Silva, César Augusto Teixeira Marques daOliveira, José Joaquim MartinsElmwafy, Ahmed Osama Mohamed Sayed Sayed2026-01-082026-01-082025-11-20http://hdl.handle.net/10400.6/19646This 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.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 [...]engEquação Diferencial FuncionalRede Neural de Cohen-GrossbergModelo de Lotka-VolterraAtraso Não LimitadoSolução PeriódicaEstabilidadeConvergência de ModelosSistema AssintóticoFunctional Differential EquationCohen-Grossberg Neural NetworkLotka-Volterra ModelUnbounded DelayPeriodic SolutionStabilityConvergence of ModelsAsymptotic Systemdoctoral thesis101732066