Allee effect acting on the prey species in a Leslie–Gower predation model. (February 2019)

• Record Type: Journal Article
• Authors: Martínez-Jeraldo, Nicole; Aguirre, Pablo
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 895
• Page End: 917
• Publication Date: 2019-02
• Subjects: Allee effect -- Leslie–Gower predator–prey model -- Stability -- Bifurcations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.08.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the consequences of an Allee effect acting on the prey species in a Leslie–Gower predator–prey model. For this goal we make extensive use of analytical tools from dynamical systems theory complemented with a numerical bifurcation analysis. By studying the dynamics at infinity under a suitable compactification we prove that the model is well-posed in the sense that all the solutions are bounded. We provide a thorough analysis of the number and stability of equilibrium points. In particular, the origin is a non-hyperbolic equilibrium and presents different regimes of local (un)stability depending on certain conditions on the model parameters. In addition, we find curves of homoclinic, Hopf, and saddle–node bifurcations around a Bogdanov–Takens point. In this process, our findings indicate that the survival threshold for both populations in the two-dimensional phase space can be either a limit cycle, a homoclinic orbit, or the stable manifold of a saddle-equilibrium.