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

• Martha Álvarez Ramírez ^[1] ; Johanna D. García Saldaña ^[2] ; Mario Medina ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
  2. [2] Universidad Católica de la Santísima Concepción

     Universidad Católica de la Santísima Concepción

     Comuna de Concepción, Chile

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01155-0
• Enlaces
  • Texto completo
• Resumen

  • 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.

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