Predator interference in a Leslie–Gower intraguild predation model. (February 2020)

• Record Type: Journal Article
• Authors: Falconi, Manuel; Vera-Damián, Yrina; Vidal, Claudio
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Intraguild predation model -- Predator interference -- Hopf bifurcation -- zero-Hopf bifurcation -- Alternative stable state; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.102974
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this paper is to analyze general dynamics features of a new Intraguild Predation (IGP) model where the top predator feeds only on the mesopredator and also affects its consumption rate. Important dynamical aspects of the model are described. Specifically, we prove that the trajectories of the associated system are bounded and defined for all positive time; there is a trapping domain; there are open subsets of parameters, such that the system in the first octant has at most five equilibrium solutions and at most three of them are of co-existence. Here we characterize the existence of Hopf bifurcations and we prove that this model exhibits either one, two or three small amplitude periodic solutions which arise from a zero-Hopf bifurcation. We prove the existence of alternative stable states. Finally, some numerical computations have been given in order to support our analytical results. The importance of some parameters of the model is discussed, in particular the role of the interference rate. The numerical exploration suggests that the equilibrium biomass of each of the three species grows as the level of interference grows. Highlights: We study a spatial system of ODEs of a three-species predator–prey model. The system has a rich dynamics of the predator–prey interactions. We study the interference of the top predator on the prey population. We obtain different types of bifurcations (Hopf and zero-Hopf bifurcation). We prove the existence of one, two or three periodic orbits (limit cycles).