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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.

##### MSC:
 35Q92 PDEs in connection with biology and other natural sciences 35B09 Positive solutions of PDE
##### Keywords:
predator-prey diffusion; index; uniqueness; stability
Full Text:
##### References:
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