A Leslie-Gower-type predation model considering generalist predators and the Allee effect on prey

• Autores: Martínez-Jeraldo, Nicole, Rozas-Torres, Elizabeth, González-Olivares, Eduardo
• Formato: artículo
• Fecha de Publicación: 2021
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/3712
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3712
• Nivel de acceso: acceso abierto
• Materia: Predator-prey model, bifurcation; limit cycles; separatrix curve; stability; functional response; Modelo depredador-presa; bifurcación; ciclo límite; curva separatriz; estabilidad; respuesta funcional

The main feature of the Leslie-Gower-type predation model is that the predator’s growth function is one of logistic-type. Thus, it is a model assuming implicitly the competition among predators. In this work the dynamics of a modified Leslie-Gower type predator-prey model is analyzed, considering two important aspects: (i) the predators capture an alternative food when the quantity of prey is scarce and (ii) the prey population is affected by an Allee effect. Considering a topological equivalent system, the main properties of the system are established. Necessary and sufficient conditions for the existence and local stability of equilibria are determined, also showing the existence of a homoclinic orbit and of at least a limit cycle. When the predators are generalists the dynamics of the model differ enough respecting the model considering predators specialist since appearing more equilibrium points and the mentioned homoclinic orbit.