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Global stability and existence of periodic solutions of discrete delayed cellular neural networks. (English) Zbl 1123.39302

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 +θ i (h) j=1 m a ij (n)f j (x j (n))+θ i (h) j=1 m b ij (n)f j (x j (n-τ ij (n)))+θ i (h)I i (n)·
i=1,2,,m·

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:
39A11Stability of difference equations (MSC2000)
37N25Dynamical systems in biology
82C32Neural nets (statistical mechanics)