Planar Kolmogorov systems with infinitely many singular points at infinity

Abstract

Altres ajuts: Consellería de Educación, Universidade e Formación Profesional (Xunta de Galicia), grant ED431C 2019/10

We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the topological classification of their phase portraits in the Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.