留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

王利敏 宋乾坤 赵振江

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近稳定性[J]. 应用数学和力学, 2017, 38(3): 333-346. doi: 10.21656/1000-0887.370221
引用本文: 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近稳定性[J]. 应用数学和力学, 2017, 38(3): 333-346. doi: 10.21656/1000-0887.370221
WANG Li-min, SONG Qian-kun, ZHAO Zhen-jiang. 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. doi: 10.21656/1000-0887.370221
Citation: WANG Li-min, SONG Qian-kun, ZHAO Zhen-jiang. 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. doi: 10.21656/1000-0887.370221

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

doi: 10.21656/1000-0887.370221
基金项目: 国家自然科学基金(61273021;61473332); 重庆市研究生科研创新项目(CYS16179)
详细信息
    作者简介:

    王利敏(1993—),女,硕士生(E-mail: liminwangm@163.com);宋乾坤(1963—),男,教授,博士(通讯作者. E-mail: qiankunsong@163.com);赵振江(1961—),男,教授,硕士(E-mail: zhaozjcn@163.com).

  • 中图分类号: O175.13

Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

Funds: The National Natural Science Foundation of China(61273021; 61473332)
  • 摘要: 研究了分数阶复值神经网络的稳定性.针对一类基于忆阻的分数阶时滞复值神经网络,利用Caputo分数阶微分意义上Filippov解的概念, 研究其平衡点的存在性和唯一性.采用了将复值神经网络分离成实部和虚部的研究方法, 将实数域上的比较原理、不动点定理应用到稳定性分析中, 得到了模型平衡点存在性、唯一性和全局渐近稳定性的充分判据.数值仿真实例验证了获得结果的有效性.
  • [1] Kilbas A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [M]. New York: Elsevier Science Inc, 2006.
    [2] Boroomand A, Menhaj M B. Fractional-Order Hopfield Neural Networks [M]//Advances in Neuro-Information Processing. Berlin, Heidelberg: Springer, 2009: 883-890.
    [3] Ahmeda E, Elgazzar A S. On fractional order differential equations model for nonlocal epidemics[J]. Physica A: Statistical Mechanics and Its Applications,2007,379(2): 607-614.
    [4] Diethelm K, Ford N J. Analysis of fractional differential equations[J]. Journal of Mathematical Analysis and Applications,2002,265(2): 229-248.
    [5] YANG Xu-jun, SONG Qian-kun, LIU Yu-rong, et al. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing,2015,152: 19-26.
    [6] ZHANG Shuo, YU Yong-guang, WANG Qing. Stability analysis of fractional-order Hopfield neural networks with discontinuous activation functions[J]. Neurocomputing,2016,171: 1075-1084.
    [7] Rakkiyappan R, CAO Jin-de, Velmurugan G. Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2015,26: 84-97.
    [8] Chua L. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory,1971,18(5): 507-519.
    [9] HU Jin, WANG Jun. Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays[C]//The 2010 International Joint Conference on Neural Networks.2010: 1-8.
    [10] WU Ai-long, WEN Shi-ping, ZENG Zhi-gang. Synchronization control of a class of memristor-based recurrent neural networks[J]. Information Sciences,2012,183: 106-116.
    [11] BAO Hai-bo, Park Ju H, CAO Jin-de. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear Dynamics,2015,82(3): 1343-1354.
    [12] Velmurugan G, Rakkiyappan R, CAO Jin-de. Finite-time synchronization of fractional-order memristorbased neural networks with time delays[J]. Neural Networks,2016,73: 36-46.
    [13] CHEN Li-ping, WU Ran-chao, CAO Jin-de, et al. Stability and synchronization of memristor-based fractional-order delayed neural networks[J]. Neural Networks,2015,71: 37-44.
    [14] Hirose A. Dynamics of fully complex-valued neural networks[J]. Electronics Letters,1992,28: 1492-1494.
    [15] Nitta T. An analysis of the fundamental structure of complex-valued neurons[J]. Neural Processing Letters,2000,12(3): 239-246.
    [16] HU Jin, WANG Jun. Global stability of complex-valued recurrent neural networks with time-delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2012,23(6): 853-865.
    [17] ZHOU Bo, SONG Qian-kun. Boundedness and complete stability of complex-valued neural networks with time delay[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(8): 1227-1238.
    [18] ZHANG Zi-ye, LIN Chong, CHEN Bing. Global stability criterion for delayed complex-valued recurrent neural networks[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25: 1704-1708.
    [19] SONG Qian-kun, ZHAO Zhen-jiang. Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales[J]. Neurocomputing,2016,171: 179-184.
    [20] HU Shou-chuan. Differential equations with discontinuous right-hand sides[J]. Journal of Mathematical Analysis and Applications, 1991,154(2): 377-390.
    [21] ZHANG Guo-dong, SHEN Yi, SUN Jun-wei. Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays[J]. Nonlinear Analysis:Hybrid Systems,2012,97: 149-154.
    [22] ZHANG Shuo, YU Yong-guang, WANG Hu. Mittag-Leffler stability of fractional-order Hopfield neural networks[J]. Nonlinear Analysis: Hybrid Systems, 2015,16: 104-121.
    [23] WANG Hu, YU Yong-guang, WEN Guo-guang, et al. Global stability analysis of fractional-order Hopfield neural networks with time delay[J]. Neurocomputing,2015,154: 15-23.
    [24] DENG Wei-hua, LI Chang-pin, LU Jin-hu, et al. Stability analysis of linear fractional differential system with multiple time delays[J]. Nonlinear Dynamics,2007,48(4): 409-416.
    [25] CHEN Jie-jie, ZENG Zhi-gang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51: 1-8.
  • 加载中
计量
  • 文章访问数:  823
  • HTML全文浏览量:  50
  • PDF下载量:  1041
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-07-19
  • 修回日期:  2016-11-09
  • 刊出日期:  2017-03-15

目录

    /

    返回文章
    返回