Effects of degeneracy and response function in a diffusion predator–prey model. (5th March 2018)

• Record Type: Journal Article
• Authors: Li, Shanbing; Wu, Jianhua; Dong, Yaying
• Is Part Of: Nonlinearity. Volume 31:Number 4(2018:Apr.)
• Page Start: 1461
• Page End: 1483
• Publication Date: 2018-03-05
• Subjects: degeneracy -- response function -- existence -- limiting behavior -- blow up; 35J65 -- 35B32 -- 35B35 -- 92D25; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaa2de
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we consider positive solutions of a diffusion predator–prey model with a degeneracy under the Dirichlet boundary conditions. We first obtain sufficient conditions of the existence of positive solutions by the Leray–Schauder degree theory, and then analyze the limiting behavior of positive solutions as the growth rate of the predator goes to infinity and the conversion rates of the predator goes to zero, respectively. It is shown that these results for Holling II response function (i.e. m > 0) reveal interesting contrast with that for the classical Lotka–Volterra predator–prey model (i.e. m = 0).