Qualitative dynamics of planar and spatial Lotka-Volterra and Kolmogorov systems

  1. Diz Pita, Érika
Dirixida por:
  1. Jaume Llibre Director
  2. María Victoria Otero Espinar Director

Universidade de defensa: Universidade de Santiago de Compostela

Fecha de defensa: 08 de xullo de 2022

Tribunal:
  1. Chara Pantazi Presidente/a
  2. Rosana Rodríguez López Secretaria
  3. Renato Colucci Vogal
Departamento:
  1. Departamento de Estatística, Análise Matemática e Optimización

Tipo: Tese

Teseo: 738236 DIALNET

Resumo

Ordinary differential equations are an important tool for the study of many real problems. In this thesis we focus in the qualitative dynamics of some ordinary differential systems, particularly, the Lotka-Volterra and Kolmogorov systems. We accomplish the study of some Lotka-Volterra systems on dimension three, which we characterize in two families of planar Kolmogorov systems. We give the complete classification of the global phase portraits in the Poincaré disk for those families. We also analyze the limit cycles of the three-dimensional Kolmogorov systems of degree three which appear through a zero-Hopf bifurcation. Some particular systems that model real problems in the field of population dynamics are also studied.