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Global stability analysis of a class of delayed cellular neural networks. (English) Zbl 1094.34052

The authors consider the exponential stability and the existence of periodic solutions of delayed cellular neural networks described by

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

in which n corresponds to the number of units in a neural network. Employing Brouwer’s fixed-point theorem, sufficient conditions for global exponential stability and the existence of periodic solutions are obtained. Two examples which illustrate the results are given.

34K20Stability theory of functional-differential equations
34K13Periodic solutions of functional differential equations
92B20General theory of neural networks (mathematical biology)