基于统计复杂度的分数阶欠阻尼双稳系统的随机共振研究

目的研究Gaussian白噪声作用下分数阶欠阻尼双稳系统的随机共振现象。方法采用统计复杂度方法探究分数阶导数、余弦信号的幅值及频率、阻尼系数等参数对分数阶系统随机共振效应的影响。结果当这些参数变化时,分数阶系统的统计复杂度曲线和标准Shannon熵曲线会产生不同的变化趋势,且在分数阶导数q=0.3时,系统最易发生随机共振现象。此外,当信号振幅增加至0.2时,可以增强随机共振效应;相反,信号频率增大至0.07时,可以削弱此现象。结论这些因素可以有效地调节分数阶双稳系统的随机共振现象。

Stochastic Resonance in Fractional-order Underdamped Bistable Systems by Statistical Complexity Measures

The paper aims to study the stochastic resonance of fractional-order bistable system under the action of Gaussian white noise. The statistical complexity method was applied to explore the effect of parameters such as fractional-order derivative, amplitude and frequency of cosine signal as well as damping coefficient on the stochastic resonance of fractional-order system. It can be observed that the trends of the curves of the statistical complexity and the normalized Shannon entropy of the system were various with the changing of the system parameters. And when the fractional derivative was q=0.3, the system was most prone to stochastic resonance phenomenon. In addition, the stochastic resonance effect can be enhanced when the signal amplitude was increased to 0.2. Conversely, increasing the signal frequency to 0.07 could weaken this phenomenon. It can be concluded that these factors can effectively adjust the stochastic resonance phenomenon of the fractional-order bistable system.