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
作者：钟苏川(四川大学空天科学与工程学院空天信息处理与应用中心)；彭皓(西南交通大学数学学院)；张路(四川大学数学学院)
Author：ZHONG Su-Chuan(Center of Aerospace Information Processing and Application, College of Aeronautics and Astronautics, Sichuan University)；PENG Hao(School of Mathematics, Southwest Jiaotong University)；ZHANG Lu(College of Mathematics, Sichuan University)
收稿日期：2017-11-21 年卷（期）页码：2018,55(4):698-704
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：广义Langevin方程; 线性过阻尼调和振子; Ornstein-Uhelnbeck噪声; 随机共振
Key words：Generalized Langevin equation; Linear over-damped harmonic oscillator; Ornstein-Uhelnbeck noise; Stochastic resonance
基金项目：国家自然科学基金（11501386,11401405,11626197）；四川省科技厅基金项目（2017JY0219）；中央高校基本科研业务费专项基金（2682016CX120）
中文摘要
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.
英文摘要
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.
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