Resonance of an over-damped generalized Langevin equation driven by Ornstein-Uhlenbeck noise

Abstract:

We explore the resonant behavior occurring in an over-damped linear generalized Langevin equation subject to a periodic force. We model the internal noise as an Ornstein-Uhlenbeck noise. The influence of fluctuations of environmental parameter on the system is modeled by a dichotomous noise. Using the stochastic average method and integral transform, we get the exact expressions of the steady-state first moment and amplitude. By studying the impacts of the noise parameters, driving frequency and system parameters, we find that the non-monotonic behaviors of the steady-state output amplitude indicate a lot of resonant behaviors and stochastic resonance (SR) in the wide sense.