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带有比例时滞的复值神经网络全局指数稳定性

张磊 宋乾坤

张磊, 宋乾坤. 带有比例时滞的复值神经网络全局指数稳定性[J]. 应用数学和力学, 2018, 39(5): 584-591. doi: 10.21656/1000-0887.380257
引用本文: 张磊, 宋乾坤. 带有比例时滞的复值神经网络全局指数稳定性[J]. 应用数学和力学, 2018, 39(5): 584-591. doi: 10.21656/1000-0887.380257
ZHANG Lei, SONG Qiankun. Global Exponential Stability of Complex-Valued Neural Networks With Proportional Delays[J]. Applied Mathematics and Mechanics, 2018, 39(5): 584-591. doi: 10.21656/1000-0887.380257
Citation: ZHANG Lei, SONG Qiankun. Global Exponential Stability of Complex-Valued Neural Networks With Proportional Delays[J]. Applied Mathematics and Mechanics, 2018, 39(5): 584-591. doi: 10.21656/1000-0887.380257

带有比例时滞的复值神经网络全局指数稳定性

doi: 10.21656/1000-0887.380257
基金项目: 国家自然科学基金(61773004);重庆高校创新团队建设计划资助项目(CXTDX201601022)
详细信息
    作者简介:

    张磊(1964—), 男, 讲师(E-mail: 1790279118@qq.com);宋乾坤(1963—), 男, 教授, 博士(通讯作者. E-mail: qiankunsong@163.com).

  • 中图分类号: O175.13

Global Exponential Stability of Complex-Valued Neural Networks With Proportional Delays

Funds: The National Natural Science Foundation of China(61773004)
  • 摘要: 研究了带有比例时滞的复值神经网络全局指数稳定性问题.借助向量Lyapunov函数思想和同胚映射原理, 并使用M-矩阵理论和不等式技巧,建立了网络平衡点存在性、唯一性和全局指数稳定性的判定条件.
  • [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] 杨志春, 徐道义. 具有变时滞和脉冲效应的Hopfield神经网络的全局指数稳定性[J]. 应用数学和力学, 2006,27(11): 1329-1334. (YANG Zhichun, XU Daoyi. Global exponential stability of Hopfield neural networks with variable delays and impulsive effects[J]. Applied Mathematics and Mechanics,2006,27(11): 1329-1334. (in Chinese))
    [4] 颜向平, 李万同. 具有扩散影响的Hopfield型神经网络的全局渐近稳定性[J]. 应用数学和力学, 2007,28(3): 328-334. (YAN Xiangping, LI Wantong. Global asymptotic stability for Hopfield-type neural networks with diffusion effects[J]. Applied Mathematics and Mechanics,2007,28(3): 328-334. (in Chinese))
    [5] ARIK S. Stability analysis of delayed neural networks[J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications,2000,47(7): 1089-1092.
    [6] KWON O, PARK J H, LEE S M, et al. New augmented Lyapunov-Krasovskii functional approach to stability analysis of neural networks with time-varying delays[J]. Nonlinear Dynamics,2014,76(1): 221-236.
    [7] SONG Qiankun, CAO Jinde, ZHAO Zhenjiang. Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays[J]. Nonlinear Analysis: Real World Applications,2006,7(1): 65-80.
    [8] BALASUBRAMANIAM P, VEMBARASAN V, RAKKIYAPPAN R. Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term[J]. Neural Computing and Applications,2012,21(7): 1593-1616.
    [9] SONG Qiankun, CAO Jinde. Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays[J]. Journal of Computational and Applied Mathematics,2006,197(1): 188-203.
    [10] ZHOU Liqun. Global asymptotic stability of cellular neural networks with proportional delays[J]. Nonlinear Dynamics,2014,77(1/2): 41-47.
    [11] ZHOU Liqun. Delay-dependent exponential stability of cellular neural networks with multi-proportional delays[J]. Neural Process Letters,2013,38(3): 347-359.
    [12] SONG Xueli, ZHAO Pan, XING Zhiwei, et al. Global asymptotic stability of CNNs with impulses and multi-proportional delays[J]. Mathematical Methods in the Applied Sciences,2016,39(4): 722-733.
    [13] YU Yuehua. Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays[J]. Neural Process Letters,2017,45(1): 141-151.
    [14] HIROSE A.Complex-Valued Neural Networks: Theories and Applications [M]. Singapore: World Scientific, 2003.
    [15] LEE D L. Relaxation of the stability condition of the complex-valued neural networks[J]. IEEE Transactions on Neural Networks,2001,12(5): 1260-1262.
    [16] RAO V, MURTHY G. Global dynamics of a class of complex valued neural networks[J]. International Journal of Neural Systems,2008,18(2): 165-171.
    [17] ZHOU Wei, ZURADA J. Discrete-time recurrent neural networks with complex-valued linear threshold neurons[J]. IEEE Transactions on Circuits and Systems II,2009,56(8): 669-673.
    [18] ZHOU Bo, SONG Qiankun. 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.
    [19] RAKKIYAPPAN R, VELMURUGAN G, LI Xiaodi. Complete stability analysis of complex-valued neural networks with time delays and impulses[J].Neural Processing Letters,2015,41(3): 435-468.
    [20] SONG Qiankun, YAN Huan, ZHAO Zhenjiang, et al. Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects[J]. Neural Networks,2016,79: 108-116.
    [21] SONG Qiankun, YAN Huan, ZHAO Zhenjiang, et al. Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays[J]. Neural Networks,2016,81: 1-10.
    [22] SONG Qiankun, ZHAO Zhenjiang. Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales[J].Neurocomputing,2016,171: 179-184.
    [23] CHEN Xiaofeng, ZHAO Zhenjiang, SONG Qiankun, et al. Multistability of complex-valued neural networks with time-varying delays[J]. Applied Mathematics and Computation,2017,294: 18-35.
    [24] ZHANG Lei, SONG Qiankun, ZHAO Zhenjiang. Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays[J]. Applied Mathematics and Computation,2017,298: 296-309.
    [25] MINC H. Nonnegative Matrices[M]. New York: John Wiley & Sons, 1988.
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出版历程
  • 收稿日期:  2017-09-14
  • 修回日期:  2017-09-14
  • 刊出日期:  2018-05-15

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