The effect of mutual interference between predators on a predator–prey model with diffusion

We consider a diffusive predator–prey model with Beddington–DeAngelis functional response under homogeneous Dirichlet boundary conditions. The effect of large k which represents the extent of mutual interference between predators is extensively studied. By making use of the fixed point index theory, we obtain a complete understanding of the existence, uniqueness and stability of positive steady-states when k is sufficiently large. Moreover, we present some numerical simulations that supplement the analytic results in one dimension.