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Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. (English) Zbl 1173.34343

Summary: Consider the following models for Hopfield neural networks (HNNs) with neutral delays:

x i ' (t)=-c i (t)x i (t)+ j=1 n a ij (t)f j (x j (t-τ ij (t)))+ j=1 n b ij (t)g j (x j ' (t-σ ij (t)))+I i (t),i=1,2,,n·

Some sufficient conditions for the existence and uniqueness of almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this work are new and complement previously known results.

MSC:
34K14Almost and pseudo-periodic solutions of functional differential equations
92B20General theory of neural networks (mathematical biology)
34K40Neutral functional-differential equations
47N20Applications of operator theory to differential and integral equations
References:
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