Stability and synchronization of fractional-order memristive neural networks with multiple delays

被引：101
作者：
Chen, Liping [1 ]
Cao, Jinde [2 ]
Wu, Ranchao [3 ]
Tenreiro Machado, J. A. [4 ]
Lopes, Antonio M. [5 ]
Yang, Hejun [1 ]
机构：
[1] Hefei Univ Technol, Sch Elect Engn & Automat, Hefei 230009, Anhui, Peoples R China
[2] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
[3] Anhui Univ, Sch Math, Hefei 230601, Anhui, Peoples R China
[4] Polytech Porto, Dept Elect Engn, Inst Engn, R Dr Antonio Bernardino de Almeida 431, P-4249015 Oporto, Portugal
[5] Univ Porto, Fac Engn, UISPA LAETA INEGI, Rua Dr Roberto Frias, P-4200465 Oporto, Portugal
来源：
NEURAL NETWORKS | 2017年 / 94卷
基金：
中国国家自然科学基金;
关键词：
Fractional-order systems; Memristor-based neural networks; Stability; Synchronization; Multiple delays; FINITE-TIME SYNCHRONIZATION; GLOBAL EXPONENTIAL SYNCHRONIZATION; PROJECTIVE SYNCHRONIZATION; ANTI-SYNCHRONIZATION; LAGRANGE STABILITY; DISCRETE; SYSTEMS;
D O I：
10.1016/j.neunet.2017.06.012
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The paper presents theoretical results on the global asymptotic stability and synchronization of a class of fractional-order memristor-based neural networks (FMNN) with multiple delays. First, the asymptotic stability of fractional-order (FO) linear systems with single or multiple delays is discussed. Delay-independent stability criteria for the two types of systems are established by using the maximum modulus principle and the spectral radii of matrices. Second, new testable algebraic criteria for ensuring the existence and global asymptotic stability of the system equilibrium point are obtained by employing the Kakutani's fixed point theorem of set-valued maps, the comparison theorem, and the stability criterion for FO linear systems with multiple delays. Third, the synchronization criterion for FMNN is presented based on the linear error feedback control. Finally, numerical examples are given demonstrating the effectiveness of the proposed results. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：76 / 85
页数：10
相关论文
共 51 条
[1]   Finite-time synchronization for memristor-based neural networks with time-varying delays [J].
Abdurahman, Abdujelil ;
Jiang, Haijun ;
Teng, Zhidong .
NEURAL NETWORKS, 2015, 69 :20-28
[2]   Memristor Bridge Synapse-Based Neural Network and Its Learning [J].
Adhikari, Shyam Prasad ;
Yang, Changju ;
Kim, Hyongsuk ;
Chua, Leon O. .
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2012, 23 (09) :1426-1435
[3]   A priori estimates for solutions of boundary value problems for fractional-order equations [J].
Alikhanov, A. A. .
DIFFERENTIAL EQUATIONS, 2010, 46 (05) :660-666
[4]  
Aubin JP., 1990, SET VALUED ANAL
[5]  
Aubin JP., 1984, Differential Inclusions: Set Valued Maps and Viability Theory
[6]   Projective synchronization of fractional-order memristor-based neural networks [J].
Bao, Hai-Bo ;
Cao, Jin-De .
NEURAL NETWORKS, 2015, 63 :1-9
[7]   Adaptive synchronization of fractional-order memristor-based neural networks with time delay [J].
Bao, Haibo ;
Park, Ju H. ;
Cao, Jinde .
NONLINEAR DYNAMICS, 2015, 82 (03) :1343-1354
[8]   Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay [J].
Bao, Haibo ;
Park, Ju H. ;
Cao, Jinde .
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2016, 27 (01) :190-201
[9]   Stability regions for fractional differential systems with a time delay [J].
Cermak, Jan ;
Hornicek, Jan ;
Kisela, Tamas .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 31 (1-3) :108-123
[10]   Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks [J].
Chen, Jiejie ;
Zeng, Zhigang ;
Jiang, Ping .
NEURAL NETWORKS, 2014, 51 :1-8
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