Resumen de Global Dynamics and Integrability of a Leslie-Gower Predator–Prey Model with Linear Functional Response and Generalist Predator

Martha Alvarez, Johanna Denise García Saldaña, Mario Medina

• We deal with a Leslie-Gower predator–prey model with a generalist or alternating food for predator and linear functional response. Using a topological equivalent polynomial system we prove that the system is not Liouvillian (hence also not Darboux) integrable.

  In order to study the global dynamics of this model, we use the Poincaré compactification of R2 to characterize all phase portraits in the Poincaré disc, obtaining two different topological phase portraits.