Impulsive Hopfield-type neural network system with piecewise constant argument

被引：47

作者：

Akhmet, M. U. ^{[1
,2
]}

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

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 04期

关键词：

Impulsive differential equations; Hopfield neural networks; Piecewise constant argument; Equilibrium; Asymptotic stability; Periodic solutions; DIFFERENTIAL-EQUATIONS; GENERALIZED TYPE; STABILITY; OSCILLATORS;

D O I：

10.1016/j.nonrwa.2009.09.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2584 / 2593

页数：10

共 20 条

[1] Continuous-time additive Hopfield-type neural networks with impulses [J].

Akça, H ;

Alassar, R ;

Covachev, V ;

Covacheva, Z ;

Al-Zahrani, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 290 (02) :436-451

[2] Stability of differential equations with piecewise constant arguments of generalized type [J].

Akhmet, M. U. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (04) :794-803

[3] On the reduction principle for differential equations with piecewise constant argument of generalized type [J].

Akhmet, M. U. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (01) :646-663

[4] Integral manifolds of differential equations with piecewise constant argument of generalized type [J].

Akhmet, M. U. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (02) :367-383

[5] LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT [J].

Akhmet, Marat ;

Arugaslan, Duygu .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (02) :457-466

[6]

[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892

[7]

[Anonymous], 1989, THEORY IMPULSIVE DIF

[8] OSCILLATOR DEATH IN SYSTEMS OF COUPLED NEURAL OSCILLATORS [J].

ERMENTROUT, GB ;

KOPELL, N .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1990, 50 (01) :125-146

[9] Stability of artificial neural networks with impulses [J].

Gopalsamy, K .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) :783-813

[10] On impulsive autoassociative neural networks [J].

Guan, ZH ;

Lam, J ;

Chen, GR .

NEURAL NETWORKS, 2000, 13 (01) :63-69

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