Ornstein-Uhlenbeck噪声驱动的过阻尼广义Langevin方程的共振

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

摘要:

本文研究了受外部周期信号激励的线性过阻尼广义Langevin方程的随机共振现象.本文将系统内噪声建模为指数型关联Ornstein-Uhlenbeck噪声,系统外噪声建模为双态噪声,并利用随机平均法和积分变换算法推导出系统响应的一阶稳态矩和稳态响应振幅的解析表达式.对解析结果的分析表明，该线性过阻尼广义Langevin方程具有丰富的共振行为,即系统的稳态响应振幅随噪声的特征参数、周期激励信号的频率及部分系统参数的变化而出现广义随机共振.

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.