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乘性噪声作用下延迟分数阶系统中的随机共振

朱建渠 金炜东 郭锋

朱建渠, 金炜东, 郭锋. 乘性噪声作用下延迟分数阶系统中的随机共振[J]. 西南交通大学学报, 2021, 56(2): 363-370. doi: 10.3969/j.issn.0258-2724.20191181
引用本文: 朱建渠, 金炜东, 郭锋. 乘性噪声作用下延迟分数阶系统中的随机共振[J]. 西南交通大学学报, 2021, 56(2): 363-370. doi: 10.3969/j.issn.0258-2724.20191181
ZHU Jianqu, JIN Weidong, GUO Feng. Stochastic Resonance of Fractional-Order System with Multiplicative Noise and Random Delay[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 363-370. doi: 10.3969/j.issn.0258-2724.20191181
Citation: ZHU Jianqu, JIN Weidong, GUO Feng. Stochastic Resonance of Fractional-Order System with Multiplicative Noise and Random Delay[J]. Journal of Southwest Jiaotong University, 2021, 56(2): 363-370. doi: 10.3969/j.issn.0258-2724.20191181

乘性噪声作用下延迟分数阶系统中的随机共振

doi: 10.3969/j.issn.0258-2724.20191181
基金项目: 国家自然科学基金(61134002)
详细信息
    作者简介:

    朱建渠(1973—),男,博士研究生,研究方向为智能信息处理、故障诊断及随机动力系统,E-mail: zhujianqu@163.com

  • 中图分类号: TN911.7

Stochastic Resonance of Fractional-Order System with Multiplicative Noise and Random Delay

  • 摘要: 时间延迟是动力系统的共同特性,在科学领域中得到广泛应用. 分数阶微积分具有时间记忆性和长程空间相关性,能更好地描述具有记忆、路径依赖性的物理过程,但很少文献研究延迟分数阶系统中的随机共振现象. 为此,研究乘性噪声作用下延迟分数阶系统中的随机共振. 基于线性系统理论,利用拉普拉斯变换和小延迟近似方法,得到了分数阶系统输出幅度增益(output amplitude gain,OAG)表达式. 研究结果表明:OAG是延迟时间的非单调函数;在OAG与乘性噪声的强度和相关率、随机延迟的相关率,以及分数指数和系统驱动信号频率的关系曲线上出现了随机共振现象;当乘性噪声强度较小,以及乘性噪声相关率相对较小或相对较大时,OAG随阻尼系数的增大而减小;而当乘性噪声强度较大,以及乘性噪声相关率取中间值时,OAG随阻尼系数的增大而增大.

     

  • 图 1  $\alpha $ 取不同值时 $G$ ${\tau _0}$ 的关系曲线

    Figure 1.  Amplitude gain $G$ versus random delay-time ${\tau _0}$ for different values of fractional exponent $\alpha $

    图 2  $\beta $ 取不同值时 $G$ ${\tau _0}$ 的关系曲线

    Figure 2.  Amplitude gain $G$ versus random delay-time ${\tau _0}$ for different values of friction coefficeint $\beta $

    图 3  $r$ 取不同值时 $G$ $D$ 的关系曲线

    Figure 3.  Amplitude gain $G$ versus multiplicative noise strength $D$ for different values of damping coefficient $r$

    图 4  $r$ 取不同值时 $G$ ${\lambda _1}$ 的关系曲线

    Figure 4.  Amplitude gain G versus correlate rate ${\lambda _1}$ of the multiplicative noise for different values of damping coefficient r

    图 5  系统频率 $\omega $ 取不同值时 $G$ ${\lambda _2}$ 的关系曲线

    Figure 5.  Amplitude gain $G$ versus correlate rate ${\lambda _2}$ of random delay noise for different values of system frequency $\omega $

    图 6  $\beta $ 取不同值时 $G$ $\alpha $ 的关系曲线

    Figure 6.  Amplitude gain $G$ versus fractional exponent $\alpha $ for different values of friction coefficeint $\beta $

    图 7  $\sigma $ 取不同值时 $G$ $\varOmega $ 的关系曲线

    Figure 7.  Amplitude gain $G$ versus driving forcefrequency $\varOmega $ for different values of couple noise intensity $\sigma $

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出版历程
  • 收稿日期:  2019-12-06
  • 修回日期:  2020-04-27
  • 网络出版日期:  2020-08-06
  • 刊出日期:  2021-04-15

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