On a second order differential equation with piecewise constant mixed arguments

Bereketoğlu, Hüseyin; Seyhan, Gizem; Karakoç, Fatma

doi:10.37193/cjm.2011.01.13

Cited by 10 publications

(1 citation statement)

References 18 publications

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“…DEPCAs are first considered by Shah and Wiener [39] in the 80's and have been developed by many authors; see [1,3,8,9,11,12,16,37,38]. Applications of DEPCA are discussed in [2,6,23,29].…”

Section: Introductionmentioning

confidence: 99%

Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks model with piecewise constant argument

CHİU

2022

Hacettepe Journal of Mathematics and Statistics

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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 Gronwall type with deviating argument. The criteria given are easily verifiable, possess many adjustable parameters, and depend on piecewise constant argument deviations, which provide flexibility for the design and analysis of Cohen-Grossberg neural networks model. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

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“…DEPCAs are first considered by Shah and Wiener [39] in the 80's and have been developed by many authors; see [1,3,8,9,11,12,16,37,38]. Applications of DEPCA are discussed in [2,6,23,29].…”

Section: Introductionmentioning

confidence: 99%

Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks model with piecewise constant argument

CHİU

2022

Hacettepe Journal of Mathematics and Statistics

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Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Chiu

2019

Mathematische Nachrichten

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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 corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed. New criteria extend and improve related results reported in the literature. The efficiency of our criteria is illustrated via several numerical examples and simulations.

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Oscillation of Second-Order Functional Differential Equations with Superlinear Neutral Terms

Özdemir

Kılıç

2021

Bull. Malays. Math. Sci. Soc.

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On a second order differential equation with piecewise constant mixed arguments

Cited by 10 publications

References 18 publications

Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks model with piecewise constant argument

Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks model with piecewise constant argument

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Oscillation of Second-Order Functional Differential Equations with Superlinear Neutral Terms

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