Global O(t-α) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays

被引：47
作者：
Chen, Boshan [1 ]
Chen, Jiejie [1 ,2 ,3 ]
机构：
[1] Hubei Normal Univ, Coll Math & Stat, Huangshi 435002, Hubei, Peoples R China
[2] Huazhong Univ Sci & Technol, Sch Automat, Wuhan 430074, Peoples R China
[3] Minist China, Key Lab Image Proc & Intelligent Control Educ, Wuhan 430074, Peoples R China
来源：
NEURAL NETWORKS | 2016年 / 73卷
关键词：
Fractional-order neural networks; Time-varying delays; Global O(t(-alpha)) stability; S-asymptotically periodic solution; Globally S-asymptotic periodicity; EXPONENTIAL STABILITY; DIFFERENTIAL-EQUATIONS; CHAOS; EXISTENCE; SYNCHRONIZATION; DYNAMICS; CALCULUS; SYSTEMS;
D O I：
10.1016/j.neunet.2015.09.007
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The present paper studies global O(t(-alpha)) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays (FDNN). Firstly, some sufficient conditions are established to ensure that a non-autonomous FDNN is global O(t(-alpha)) stable based on a new Lyapunov function method and Leibniz rule for fractional differentiation. Next it is shown that the periodic or autonomous FDNN cannot generate exactly nonconstant periodic solution under any circumstances. Finally, we show that all solutions converge to a same periodic function for a periodic FDNN by using a fractional-order differential inequality technique. Our issues, methods and results are all new. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：47 / 57
页数：11
相关论文
共 54 条
[1]   Existence and Uniqueness of Pseudo Almost-Periodic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays [J].
Ammar, Boudour ;
Cherif, Farouk ;
Alimi, Adel M. .
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2012, 23 (01) :109-118
[2]  
[Anonymous], 1993, INTRO FRACTIONAL CA
[3]  
[Anonymous], 1987, FRACTIONAL INTEGRALS
[4]   Chaotic behavior in noninteger-order cellular neural networks [J].
Arena, P ;
Fortuna, L ;
Porto, D .
PHYSICAL REVIEW E, 2000, 61 (01) :776-781
[5]   Bifurcation and chaos in noninteger order cellular neural networks [J].
Arena, P ;
Caponetto, R ;
Fortuna, L ;
Porto, D .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1998, 8 (07) :1527-1539
[6]   Projective synchronization of fractional-order memristor-based neural networks [J].
Bao, Hai-Bo ;
Cao, Jin-De .
NEURAL NETWORKS, 2015, 63 :1-9
[7]  
Boroomand A, 2009, LECT NOTES COMPUT SC, V5506, P883, DOI 10.1007/978-3-642-02490-0_108
[8]   Calculation of the tensile and flexural strength of disordered materials using fractional calculus [J].
Carpinteri, A ;
Cornetti, P ;
Kolwankar, KM .
CHAOS SOLITONS & FRACTALS, 2004, 21 (03) :623-632
[9]   Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays [J].
Chen, Boshan ;
Wang, Jun .
NEURAL NETWORKS, 2007, 20 (10) :1067-1080
[10]   Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks [J].
Chen, Boshan ;
Chen, Jiejie .
NEURAL NETWORKS, 2015, 68 :78-88
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