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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
\[ x_i'(t)= -c_i(t) x_i(t)+ \sum^n_{j=1} a_{ij}(t) f_j(x_j(t))+ \sum^n_{j=1} b_{ij}(t) f_j(x_j(t- \tau_{ij}(t)))+ I_i(t),\;i= 1,2,\dots,n, \]
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.

MSC:

34K20 Stability theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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References:

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