Levy噪声激励下的幂函数型单稳随机共振特性分析

将Levy噪声与幂函数型单稳随机共振系统相结合, 为确保实验数据的可靠性, 以平均信噪比增益为衡量指标, 针对Levy噪声激励下的随机共振现象进行了研究. 详细介绍了单稳系统势函数形式及Levy噪声的产生原理, 深入探究了不同特征指数α 和不同对称参数β 取值条件下, 单稳系统参数a和b、Levy噪声强度放大系数D对幂函数型单稳系统共振输出的作用规律. 研究结果表明, 在任意Levy噪声分布条件下, 通过对系统参数a和b的适当调整均能诱导随机共振, 完成微弱信号检测, 且有多个随机共振区间与之对应, 同时这些区间不随α 或β 的改变而改变; 此外, 在研究噪声诱导的随机共振时也发现了同样的规律, 通过调节噪声强度放大系数D也能产生随机共振, 且随机共振区间也不随α 或β 的改变而改变; 最后, 在研究系统参数a和b之间的相互作用关系时发现, 一个系统参数的随机共振取值区间会随着另一个系统参数的改变而改变. 所获得的研究结果有效解决了Levy噪声激励下幂函数型单稳随机共振系统的系统参数、噪声强度放大系数的选择问题, 为其应用于工程实践提供了可靠的理论依据.

Characteristic analysis of power function type monostable stochastic resonance with Levy noise

In this paper, the Levy noise is combined with a power function type monostable stochastic resonance system for the first time. In order to ensure the reliability of the experimental data, the average signal-to-noise ratio gain is regarded as an index to investigate the stochastic resonance phenomenon stimulated by Levy noise. Potential function form of the monostable system and the method of generating Levy noise are presented in detail. The pulse characteristic and smear characteristic of Levy noise are also presented in detail. The laws for the resonant output of monostable system, governed by parameters a and b, the intensity amplification factor D of Levy noise, are explored under different values of characteristic index α and symmetry parameter β of Levy noise. Results show that no matter whether it is under any different characteristic index α or symmetry parameter β of Levy noise, the weak signal can be detected by adjusting the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with α nor β . Moreover, the same rule is founded which by adjusting the intensity amplification factor D of Levy noise can also realize synergistic effect when studying the noise-induced stochastic resonance, and the interval of D does not change with α nor β; the best value of characteristic index is α =1 under any system parameter, and the best value of symmetry parameter is β =1 under any system parameter. So, the system performance is best when α =1 and β =1. Finally, the interaction relationship between system parameters a and b is investigated, and it is found that the interval of a or b will change with b or a when characteristic index α, symmetry parameter β and the intensity amplification factor D of Levy noise are fixed. These results will contribute to reasonably choosing the system parameters and intensity amplification factor of power function type monostable stochastic resonance system under Levy noise, and provide a reliable basis for practical engineering application of weak signal detection by stochastic resonance.