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29

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Introduction

## Publications

Publications (29)

In this paper we investigate the existence of the periodic solutions of a quasilinear differential equation with piecewise constant argument of generalized type. By using some fixed point theorems and some new analysis technique, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these systems. A new Gronwa...

This paper is concerned with existence, uniqueness and global exponential stability of a periodic solution for recurrent neural network described by a system of differential equations with piecewise constant argument of generalized type (in short DEPCAG). The model involves both advanced and delayed arguments. Employing Banach fixed point theorem c...

We study scalar advanced and delayed differential equations with piecewise constant generalized arguments, in short DEPCAG of mixed type, that is, the arguments are general step functions. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the correspondi...

Bidirectional associative memories (BAMs) have been extensively applied in autoassociative and heteroassociative learning. However, the research on the implementation of BAM neural networks model with the effects of the constant delay is relatively few. The present work accumulates the global exponential stability criteria for the BAM neural networ...

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

In this paper, we investigate the models of the impulsive cellular neural network with piecewise alternately advanced and retarded argument of generalized argument (in short IDEPCAG). To ensure the existence, uniqueness and global ex- ponential stability of the equilibrium state, several new sufficient conditions are obtained. The method is based o...

This work presents a mathematical model that assumes the existence of an animal population that, from an epidemiological point of view, is being affected by an infectious disease of the SIR type and, from an ecological perspective, its habitat is in a gradual process of fragmentation. We make a first approximation to its dynamic behavior through gr...

In this paper, we introduce a Cohen-Grossberg neural networks model with piecewise alternately advanced and retarded argument.
Some sufficient conditions are established for the existence and global exponential stability of periodic solutions.
The approaches are based on employing Brouwer's fixed-point theorem and an integral inequality of Gronwa...

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 an...

We investigate the existence of the periodic solutions of a quasilinear impulsive differential equation with alternately advanced and retarded arguments of generalized type, in short IDEPCAG. By using some fixed point theorems and some new analysis techniques, sufficient conditions are obtained for the existence and uniqueness of periodic solutions...

In this paper, the global exponential stability and periodicity are investigated for impulsive neural network models with Lipschitz continuous activation functions and piecewise alternately advanced and retarded argument of generalized argument (in short IDEPCAG). The sufficient conditions for the existence and uniqueness of periodic solutions of t...

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is base...

This article is concerned with the effects of piecewise constant argument on exponential stability to a unique equilibrium state of bidirectional associative memories (BAMs) neural networks model. Based on the fixed point theorem approach and an integral inequality of Gronwall type with deviation arguments, we have derived sufficient criteria to gu...

The main goal of our paper is to obtain sufficient conditions for the asymptotic equivalence of a linear differential system and a quasilinear system of impulsive differential equations with piecewise constant argument of generalized type, in short IDEPCAG. A deviating argument is of the advanced and delayed type. As an auxiliary result, the struct...

In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach’s fixed point theorem and the...

In this paper we employ the method of maximal and minimal solutions coupled with comparison principles and the monotone iterative technique to obtain results of existence and approximation of solutions for differential equations with piecewise constant delay of generalized type (DEPCAG).

In this paper we investigate the existence of the periodic solutions of a nonlinear differential equation with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence...

We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of the conclusions.

We study the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations on time scales by employing Krasnoselskii’s fixed point theorem. Two examples are given to illustrate the significance of the conclusions.

In this paper, we investigate the existence, uniqueness and the asymptotic equivalence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a...

In this paper we introduce an impulsive cellular neural network models with piecewise alternately advanced and retarded argument. The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique periodic solution. The approaches are bas...

A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained. They include existence and...

We examine scalar differential equations with general piecewise constant arguments of mixed type, in short DEPCAG of mixed type, that is, the arguments are general step functions. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero soluti...

We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic soluti...

We examine scalar differential equations with a general piecewise constant argument (DEPCAG). It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of su...

We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on...

We examine scalar differential equations with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Appropriate...

A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general
piecewise alternately advanced and retarded argument.
Keywordsvariation of parameters formula–Gronwall integral inequality–alternately advanced and retarded argument