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

In this paper, we study the existence, multiplicity, bifurcation and stability of positive solutions to a prey–predator model with predator saturation and competition ⎧⎪ ⎨⎪ ⎩ − u = u a − u −bvf (u, v) , x ∈ Ω, − v = v c − v +duf (u, v) , x ∈ Ω, u = v = 0, x ∈ ∂Ω, where f (u, v) = 1 (1+αu)(1 + βv) , and parameters are all positive constants, and u and v are the densities of the prey and predator, respectively.