相关噪声驱动下一种特殊非对称非线性系统的随机共振研究

Stochastic Resonance in a special type of Asymmetric Nonlinear System Driven by Correlated Noise

摘要:

本文分析了在乘性非高斯噪声与加性高斯噪声驱动下的一种特殊非对称双稳系统的随机共振现象. 我们使用统一色噪声逼近、路径积分法、二态模型理论对本文郎之万方程进行马尔科夫逼近，从而得到系统的稳态概率分布与信噪比. 仿真结果得知，非高斯噪声与高斯噪声强度驱动下的信噪比均存在随机共振，且非高斯噪声偏差参数、噪声相关时间、非对称系数、互相关强度等参数均对其有影响. 本文分别讨论了非高斯噪声偏差参数，非高斯噪声的相关时间，互相关强度，周期信号幅度和非对称系数等参数对信噪比的影响.

Abstract:

We have analyzed the phenomenon of stochastic resonance in an asymmetric bistable system driven by multiplicative non-Gaussian noise and additive Gaussian noise. Using a path-integral approach, together with the unified colored noise approximation and two-state model theory, we have obtained a consistent Markovian approximation, which enables us to get the analytical expressions for the stationary probability distribution and the signal-to-noise ratio. Under the influence of non-Gaussian noise deviation parameter, noise correlation time, asymmetric coefficient and mutual correlation strength, there are stochastic resonance on signal-to-noise ratio as non-Gaussian noise intensity and Gaussian noise intensity. Besides, the influence of different parameters on signal-to-noise ratio is discussed respectively, including non-Gaussian noise deviation parameter, correlation times of the non-Gaussian noise, cross-correlation strengths, amplitudes of periodic signal, and asymmetric coefficient.