Stability and turing instability in a diffusive predator–prey system with Beddington–DeAngelis functional response

A diffusive two-species predator–prey system with the Beddington–DeAngelis functional response and subject to homogeneous Neumann boundary conditions is considered. In the region of parameters where the positive constant steady state is globally asymptotically stable when there exists no diffusion, the impact of the diffusion on the stability is analyzed in detail. The global asymptotic stability of the positive constant steady state is also considered by means of the upper and lower solutions method and the monotone iteration principle.