具有随机特征频率和延迟核函数的分数阶线性振荡器中的随机共振

Stochastic resonance in a fractional order linear oscillator with random characteristic frequency and time-delayed kernel function

研究了具有延迟核函数和随机特征频率的分数阶线性振荡器中的随机共振(stochastic resonance,SR)现象。基于线性系统理论,利用拉普拉斯变换,推导出了分数维振荡器系统输出幅度(system output amplitude,SOA)的解析表达式。分析表明,SOA是核函数延迟时间的周期函数。在SOA与噪声相关率、噪声幅值、分数维数的关系曲线上都发现了随机共振现象。分析了SOA与系统参数及噪声稳态概率间的非单调依赖行为。

Stochastic resonance(SR)phenomena in a fractional order linear oscillator with time-delayed kernel function and random characteristic frequency were investigated.Base on the linear system theory,using Laplace transformation,the analytical expression for the system output amplitude(SOA)of a fractional order oscillator was derived.It was shown that SOA is a periodic function of delayed-time of the kernel function;SR phenomena appear in relation curves of SOA versus noise correlation rate,SOA versus noise amplitude,and SOA versus fractional dimension,respectively.The non-monotonous dependence of SOA on system parameters and noise steady-state probability was analyzed.