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The effect of mutual interference between predators on a predator-prey model with diffusion. (English) Zbl 1234.35284
Summary: 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.

35Q92PDEs in connection with biology and other natural sciences
35B09Positive solutions of PDE
Full Text: DOI
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