| 党蒲妮,孙中奎,吕锦锋.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[J].装备环境工程,2020,17(9):83-88. DANG Pu-ni,SUN Zhong-kui,LYU Jin-feng.Stochastic Resonance in Fractional-order Underdamped Bistable Systems by Statistical Complexity Measures[J].Equipment Environmental Engineering,2020,17(9):83-88. |
| 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 |
| Stochastic Resonance in Fractional-order Underdamped Bistable Systems by Statistical Complexity Measures |
| 投稿时间：2020-07-02 修订日期：2020-08-06 |
| DOI：10.7643/issn.1672-9242.2020.09.015 |
| 中文关键词: 分数阶双稳系统 统计复杂度 标准Shannon熵 随机共振 |
| 英文关键词:fractional-order bistable system statistical complexity normalized Shannon entropy stochastic resonance |
| 基金项目:国家自然科学基金(11772254) |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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