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

Abstract

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.

Keywords

• Cohen-Grossberg neural networks model
• piecewise constant argument
• periodic solutions
• global exponential stability
• Gronwall integral inequality

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