The resonant behavior of an over-damped linear fractional Langevin equation

Abstract

By choosing the internal noise as a fractional Gaussian noise, we obtain the fractional Langevin equation. We explore the phenomenon of stochastic resonance in an over-damped linear fractional Langevin equation subjected to an external sinusoidal forcing. The influence of fluctuations of environmental parameters on the dynamics of the system is modeled by a dichotomous noise. Using the Shapiro-Loginov formula and the Laplace transformation technique, we obtain the exact expressions of the first and second moment of the output signal, the mean particle displacement and the variance of the output signal in the long-time limit t→∞. Finally, the numerical simulation shows that the over-damped linear fractional Langevin equation reveals a lot of dynamic behaviors and the stochastic resonance (SR) in a wide sense can be found with internal noise and external noise.