Convergence of asymptotic systems: applications toneural network and biological models with delays

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Convergence of asymptotic systems with unbounded delays with applications to Cohen-Grossberg neural networks and Lotka-Volterra systems

Publication . Elmwafy, Ahmed Osama Mohamed Sayed Sayed; Silva, César Augusto Teixeira Marques da; Oliveira, José Joaquim Martins

This thesis studies the dynamics of two prominent classes of models: Cohen-Grossberg neural network (CGNN) and Lotka-Volterra ecological systems. Firstly, we investigate 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 by applying the coincidence degree theorem. We use the main results to obtain criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic CGNN model with discrete-time varying delays and infinite distributed delays. Moreover, we study the convergence of asymptotic systems in nonautonomous CGNN models. We derive stability results under conditions where the non-delay terms asymptotically dominate the delay terms. In the second part, we explore Lotka–Volterra-type ecological models with delays. We investigate the concept of permanence of a general delay differential system and apply it to a general Lotka-Volterra type model. Moreover, we obtain a partial result on the convergence of the system to its asymptotic systems. Additionally, we provide a comparison with results in the literature and numerical examples to illustrate the effectiveness of some of our results.

2025-11-20Tese de doutoramento

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Palavras-chave

, Exact sciences ,Exact sciences/Mathematics

Entidade financiadora

Fundação para a Ciência e a Tecnologia, I.P.

Número da atribuição

UI/BD/151492/2021