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Sistemas dinámicos. Aplicaciones a las redes complejas


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Author: Álvarez-Rementería Rodríguez, Alberto
Director: Langa Rosado, José Antonio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2018
Document type: Final Degree Work
Academic Title: Universidad de Sevilla. Grado en Matemáticas
Abstract: This work is framed within the field of Dynamical System and their applicaitons to complex networks. In this text we investigate the existence of global attractors for ordinary differential systems and the existence of a Lyapunov function associated to a gradient-like system, semigroups or evolution processes. Because of that, a detailed study of Morse theory plays a central rule. The applicability of the results explained here is exemplified by studying the global attractor of an n-dimensional mutualistic model. We also study the structure of the attractor in mutualistic systems for which we will prove that it has a Morse decomposition describing all the future scenarios in this Ecological models.
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