| Abstract: | A predator-prey system with Holling-IV functional response is investigated. It is shown that the system has a positive equilibrium?which is a cusp of co-dimension 2 under certain conditions. When the parameters vary in a small neighborhood of the values of parameters, the model undergoes the Bogdanov-Takens bifurcation. Different kinds of bifurcation phenomena are exhibited, which include the saddle~node bifurcation, the Hopf bifurcation and the homo-clinic bifurcation. Some computer simulations are presented to illustrate the conclusions. |
