Trabajo Fin de Grado
Sistemas dinámicos. Aplicaciones a las redes complejas
Autor/es | Álvarez-Rementería Rodríguez, Alberto |
Director | Langa Rosado, José Antonio |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2018 |
Fecha de depósito | 2018-07-23 |
Titulación | Universidad de Sevilla. Grado en Matemáticas |
Resumen | 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 ... 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. |
Cita | Álvarez-Rementería Rodríguez, A. (2018). Sistemas dinámicos. Aplicaciones a las redes complejas. (Trabajo Fin de Grado Inédito). Universidad de Sevilla, Sevilla. |
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