Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

Chiu, Kuo-Shou

doi:10.1007/s10440-017-0108-3

Cited by 21 publications

(15 citation statements)

References 44 publications

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“…First, we prove the existence and uniqueness of solutions of the IDEGPCD system (4a)-(4b). A natural extension of the original definition of a solution of IDEPCA [9,11,37] allows us to define a solution of the IDEGPCD system. Definition 2.1.…”

Section: (L) Lipschitz Conditionmentioning

confidence: 99%

Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays

Chiu¹

2022

DCDS-B

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In this paper, the global exponential stability and periodicity are investigated for impulsive neural network models with Lipschitz continuous activation functions and generalized piecewise constant delay. The sufficient conditions for the existence and uniqueness of periodic solutions of the model are established by applying fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of impulsive neural network models with variable and/or deviating arguments. The results extend some previous results. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion.

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Section: (L) Lipschitz Conditionmentioning

confidence: 99%

Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays

Chiu¹

2022

DCDS-B

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“…So, the impulsive differential c 2020 Miskolc University Press equations with piecewise constant argument which are named by Wiener ([15]) in 1993 have been important. Recently, impulsive cellular neural networks models with piecewise constant argument have been studied in the papers ( [1], [4], [12]).…”

Section: Introductionmentioning

confidence: 99%

“…They gave several sufficient conditions for the exponential and global attractivity of the solution. [4] introduced the following impulsive cellular neural network models with piecewise alternately advanced and retarded argument. Some sufficient conditions were established for the existence and global exponential stability of a unique periodic solution.…”

Section: Introductionmentioning

confidence: 99%

Behavior of solutions of a nonlinear impulsive system with piecewise constant mixed arguments

Büyükkahraman¹,

Oztepe²,

Bereketoğlu³

2020

MMN

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“…Akhmet [18][19][20] generalized the concept of DEPCA by considering arbitrary piecewise constant functions as arguments; the proposed approach overcomes the limitations in the previously used method of study, namely reduction to discrete equations. Afterward, the results of the theory have been further developed [21,22] and applied for qualitative anal-ysis and control problem of real models, for example, in neural network models with or without impulsive perturbations [23][24][25][26][27][28][29][30][31][32][33], which have great significance in solving engineering and electronic problems.…”

Section: Introductionmentioning

confidence: 99%

Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type

2018

Adv Differ Equ

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In this paper, we focus on developing Razumikhin technique for stability analysis of impulsive differential equations with piecewise constant argument. Based on the Lyapunov-Razumikhin method and impulsive control theory, we obtain some Razumikhin-type theorems on uniform stability, uniform asymptotic stability, and global exponential stability, which are rarely reported in the literature. The significance and novelty of the results lie in that the stability criteria admit the existence of piecewise constant argument and impulses, which may be either slight at infinity or persistently large. Examples are given to illustrate the effectiveness and advantage of the theoretical results.

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Exponential Stability and Periodic Solutions of Impulsive Neural Network Models with Piecewise Constant Argument

Cited by 21 publications

References 44 publications

Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays

Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays

Behavior of solutions of a nonlinear impulsive system with piecewise constant mixed arguments

Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type

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