Global Bifurcation for a Predator-Prey Model with Ivlev Functional Response

The steady-state of a diffusive predator-prey system with Ivlev functional response is considered. Taking the diffusion coefficient as a bifurcation parameter, the local bifurcation from the unique positive constant steady-state solution is obtained and the structure of positive steady-states near the bifurcation point is given. Moreover, we find that the local branch can be extended to the global one. Our method used here is based on the bifurcation theory and Leray-Schauder degree.