Stability in a modified Leslie-Gower type predation model considering competence among predators

• Autores: González-Olivares, Eduardo, Gallegos-Zuñiga, Javiera
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revista UNITRU - Selecciones Matemáticas
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/2952
• Enlace del recurso: http://revistas.unitru.edu.pe/index.php/SSMM/article/view/2952
• Nivel de acceso: acceso abierto
• Materia: Predator-prey model; functional response; bifurcation; limit cycle; separatrix curve; stability; Modelo depredador-presa; respuesta funcional; bifurcación; ciclo límite; curva separatriz; estabilidad

In the ecological literature, the interference (self-interference) or competition among predators to effect the harvesting of their prey has been modeled by different mathematical formulations.In this work, we will establish the dynamical properties of the Leslie-Gower type predation model, in which is incorporated one of these form, described by the function b (y) = yalfa , with 0 < alfa < 1.The main difficulty of the analysis is due to this function is not differentiable for y = 0, and the Jacobian matrix is not defined in the equilibrium points over the horizontal axis (x-axis).Previously, we showed a summary with the fundamental properties of the Leslie-Gower type model, in order to carry out an adequate comparative analysis with models where self-interference between predators is incorporated.To reinforce our results, some numerical simulations are shown.