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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stability of Hopfield Neural Networks with Delay and Piecewise Constant Argument

Discontinuity, Nonlinearity, and Complexity 5(1) (2016) 33--42 | DOI:10.5890/DNC.2016.03.005

M.U. Akhmet; M. Karacaören

Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

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Abstract

In this paper, by using the concept of differential equations with piecewise constant argument, the model of Hopfield neural networks with constant delay is developed. Sufficient conditions for the existence of an equilibrium as well as its global exponential stability by means of Lyapunov functionals and a linear matrix inequality (LMI) are obtained. An example is given to illustrate our results.

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