Dynamic behaviors of a predator–prey model with weak additive Allee effect on prey. (October 2020)

• Record Type: Journal Article
• Authors: Zhang, Conghui; Yang, Wenbin
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Predator–prey model -- Allee effect -- Stability -- Bifurcation -- Pattern formation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103137
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with a reaction–diffusion system modeling predator–prey interaction with additive Allee effect. We first analyze nonnegative constant equilibrium solutions and study the stability of the unique positive solution. Then we investigate the steady state bifurcation and Hopf bifurcation from the unique positive constant solution, respectively. The main tools used here include the bifurcation theory, the space decomposition and the implicit function theorem. Moreover, we describe the global structure from a simple eigenvalue. Finally, for the case d 1 = 0, we prove the existence of far-from-equilibrium steady states with jump discontinuities. Moreover, by applying the singular perturbation method, we give a proof of the existence of large amplitude solutions when d 1 is sufficiently small.