线性过阻尼分数阶Langevin方程的共振行为

通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声,推导出分数阶Langevin方程, 其分数阶导数项阶数由系统内噪声的Hurst指数所确定.讨论了处于强噪声环境下的线性过阻尼分数阶 Langevin方程在周期信号激励下的共振行为,利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式.分析表明,适当参数下, 系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了 广义的随机共振现象.

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

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.