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Discrete analogues of continuous-time neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable coefficients and multiple delays is investigated. By Lyapunov functional, continuation theorem of topological degree, inequality technique and matrix analysis, sufficient conditions guaranteeing the existence and globally exponential convergence of periodic solutions are obtained, without assuming the boundedness and differentiability of activation functions. To show the effectiveness of our method, an illustrative example is presented along with numerical simulations. MSC: 34D23, 34K20, 39A12, 92B20. © 2013 Xu and Wu; licensee Springer.

Periodicity and exponential stability of discrete-time neural networks with variable coefficients and delays