonance in the system.

Findings

Lower mean first passage time with temperature-dependent friction

Identification of conditions for stochastic resonance

Enhanced system response due to interplay of noise and external force

Abstract

We study noise induced thermally activated barrier crossing of a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a spatially uniform temperature. The viscous friction is considered to decrease exponentially when the temperature $T$ of the medium increases as proposed originally by Reynolds. The results obtained in this work show that the mean first passage time of the particle is considerably lower when the viscous friction is temperature dependent than that of the case where the viscous friction is temperature independent. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. In this case, the interplay between noise and sinusoidal driving force in the bistable system may lead the system into stochastic resonance provided that the random tracks are adjusted in an optimal way to the recurring external force.