Copyright © 2011 Guohong Zhang and Xiaoli Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary condition. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, the local and global bifurcations from a semitrivial state are also investigated on the basis of bifurcation theory. The results indicate diffusion, and functional response does help to create stationary pattern.