Global phase portraits of a predator-prey system

Érika Diz-Pita; Jaume Llibre; M. V. Otero-Espinar

doi:10.14232/EJQTDE.2022.1.16

Global phase portraits of a predator-prey system

Dynamical Systems 2025-01-27 v1

Authors: Érika Diz-Pita , Jaume Llibre , M. V. Otero-Espinar

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Abstract

We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator-prey system. We obtain all their topologically distinct global phase portraits in the positive quadrant of the Poincar\'e disc, so we provide all the possible distinct dynamics of these systems.

Keywords

predator-prey system Kolmogorov system global phase portrait Poincaré disc topological dynamics

Cite

@article{arxiv.2501.13728,
  title  = {Global phase portraits of a predator-prey system},
  author = {Érika Diz-Pita and Jaume Llibre and M. V. Otero-Espinar},
  journal= {arXiv preprint arXiv:2501.13728},
  year   = {2025}
}

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