Publicação
Convergence of asymptotic systems with unbounded delays with applications to Cohen-Grossberg neural networks and Lotka-Volterra systems
| Resumo: | 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. |
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| Autores principais: | Elmwafy, Ahmed Osama Mohamed Sayed Sayed |
| Assunto: | Equação Diferencial Funcional Rede Neural de Cohen-Grossberg Modelo de Lotka-Volterra Atraso Não Limitado Solução Periódica Estabilidade Convergência de Modelos Sistema Assintótico Functional Differential Equation Cohen-Grossberg Neural Network Lotka-Volterra Model Unbounded Delay Periodic Solution Stability Convergence of Models Asymptotic System |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade da Beira Interior |
| Idioma: | inglês |
| Origem: | uBibliorum |
| Resumo: | 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. |
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