The Uniqueness of Positive Solutions for a Predator-Prey Model with B-D Functional Response

Abstract

In this paper, we investigate a diffusive predator-prey model with Beddington-DeAngelis functional response, which is subject to homogeneous Dirichlet boundary conditions. Based on the fixed point index theory, a good understanding of the existence, uniqueness and stability of positive solutions is obtained when b is sufficiently small. We always reduce the proof of uniqueness and stability to the proof of the fact that any possible positive solution is non-degenerate and linearly stable.KeywordsPredator-preyBeddington-DeAngelis functional responseIndexUniqueness