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))inΩ,u=0on∂Ω,−Δv=v(b−mv/(m+u))inΩ,v=0on∂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.