Exponential periodic attractor of impulsive Hopfield-type neural network system with piecewise constant argument

被引：14

作者：

Pinto, Manuel ^{[1
]}

Sepulveda, Daniel ^{[2
]}

Torres, Ricardo ^{[3
]}

机构：

[1] Univ Chile, Fac Ciencias, Dept Matemat, Santiago, Chile

[2] Univ Tecnol Metropolitana, Dept Matemat, Santiago, Chile

[3] Univ Austral Chile, Fac Ciencias, Inst Ciencias Fis & Matemat, Campus Isla Teja, Valdivia, Chile

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2018年 / 34期

关键词：

piecewise constant arguments; Cauchy and Green matrices; hybrid equations; stability of solutions; Gronwall's inequality; periodic solutions; impulsive differential equations; cellular neural networks; DELAY-DIFFERENTIAL-EQUATIONS; NUMERICAL APPROXIMATION; SEQUENCE SOLUTION; STABILITY; EXISTENCE; MODEL;

D O I：

10.14232/ejqtde.2018.1.34

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a periodic impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Under general conditions, existence and uniqueness of solutions of such systems are established using ergodicity, Green functions and Gronwall integral inequality. Some sufficient conditions for the existence and stability of periodic solutions are shown and a new stability criterion based on linear approximation is proposed. Examples with constant and nonconstant coefficients are simulated, illustrating the effectiveness of the results.

引用

页码：1 / 28

页数：28

共 59 条

[21] CELLULAR NEURAL NETWORKS - APPLICATIONS [J].

CHUA, LO ;

YANG, L .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (10) :1273-1290

[22] CELLULAR NEURAL NETWORKS - THEORY [J].

CHUA, LO ;

YANG, L .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (10) :1257-1272

[23]

COOKE KL, 1991, LECT NOTES MATH, V1475, P1

[24] RETARDED DIFFERENTIAL-EQUATIONS WITH PIECEWISE CONSTANT DELAYS [J].

COOKE, KL ;

WIENER, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 99 (01) :265-297

[25] NUMERICAL APPROXIMATION OF THE SOLUTIONS OF DELAY-DIFFERENTIAL EQUATIONS ON AN INFINITE INTERVAL USING PIECEWISE-CONSTANT ARGUMENTS [J].

COOKE, KL ;

GYORI, I .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1994, 28 (1-3) :81-92

[26] Dichotomies and asymptotic equivalence in alternately advanced and delayed differential systems [J].

Coronel, Anibal ;

Maulen, Christopher ;

Pinto, Manuel ;

Sepulveda, Daniel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 450 (02) :1434-1458

[27]

Dai L., 2008, Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments

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

Gopalsamy, K .

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

[29]

GOPALSAMY K, 1992, MATH ITS APPL, V0074, DOI DOI 10.1007/978-94-015-7920-9

[30] Global stability in a population model with piecewise constant arguments [J].

Gurcan, F. ;

Bozkurt, F. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (01) :334-342

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