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Estudio y comparación de diversos modelos de depredador-presa


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Author: Gálvez García, Miriam
Director: Suárez Fernández, Antonio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2018-06-20
Document type: Final Degree Work
Academic Title: Universidad de Sevilla. Grado en Matemáticas
Abstract: In this work we study different population models of ordinary differential equations of one and two species, respectively. In particular, we study in detail the prey-predator Lotka-Volterra model. We compare the behavior of the species in the Lotka-Volterra model and in different variants of that system. An outline of this work is as follows: in Chapter 2 we describe the different population models and show its corresponding behavior. In Chapter 3, we study theoretically the original model of Lotka-Volterra, where its stationary points, trajectories and the local stability of such model are analyzed. In Chapter 4, we study the Lotka-Volterra logistic model. We analyze the existence and uniqueness of solutions for system, stationary points and their local and global stability. Finally, in Chapter 5 we make numerical simulations related to the previous chapters and show the difference between the classic Lotka-Volterra model and some of its variants.
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