Abstract
In this paper, we consider a predator–prey mutualist model with diffusion under homogeneous Dirichlet boundary conditions. By making use of the index theory of fixed points, we obtain some sufficient conditions for the existence of positive steady states and derive the multiplicity result when β is suitably large. The effect of γ, which represents the extent of a mutualist deterring predation on a prey, is extensively studied and a good understanding of the existence, uniqueness and stability of positive steady states is gained when γ is sufficiently large. Finally, we discuss some numerical simulations that support the analytic results in one-dimensional cases.
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