Codimension two bifurcations in a predator-prey system with group defense

In this paper we study the qualitative behavior of a predator-prey system w ith nonmonotonic functional response. The system undergoes a series of bifu rcations including the saddle-node bifurcation, the supercritical Hopf bifu rcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic. loop, or exhibit the so-c alled "paradox of enrichment" phenomenon. In the generic case, the model ha s the bifurcation of cusp-type codimension two (i.e. the Bogdanov-Takens bi furcation) but no bifurcations of codimension three.