双稳系统中的随机共振乘性信噪作用研究

Stochastic Resonance in a Bistable System with Multiplicative Square-wave Signal and Multiplicative Dichotomous Noise

方波信号和双值噪声在科学领域广泛应用,而乘性信号在工程中广泛存在。但是,乘性方波信号和乘性双值噪声对双稳系统的非线性影响方面的研究还较少,因此,本文研究乘性方波信号和乘性双值噪声作用下双稳系统中的随机共振现象。基于绝热近似条件,推导系统信噪比的表达式,并基于该公式进行了不同输入条件的仿真研究。研究结果表明,信噪比随着乘性方波信号和乘性双值噪声幅度的变化可以取得一个最大值和一个最小值。大的乘性方波信号幅值会抑制信噪比,对于噪声相关率λ=0.65的情形,方波幅值A=1.0时的系统输出幅度比A=0.3时的输出幅值下降约29%;而较大的乘性双值噪声强度可以提升系统的输出性能,当系统参数b=3.8,乘性双值噪声强度ε=3.5时的系统输出幅度为ε=0.25时的输出幅值的2.5倍。随着乘性白噪声、加性白噪声及系统参数的变化,信噪比曲线出现一个峰值。

Square-wave signal and dichotomous noise are widely used in scientific fields,and multiplicative signal is widely used in engineering practice.However,little study has been done on the nonlinear influence of multiplicative square-wave signal and multiplicative dichotomous noise on a bistable system,so in this paper we investigate the stochastic resonance phenomenon in a bistable system driven by multiplicative square-wave signal and multiplicative dichotomous noise is investigated.Under the adiabatic condition,the output signal-to-noise ratio(SNR)for the system is obtained.It is found that the SNR can obtain one maximum value and one minimum value with increasing the amplitude of the multiplicative square-wave signal and multiplicative dichotomous noise.Large values of the amplitude of the multiplicative square-wave signal can depress the system SNR,in the case of noise correlation rateλ=0.65,the system output amplitude for square-wave amplitude A=1.0 declines almost 29%by comparison with that for A=0.3,while a larger amount of the multiplicative dichotomous will improve the system output,in the case of system parameter b=3.8,the system output amplitude for multiplicative dichotomous noise intensityε=3.5 is 2.5 times of that whenε=0.25.One resonance peak can be observed when the system SNR varies with the multiplicative white noise,with the additive white noise,as well as with the system parameters.