Turing Instability and Bifurcation in a Diffusion Predator–Prey Model with Beddington–DeAngelis Functional Response

Abstract

In this paper, we consider a predator–prey model with Beddington–DeAngelis functional response with or without diffusion. For this system, we give a complete and rigorous analysis of the dynamics including the existence of a global positive solution, the stability/Turing instability and the Hopf bifurcation. In the meanwhile, we show, via numerical simulations, that there appears Hopf bifurcation, steady state solution and Turing–Hopf bifurcation with the changes of some parameters of the system.