Journal of Statistical Physics

, Volume 171, Issue 5, pp 878–896 | Cite as

Stochastic Resonance and First Arrival Time for Excitable Systems

  • Solomon Fekade Duki
  • Mesfin Asfaw Taye


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).


Brownian motion Stochastic resonance Statistical physics 



We would like to thank Mulugeta Bekele for the interesting discussions we had. MA would like to thank Mulu Zebene for the constant encouragement. SFD’s research was supported in part by the Intramural Research Program of the National Institute of Health, National Library of Medicine.


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© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.National Center for Biotechnology InformationNational Library of Medicine and National Institute of HealthBethesdaUSA
  2. 2.Department of PhysicsCalifornia State University Dominguez HillsCarsonUSA

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