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arXiv · 2211.04853

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
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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 Poincar\'e 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).

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António J. G. Bento, José J. Oliveira, César M. Silva. 2022-11-09. Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms. https://doi.org/10.1016/j.cnsns.2023.107429

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