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
⎧⎪
⎨⎪
⎩
− 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.
