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

• Autores: Érika Diz Pita
• Directores de la Tesis: Jaume Llibre (dir. tes.), María Victoria Otero Espinar (dir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2022
• Idioma: inglés
• Tribunal Calificador de la Tesis: Chara Pantazi (presid.), Rosana Rodríguez López (secret.), Renato Colucci (voc.)
• Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad de Santiago de Compostela
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Ecuaciones diferenciales ordinarias
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • 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.