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Zbl 1094.34052
Huang, Chuangxia; Huang, Lihong; Yuan, Zhaohui
Global stability analysis of a class of delayed cellular neural networks. (English)
[J] Math. Comput. Simul. 70, No. 3, 133-148 (2005). ISSN 0378-4754

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.
[Miklavž Mastinšek (Maribor)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K13 Periodic solutions of functional differential equations
92B20 General theory of neural networks

Keywords: cellular neural network; exponential stability; periodic solution; Lyapunov functional; coincidence degree

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