Planar Kolmogorov systems with infinitely many singular points at infinity
Dynamical Systems
2025-01-27 v1
Abstract
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems \begin{equation*} \begin{split} \dot{y}&=y \left( b_0+ b_1 y z + b_2 y + b_3 z\right), \dot{z}&=z\left( c_0 + b_1 y z + b_2 y + b_3 z\right), \end{split} \end{equation*} which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at inifnity. We give the topological classification of their phase portraits in the Poincar\'e disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.
Cite
@article{arxiv.2501.14416,
title = {Planar Kolmogorov systems with infinitely many singular points at infinity},
author = {Érika Diz-Pita and Jaume Llibre and M. Victoria Otero-Espinar},
journal= {arXiv preprint arXiv:2501.14416},
year = {2025}
}