Modelos presa-predador: dinâmica e bifurcações

• Ano de defesa: 2019
• Autor(a) principal: Estrada, Edith Janeth Potosí
• Orientador(a): Medrado, João Carlos da Rocha
• Banca de defesa: Medrado, João Carlos da Rocha, Andrade, Kamila da Silva, Tonon, Durval José, Larrosa, Juliana Fernandes
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/38995/0013000002p6k
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
• Departamento: Instituto de Matemática e Estatística - IME (RG)
• País: Brasil
• Palavras-chave em Português: Sistemas dinâmicos; Sistemas de Filippov; Modelos presa-predador; Colheita do predador; Análise de estabilidade
• Palavras-chave em Inglês: Dynamic systems; Filippov systems; Predator-prey models; Harvesting of the predator; Stability analysis
• Área do conhecimento CNPq: GEOMETRIA E TOPOLOGIA::SISTEMAS DINAMICOS
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/9451

In this work we study some classic bifurcations of smooth and piecewise smooth systems that appear naturally in predator-prey systems. In the theoretical part, we study the normal forms of each bifurcation and make a description of its bifurcation diagrams. In the application part we study three predator-prey models, the first model is the traditional Lotka-Volterra model where the necessary conditions for the existence of equilibrium points are shown and the existence of limit cycles is studied; the second model differs from the first one because it has non-linear harvesting in the predator population and the existence of the bifurcations of the saddle-node, Hopf and Bogdanov-Takens is proved, as well as some numerical simulations to observe the effect of the variation of the harvest parameter; finally, the third model, which makes the change from one model to another from an economic threshold, we perform a stability analysis accordingly to the bifurcation curves and a numerical experiment where the emergence of the bifurcations can be visualized.