Publicação
Convergence of asymptotic systems with unbounded delays with applications to Cohen-Grossberg neural networks and Lotka-Volterra systems
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| dc.contributor.advisor | Silva, César Augusto Teixeira Marques da | |
| dc.contributor.advisor | Oliveira, José Joaquim Martins | |
| dc.contributor.author | Elmwafy, Ahmed Osama Mohamed Sayed Sayed | |
| dc.date.accessioned | 2026-01-08T11:28:27Z | |
| dc.date.available | 2026-01-08T11:28:27Z | |
| dc.date.issued | 2025-11-20 | |
| dc.description.abstract | 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. | eng |
| dc.description.abstract | Esta tese estuda a dinâmica de duas classes proeminentes de modelos: modelos de redes neurais de Cohen-Grossberg e sistemas ecológicos de Lotka-Volterra. Na primeira parte da tese, fornecemos condições suficientes para a estabilidade exponencial global e a existência de uma solução periódica do seguinte sistema diferencial geral com atrasos distribuídos sem limites Cohen-Grossberg de ordem superior com atrasos discretos e distribuídos não necessariamente limitados [...] | por |
| dc.identifier.tid | 101732066 | |
| dc.identifier.uri | http://hdl.handle.net/10400.6/19646 | |
| dc.language.iso | eng | |
| dc.relation | Convergence of asymptotic systems: applications toneural network and biological models with delays | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.subject | Equação Diferencial Funcional | |
| dc.subject | Rede Neural de Cohen-Grossberg | |
| dc.subject | Modelo de Lotka-Volterra | |
| dc.subject | Atraso Não Limitado | |
| dc.subject | Solução Periódica | |
| dc.subject | Estabilidade | |
| dc.subject | Convergência de Modelos | |
| dc.subject | Sistema Assintótico | |
| dc.subject | Functional Differential Equation | |
| dc.subject | Cohen-Grossberg Neural Network | |
| dc.subject | Lotka-Volterra Model | |
| dc.subject | Unbounded Delay | |
| dc.subject | Periodic Solution | |
| dc.subject | Stability | |
| dc.subject | Convergence of Models | |
| dc.subject | Asymptotic System | |
| dc.title | Convergence of asymptotic systems with unbounded delays with applications to Cohen-Grossberg neural networks and Lotka-Volterra systems | por |
| dc.type | doctoral thesis | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Convergence of asymptotic systems: applications toneural network and biological models with delays | |
| oaire.awardURI | http://hdl.handle.net/10400.6/19645 | |
| person.familyName | Elmwafy | |
| person.givenName | Ahmed Osama Mohamed Sayed Sayed | |
| person.identifier.ciencia-id | 8912-B076-200B | |
| person.identifier.gsid | https://scholar.google.com/citations?user=FAKjcmAAAAAJ&hl=en | |
| person.identifier.orcid | 0000-0001-5810-5401 | |
| relation.isAuthorOfPublication | 7c24bd85-3a16-40df-921d-856bf88b62b8 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7c24bd85-3a16-40df-921d-856bf88b62b8 | |
| relation.isProjectOfPublication | 170b8a68-d4c2-4442-9690-16ff8452b0d6 | |
| relation.isProjectOfPublication.latestForDiscovery | 170b8a68-d4c2-4442-9690-16ff8452b0d6 | |
| thesis.degree.name | Doutoramento em Matemática e Aplicações |