On multiplicity and stability of positive solutions of a diffusive prey–predator model ✩

In the paper, we consider the following diffusive prey–predator model: −Δu = u(a −u −v/(1+ mu)) in Ω, u =0 on∂Ω, −Δv = v(b −mv/(m+ u)) in Ω, v =0 on∂Ω. We are mainly concerned with the positive solutions of the system in the case that the parameter m is large, and obtain a complete understanding for the existence, multiplicity and stability of positive solutions.  2005 Elsevier Inc. All rights reserved