Phase portraits of a family of Kolmogorov systems with infinitely many singular points at infinity

We give the topological classification of the global phase portraits in the Poincare disc of the Kolmogorov systems x = x z = z (a0 + c1x + c2z2 + c3z) , (c0 + c1x + c2z2 + c3z) , which depend on five parameters and have infinitely many singular points at the infinity. We prove that these systems have 22 topologically distinct phase portraits. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study provided a topological classification of the global phase portraits of Kolmogorov systems in the Poincare disc, revealing a total of 22 topologically distinct phase portraits.