Stationary patterns of a diffusive predator–prey model with Crowley–Martin functional response. (February 2018)

• Record Type: Journal Article
• Authors: Chen, Shanshan; Wei, Junjie; Yu, Jinzhu
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 33
• Page End: 57
• Publication Date: 2018-02
• Subjects: Reaction–diffusion -- Nonexistence -- Steady state -- Global stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.05.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A diffusive predator–prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there exist no nonconstant stationary solutions when the effect of the predator interference is strong or the conversion rate of the predator is large, and nonconstant stationary solutions emerge when the diffusion rate of the predator is large. Highlights: A diffusive predator–prey system with predator interference and Neumann boundary conditions is considered. We show the existence and nonexistence of the nonconstant stationary solutions. The methods used here can be applied to other predator–prey model with predator interference.