Multiplicity and uniqueness of positive solutions for a predator–prey model with B–D functional response

Abstract

In this paper, we consider positive solutions of a predator–prey model with Beddington–DeAngelis functional response. First, we establish the existence of positive solutions and present some sufficient and necessary conditions mainly using the standard fixed point index theory in cone. Second, the multiplicity, uniqueness and stability of positive solutions are obtained by means of bifurcation theory, perturbation theory of eigenvalues and the fixed point index theory. The parameters k and m play very important roles in deciding the number of positive solutions, which are showed explicitly in this paper.