Stability analysis of recurrent neural networks with piecewise constant argument of generalized type

被引：57
作者：
Akhmet, M. U. [1 ]
Arugaslan, D. [3 ]
Yilmaz, E. [2 ]
机构：
[1] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey
[2] Middle E Tech Univ, Inst Appl Math, TR-06531 Ankara, Turkey
[3] Suleyman Demirel Univ, Dept Math, TR-32260 Isparta, Turkey
来源：
NEURAL NETWORKS | 2010年 / 23卷 / 07期
关键词：
Neural networks; Piecewise constant argument of generalized type; Method of Lyapunov functions; GLOBAL EXPONENTIAL STABILITY; TIME-VARYING DELAYS; DIFFERENTIAL-EQUATIONS; ASYMPTOTIC STABILITY; PERIODIC-SOLUTIONS; TRAVELING-WAVES;
D O I：
10.1016/j.neunet.2010.05.006
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：805 / 811
页数：7
相关论文
共 56 条
[11]  
[Anonymous], 2006, Proceedings of the Conference on Differential and Difference Equations at the Florida Institute of Technology, Melbourne, Florida, 1-5 August 2005
[12]   An analysis of global asymptotic stability of delayed cellular neural networks [J].
Arik, S .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 2002, 13 (05) :1239-1242
[13]   Frustration, stability, and delay-induced oscillations in a neural network model [J].
Belair, J ;
Campbell, SA ;
VandenDriessche, P .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1996, 56 (01) :245-255
[14]   MECHANISM OF RHYTHMIC SYNCHRONOUS FLASHING OF FIREFLIES [J].
BUCK, J ;
BUCK, E .
SCIENCE, 1968, 159 (3821) :1319-&
[15]   Global asymptotic stability of neural networks with transmission delays [J].
Cao, JD .
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2000, 31 (10) :1313-1316
[16]   Global stability conditions for delayed CNNs [J].
Cao, J. .
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2001, 48 (11) :1330-1333
[17]   On stability of delayed cellular neural networks [J].
Cao, JD .
PHYSICS LETTERS A, 1999, 261 (5-6) :303-308
[18]   Global exponential stability of delayed Hopfield neural networks [J].
Chen, TP .
NEURAL NETWORKS, 2001, 14 (08) :977-980
[19]   Exponential convergence of delayed dynamical systems [J].
Chen, TP ;
Amari, S .
NEURAL COMPUTATION, 2001, 13 (03) :621-635
[20]  
Chua L.O., 1998, CNN: A Paradigm for Complexity, V31
123456