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

In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincaré map. The results are used to obtain stability criteria for a general discrete-time neural network model with a delay in the leakage terms. As particular cases, we obtain new stability criteria for neural network models recently studied in the literature, in particular for low-order and high-order Hopfield and Bidirectional Associative Memory (BAM). • Global exponential stability criterion for a general delay difference system. • New method to prove global exponential stability of a delay difference system. • Existence of a periodic solution of a general delay difference system. • Exponential stability criteria for neural networks with delay in leakage terms. • Existence of periodic solution for neural networks with delay in the leakage terms. [ABSTRACT FROM AUTHOR]