Positive solutions of a prey–predator model with predator saturation and competition☆

Abstract In this paper, we study the existence, multiplicity, bifurcation and stability of positive solutions to a prey–predator model with predator saturation and competition { − Δ u = u ( a − u − b v f ( u , v ) ) , x ∈ Ω , − Δ v = v ( c − v + d u f ( u , v ) ) , x ∈ Ω , u = v = 0 , x ∈ ∂ Ω , where f ( u , v ) = 1 ( 1 + α u ) ( 1 + β v ) , and parameters are all positive constants, and u and v are the densities of the prey and predator, respectively.

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