Dynamics analysis of a reaction–diffusion system with Beddington–DeAngelis functional response and strong Allee effect. (February 2020)

• Record Type: Journal Article
• Authors: Liu, Ping; Yang, Bowen
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Predator–prey model -- Strong Allee effect -- Beddington–DeAngelis functional response -- Steady state bifurcation -- Hopf bifurcation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.06.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, the dynamics of a diffusive predator–prey model with modified Leslie–Gower term and strong Allee effect on prey under homogeneous Neumann boundary condition is considered. Firstly, we obtain the qualitative properties of the system including the existence of the global positive solution and the local and global asymptotical stability of the constant equilibria. In addition, we investigate a priori estimate and the nonexistence of nonconstant positive steady state solutions. Finally, we establish the existence and local structure of steady state patterns and time-periodic patterns for the system.