Modelos presa-predador: muito além do Lotka-Volterra

• Ano de defesa: 2024
• Autor(a) principal: Strapazzon, Fernando Luis
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Matemática; UFSM; Programa de Pós-Graduação em Matemática; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Presa-presador; Moldelo Lotka-Volterra; Resposta funcional; Bifurcações; Predator-prey; Lotka-Volterra model; Functional response; Bifurcation; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/33475

Mathematical models have played a very important role in the study of population interations. This dissertation presents a review of prey-predator models that consider specialist predators and logistic growth for prey. Five models are analyzed: Lotka-Volterra, modified Lotka-Volterra, Rosenweig-MacArthur, Freedman and Wolkowicz and DeAngelis. Each of them addresses peculiar modifications that are analyzed qualitatively in order to elucidate the dynamics of the models. For the qualitative analysis, some techniques are used, such as the non-dimensionalization of the systems, determination of equilibrium solutions and their stabilities, as well as possible bifurcations. With the help of Python, numerical solutions of the models are obtained, illustrated through the phase plane.