一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振；当乘性噪声强度和调制噪声强度的比值大于等于1时，系统出现随机多共振现象.通过数值计算的系统响应功率谱，验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子

Stochastic resonance of a damped linear oscillator

The stochastic resonance is studied for a damped linear oscillator subject to both parametric excitation of random noise and external excitation of periodically modulated random noise. By means of the Shapiro-Loginov formula, the expressions of the first-order and the second-order moments are obtained for the system response. It is found that there exist conventional stochastic resonance, bona fide stochastic resonance and stochastic resonance in a broad sense in the system. When the noise intensity ratio R≥1, the stochastic multi_resonance is found in the system. Moreover, the numerical results of power spectrum density of system response are presented to verify the analytic results.