Existence and exponential stability of a periodic solution of an infinite delay differential system with applications to Cohen-Grossberg neural networks

• Main Author: Elmwafy, Ahmed
• Publication Date: 2024
• Other Authors: Oliveira, José J., Silva, César M.
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: https://hdl.handle.net/1822/91922
• topic: Cohen-Grossberg neural network; Periodic solution; Global exponential stability; Coincidence degree theorem; Discrete and distributed delays; Ciências Naturais::Matemáticas

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincidence degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen-Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and two numerical examples to illustrate the effectiveness of some of our results.