Stability in cellular neural networks with a piecewise constant argument

Authors:
M. U. Akhmet;D. Aruğaslan;E. Yılmaz
Affiliations:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey;Department of Mathematics, Süleyman Demirel University, 32260, Isparta, Turkey;Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.