过阻尼谐振子的随机共振

Stochastic resonance in an overdamped harmonic oscillator

研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式.

The stochastic resonance in an overdamped harmonic oscillator driven by cross-correlation Gaussian white noises in which one of the noises is modulated by a periodic signal is studied. By means of the Fourier transform of the stationary correlation function, an exact expression of the signal-to-noise ratio for the overdamped harmonic oscillator stochastic model is derived. Results reveal that there are two types of stochastic resonance in an overdamped harmonic oscillator stochastic model. One type of stochastic resonance is that a resonance peak exists in the curves of signal-to-noise ratio versus the multiplicative noise intensity Q. Another type of stochastic resonance is that a resonance peak exists in the curves of signal-to-noise ratio versus the oscillator frequency ω . By changing the value of signal frequency Ω, the signal-to-noise ratio versus Q curve can exhibit three different forms： the form with a signal peak, the form with a peak following a valley, and the monotonic form.