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离散分数阶神经网络的全局Mittag-Leffler稳定性

游星星 梁伦海

游星星, 梁伦海. 离散分数阶神经网络的全局Mittag-Leffler稳定性[J]. 应用数学和力学, 2019, 40(11): 1224-1234. doi: 10.21656/1000-0887.400163
引用本文: 游星星, 梁伦海. 离散分数阶神经网络的全局Mittag-Leffler稳定性[J]. 应用数学和力学, 2019, 40(11): 1224-1234. doi: 10.21656/1000-0887.400163
YOU Xingxing, LIANG Lunhai. Global MittagLeffler Stability of Discrete-Time Fractional-Order Neural Networks[J]. Applied Mathematics and Mechanics, 2019, 40(11): 1224-1234. doi: 10.21656/1000-0887.400163
Citation: YOU Xingxing, LIANG Lunhai. Global MittagLeffler Stability of Discrete-Time Fractional-Order Neural Networks[J]. Applied Mathematics and Mechanics, 2019, 40(11): 1224-1234. doi: 10.21656/1000-0887.400163

离散分数阶神经网络的全局Mittag-Leffler稳定性

doi: 10.21656/1000-0887.400163
基金项目: 重庆市研究生教育创新基金(CYS18230)
详细信息
    作者简介:

    游星星(1994—),男,硕士生(通讯作者. E-mail: youxingxing11@163.com);梁伦海(1995—),男,硕士生(E-mail: 765046989@qq.com).

  • 中图分类号: O357.41

Global MittagLeffler Stability of Discrete-Time Fractional-Order Neural Networks

  • 摘要: 研究了一类离散分数阶神经网络的Mittag-Leffler稳定性问题.首先, 基于离散分数阶微积分理论、神经网络理论,提出了一类离散分数阶神经网络.其次,利用不等式技巧和离散Laplace变换,通过构造合适的Lyapunov函数,得到了离散分数阶神经网络全局Mittag-Leffler稳定的充分性判据.最后,通过一个数值仿真算例验证了所提出理论的有效性.
  • [1] 廖晓昕. Hopfield 型神经网络的稳定性[J]. 中国科学(A辑), 1993,23(10): 1025-1035.(LIAO Xiaoxin. Stability of Hopfield neural networks[J]. Science in China (Series A),1993,23(10): 1025-1035.(in Chinese))
    [2] 马儒宁, 陈天平. 基于投影算子的回归神经网络模型及其在最优化问题中的应用[J]. 应用数学和力学, 2006,27(4): 484-494.(MA Runing, CHEN Tianping. Recurrent neural network model based on projective operator and its application to optimization problems[J]. Applied Mathematics and Mechanics,2006,27(4): 484-494.(in Chinese))
    [3] 王利敏, 宋乾坤, 赵振江. 基于忆阻的分数阶时滞复值神经网络的全局渐进稳定性[J]. 应用数学和力学, 2017,38(3): 333-346.(WANG Limin, SONG Qiankun, ZHAO Zhenjiang. Global asymptotic stability of memristor-based fractional-order complex-valued neural networks with time delays[J]. Applied Mathematics and Mechanics,2017,38(3): 333-346.(in Chinese))
    [4] 曾德强, 吴开腾, 宋乾坤, 等. 时滞神经网络随机抽样控制的状态估计[J]. 应用数学和力学, 2018,39(7): 821-832.(ZENG Deqiang, WU Kaiteng, SONG Qiankun, et al. State estimation for delayed neural networks with stochastic sampled-data control[J]. Applied Mathematics and Mechanics,2018,39(7): 821-832.(in Chinese))
    [5] ZHANG L, SONG Q, ZHAO Z. Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays[J]. Applied Mathematics and Computation,2017,298: 296-309.
    [6] LI Y, CHEN Y Q, PODLUBNY I. Mittag-Leffler stability of fractional order nonlinear dynamic systems[J]. Automatica,2009,45(8): 1965-1969.
    [7] LI Y, CHEN Y Q, PODLUBNY I. Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability[J]. Computers & Mathematics With Applications,2010,59(5): 1810-1821.
    [8] CHEN J, ZENG Z, JIANG P. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51: 1-8.
    [9] CHEN J, LI C, YANG X. Global Mittag-Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control[J]. Neurocomputing,2018,313: 324-332.
    [10] YANG X, LI C, HUANG T, SONG Q, et al. Global Mittag-Leffler synchronization of fractional-order neural networks via impulsive control[J]. Neural Processing Letters,2018,48(1): 459-479.
    [11] PRATAP A, RAJA R, CAO J, et al. Stability and synchronization criteria for fractional order competitive neural networks with time delays: an asymptotic expansion of Mittag Leffler function[J]. Journal of the Franklin Institute,2019,356(4): 2212-2239.
    [12] YE R, LIU X, ZHANG H, et al. Global Mittag-Leffler synchronization for fractional-order BAM neural networks with impulses and multiple variable delays via delayed-feedback control strategy[J]. Neural Processing Letters,2019,49(1): 1-18.
    [13] ABDELJAWAD T, JARAD F, BALEANU D. A semigroup-like property for discrete Mittag-Leffler functions[J]. Advances in Difference Equations,2012,2012(1): 72.
    [14] ABDELJAWAD T, AL-MDALLAL Q M. Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall’s inequality[J]. Journal of Computational and Applied Mathematics,2018,339: 218-230.
    [15] ALZABUT J, TYAGI S, ABBAS S. Discrete fractional-order BAM neural networks with leakage delay: existence and stability results[J]. Asian Journal of Control,2018. DOI: 10.1002/asjc.1918.
    [16] ALZABUT J, ABDELJAWAD T, BALEANU D. Nonlinear delay fractional difference equations with applications on discrete fractional Lotka-Volterra competition model[J]. Journal of Computational Analysis and Applications,2018,25(5): 889-898.
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出版历程
  • 收稿日期:  2019-05-07
  • 修回日期:  2019-05-23
  • 刊出日期:  2019-11-01

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