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In this paper, a new global exponential stability criterion is obtained for ageneral multidimensional delay difference equation using induction arguments.In the cases that the difference equation is periodic, we prove the existenceof a periodic solution by constructing a type of Poincar\'e map. The resultsare used to obtain stability criteria for a general discrete-time neuralnetwork model with a delay in the leakage terms. As particular cases, we obtainnew stability criteria for neural network models recently studied in theliterature, in particular for low-order and high-order Hopfield andBidirectional Associative Memory(BAM).

communications in nonlinear science and numerical simulation/communications in nonlinear science and numerical simulation

Existence and stability of a periodic solution of a general difference  equation with applications to neural networks with a delay in the leakage  terms