Nonuniform behavior and stability of Hopfield neural networks with delay

2015/04/16 by António J. G. Bento, Bento, António J. G., José J. Oliveira +3
Mathematics · #39A23 #39A30 #92B20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:39A23 #msc:39A30 #msc:92B20

paper · pdf · doi:10.48550/arxiv.1504.04318

arxiv created 2015/04/16 · arxiv updated 2015/04/17

Abstract

We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some conditions to control the nonlinear part of the equations. We then apply this result to improve some existent results on the stability of Hopfield models. Our results are based on a new abstract result on the behavior of nonautonomous delayed equations.

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