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Zbl 1123.39302
Li, Yongkun
Global stability and existence of periodic solutions of discrete delayed cellular neural networks. (English)
[J] Phys. Lett., A 333, No. 1-2, 51-61 (2004). ISSN 0375-9601

Summary: We use the continuation theorem of coincidence degree theory and Lyapunov functions to study the existence and stability of periodic solutions for the discrete cellular neural networks (CNNs) with delays $$x_i(n+1)=x_i (n) e^{-b_i(n)h}+ \theta_i(h) \sum^m_{j=1} a_{ij}(n)f_j(x_j(n))+\theta_i(h)\sum ^m_{j=1} b_{ij}(n)f_j (x_j(n-\tau_{ij}(n))) + \theta_i(h)I_i(n).$$ $$i = 1,2,\cdots, m.$$ \par We obtain some sufficient conditions to ensure that for the networks there exists a unique periodic solution, and all its solutions converge to such a periodic solution.

MSC 2000:: *39A11 Stability of difference equations
37N25 Dynamical systems in biology
82C32 Neural nets

Keywords: discrete cellular neural networks; delay; periodic solution; stability; coincidence degree

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