Global stability and existence of periodic solutions of discrete delayed cellular neural networks

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(-bi(n)h) + theta(i)(h) Sigma(j=1)(m) a(ij)(n)f(j)(x(j)(n)) + theta(i)(h) Sigma(j=1)(m) b(ij)(n)f(j)(x(j)(n - tau(ij)(n))) + theta(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. (C) 2004 Elsevier B.V. All rights reserved.