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