Qualitative analysis on a predator-prey model with Ivlev functional response

The diffusive predator-prey model with Ivlev functional response is considered under homogeneous Dirichlet boundary conditions. Firstly, we investigate the bifurcation of positive solutions and derive the multiplicity result for γ suitably large. Furthermore, a range of parameters for the uniqueness of positive solutions is described in one dimension. The method we used is based on a comparison principle, Leray-Schauder degree theory, global bifurcation theory and generalized maximum principle.