Stochastic Resonance and First Arrival Time for Excitable Systems

Abstract

We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification ( $$\eta $$ ) on model parameters is explored. $$\eta $$ and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, $$\eta $$ is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction $$\gamma $$ is considered to decrease exponentially when the temperature T of the medium increases ( $$\gamma =Be^{-A T}$$ ) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).