乘性双态噪声和周期调制简谐噪声激励下的线性过阻尼谐振子的随机共振

Stochastic resonance in an over-damped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise

针对乘性双态噪声和加性周期调制简谐噪声联合作用的线性过阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一阶矩以及稳态响应振幅的解析表达式,得出了稳态幅值关于各种噪声参数出现随机共振的条件。研究表明在一定条件下,系统稳态响应振幅关于各种噪声参数具有非单调依赖关系,即出现了随机共振现象;特别地,简谐噪声和普通白噪声相比,不仅具有传统的刻画指标-噪声强度参数,还具有另外两个新的指标参数,即阻尼参数和频率参数。通过对这两种参数的调节可以有效控制系统稳态响应振幅的随机共振现象,有助于增强系统对外部周期信号的响应程度,从而提高系统对微弱周期信号检测的灵敏度和实现对周期信号的频率估计。

For an over-damped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise,the exact analytical expression of the first moments and the amplitude of the system steady-state response were obtained based on the Shapiro-Loginov formula. Moreover,the conditions of stochastic resonance were also obtained.It is found that when the factors of the noise satisfy certain conditions,the amplitude of the system steady-state response has monotonous dependencies on the noise parameters,i. e.,the phenomenon of stochastic resonance appears. In particular,compared with the normal white noise,the intensity,damping,and frequency parameters of the harmonic can be regulated to effectively control the stochastic resonance,and thus enhance the system response to external periodic signal.