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分数阶变时滞惯性Cohen-Grossberg神经网络Mittag-Leffler稳定和渐近$\omega$-周期

蒋望东, 章月红, 刘伟   

  1. 绍兴文理学院元培学院 绍兴 312000
  • 收稿日期:2020-09-10 修回日期:2021-12-23 出版日期:2022-04-25 发布日期:2022-06-18
  • 通讯作者: 章月红,Email:zhangyhmath@163.com.
  • 基金资助:
    教育部产学合作协同育人项目(202102034006),浙江省教育厅一般科研项目(Y202145903),绍兴文理学院校级科研项目(2020LG1009),绍兴文理学院元培学院院级科研项目(KY2020C01)资助课题.

蒋望东, 章月红, 刘伟. 分数阶变时滞惯性Cohen-Grossberg神经网络Mittag-Leffler稳定和渐近$\omega$-周期[J]. 系统科学与数学, 2022, 42(4): 867-885.

JIANG Wangdong, ZHANG Yuehong, LIU Wei. Global Mittag-Leffler Stability and Global Asymptotic ω-Period for a Class of Fractional-Order Cohen-Grossberg Inertial Neural Networks with Time-Varying Delays[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4): 867-885.

Global Mittag-Leffler Stability and Global Asymptotic ω-Period for a Class of Fractional-Order Cohen-Grossberg Inertial Neural Networks with Time-Varying Delays

JIANG Wangdong, ZHANG Yuehong, LIU Wei   

  1. Yuanpei College, Shaoxing University, Shaoxing 312000
  • Received:2020-09-10 Revised:2021-12-23 Online:2022-04-25 Published:2022-06-18
This paper focuses on the dynamic behavior of fractional-order inertial Cohen-Grossberg neural networks with time-varying delays. Using Riemann-Liouville fractional calculus properties and initial value conditions, we divide the definition field $[0, + \infty)$ of $t$ into two intervals according to the time-varying delays $\tau_{ij}(t)$ of the system: $[0,\tau_{ij}(t)]$ and $[\tau_{ij}(t),+\infty)$, and then we deduce the relationship between the fractional integrals of the state function $x_{i}(t-\tau_{ij}(t))$ when $t$ is in $[0,\tau_{ij}(t)]$ and $[\tau_{ij}(t),+\infty)$. By introducing the Mittag-Leffler function, with the help of finite increment formula of Lagrange mean-value theorem and Arzela-Ascoli theorem that when the function sequence is equi-continuous and uniform, there is a uniformly convergent subsequence, we get the sufficient conditions to determine the global Mittag-Leffler stability and global asymptotic $\omega$-periodicity. Finally, we give numerical simulation examples to verify the effectiveness of the theoretical results.

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