Global bifurcation and pattern formation for a reaction–diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses. (October 2022)

• Record Type: Journal Article
• Authors: Luo, Demou; Wang, Qiru
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: A reaction–diffusion predator–prey model with prey-taxis -- Double Beddington–deAngelis functional responses -- a priori estimates and pattern formation -- Global bifurcation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103638
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Of concern in this paper is to propose an accurate description for the global bifurcation structure of the nonconstant steady states for a reaction–diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses systematically. By treating the coefficient of nonlinear prey-taxis as a bifurcation parameter and utilizing the user-friendly version of Crandall–Rabinowitz bifurcation theory, we study the global bifurcation theory of the system. Meanwhile, the existence of nonconstant steady states will be offered by the exported global bifurcation theorem under a rather natural condition. In the proof, a priori estimate of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given.