Multiple Mittag-Leffler Stability of Fractional-Order Recurrent Neural Networks

被引：186
作者：
Liu, Peng [1 ,2 ,3 ]
Zeng, Zhigang [1 ,3 ]
Wang, Jun [4 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Automat, Wuhan 430074, Hubei, Peoples R China
[2] Wuhan Inst Technol, Sch Elect & Informat Engn, Wuhan 430205, Hubei, Peoples R China
[3] Educ Minist China, Key Lab Image Proc & Intelligent Control, Wuhan 430074, Hubei, Peoples R China
[4] City Univ Hong Kong, Dept Comp Sci, Coll Sci & Engn, Hong Kong, Hong Kong, Peoples R China
来源：
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS | 2017年 / 47卷 / 08期
关键词：
Fractional-order recurrent neural networks; Mittag-Leffler stability; multistability; ACTIVATION FUNCTIONS; SYNCHRONIZATION; MULTISTABILITY; EXISTENCE;
D O I：
10.1109/TSMC.2017.2651059
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, coexistence and stability of multiple equilibrium points of fractional-order recurrent neural networks are addressed. Several sufficient conditions are derived for ascertaining the existence of Pi(n)(i = 1)(2K(i) + 1) equilibrium points (K-i >= 0) and the local Mittag-Leffler stability of Pi(n)(i = 1)(K-i + 1) equilibrium points of them by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. In contrast with many existing results, the derived results cover both mono-stability and multistability, and the activation functions herein could be nonmonotonic and nonlinear in any open interval. In addition, three numerical examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.
引用
收藏
页码：2279 / 2288
页数：10
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    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2013, 60 (02) : 189 - 193
  • [42] Robust Synchronization of Multiple Memristive Neural Networks With Uncertain Parameters via Nonlinear Coupling
    Yang, Shaofu
    Guo, Zhenyuan
    Wang, Jun
    [J]. IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, 2015, 45 (07): : 1077 - 1086
  • [43] Transmissive color filtering using plasmonic multilayer structure
    Yu, Chih-Jui
    Liang, Yi-Ping
    Hong, Hwen-Fen
    Wang, Chih-Ming
    [J]. OPTICAL ENGINEERING, 2012, 51 (04)
  • [44] Projective synchronization for fractional neural networks
    Yu, Juan
    Hu, Cheng
    Jiang, Haijun
    Fan, Xiaolin
    [J]. NEURAL NETWORKS, 2014, 49 : 87 - 95
  • [45] α-stability and α-synchronization for fractional-order neural networks
    Yu, Juan
    Hu, Cheng
    Jiang, Haijun
    [J]. NEURAL NETWORKS, 2012, 35 : 82 - 87
  • [46] Stability analysis of delayed cellular neural networks described using cloning templates
    Zeng, ZG
    Wang, J
    Liao, XX
    [J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2004, 51 (11) : 2313 - 2324
  • [47] Analysis and design of associative memories based on recurrent neural networks with linear saturation activation functions and time-varying delays
    Zeng, Zhigang
    Wang, Jun
    [J]. NEURAL COMPUTATION, 2007, 19 (08) : 2149 - 2182
  • [48] Mittag-Leffler stability of fractional-order Hopfield neural networks
    Zhang, Shuo
    Yu, Yongguang
    Wang, Hu
    [J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2015, 16 : 104 - 121
  • [49] On electromagnetic wave propagation in fractional space
    Zubair, M.
    Mughal, M. J.
    Naqvi, Q. A.
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (05) : 2844 - 2850
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