Bifurcation analysis of a diffusive predator-prey model with Beddington-DeAngelis response

Abstract

In this paper, we discuss a diffusive predator-prey system with Beddington-DeAngelis response subject to homogeneous Neumann boundary condition by choosing the bifurcation parameter r as the efficiency of predation. We find the spatially homogeneous and non-homogeneous Hopf bifurcations occur at positive constant steady state as r varies while the system parameters are all spatially homogeneous. In order to verify our theoretical results, some numerical simulations are also included.