Noise and periodic signal induced stochastic resonance in a Langevin equation with random mass and frequency

Abstract

The noise and external periodic signal induced stochastic resonance phenomena in a Langevin equation for the cases of random mass with dichotomous noise and random frequency with nonlinear noise is investigated. The random mass implies that the surrounding molecules not only collide with the Brownian particle but also adhere to it, thereby changing its mass. While the random frequency indicates the stochastic perturbation on the potential field. Applying the moment equations and the Shapiro–Loginov formula, the analytical steady-state response Ast and its stability criteria are derived. Based on the graphical and simulation methods, it is shown that the stochastic resonance phenomena exist in this system. Furthermore, a stochastic multi-resonance behavior of the Ast as function of the driving frequency as well as the one-valley and one-peak stochastic resonance behavior of the Ast as function of the frequency fluctuation strength are observed, which is previously reported and believed to be absent in the case of the multiplicative noise with only a dichotomous noise. Moreover, some numerical simulations are performed to support the theoretical analyses. We believe that the results that we found might be a possible explanation of some laboratory experiment in biological and chemical mechanisms.