In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance.

中文翻译：

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阻尼不足的双稳态系统中不同噪声的随机共振现象

本文研究了欠阻尼双稳态系统中四种噪声（白噪声，谐波噪声，不对称二分噪声和李维噪声）的随机共振（SR）现象。通过将随机微分方程理论应用到随机共振问题的数值模拟中，我们对系统的响应进行了仿真和分析，并密切关注所提出系统的随机控制。然后，分别用Euler-Maruyama算法，Milstein算法和四阶Runge-Kutta算法研究影响SR的因素。结果表明，在一定条件下，通过调节不同噪声下的控制效果参数，可以在所提出的系统中产生SR现象。我们还发现，噪声的类型对输出功率谱密度的谐振峰影响很小，这在仅由阻尼系数较大的乘性噪声驱动的常规谐波系统中没有观察到。因此，本文的结论可为进一步研究随机共振提供实验依据。