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

António J. G. Bento; José J. Oliveira; César M. Silva

doi:10.1016/j.cnsns.2023.107429

paper

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

arXiv:2211.04853 · doi:10.1016/j.cnsns.2023.107429

Abstract

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).

20 pages, 3 figures