RT Dissertation/Thesis
T1 Qualitative dynamics of planar and spatial Lotka-Volterra and Kolmogorov systems
A1 Diz Pita, Érika
K1 Lotka-Volterra system
K1 Kolmogorov system
K1 phase portrait
K1 Poincaré disk
K1 population dynamics
AB 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.
YR 2022
FD 2022
LK http://hdl.handle.net/10347/29268
UL http://hdl.handle.net/10347/29268
LA eng
DS Minerva
RD 26 abr 2026