With Non-monotonic Functional Response Of Predator - Prey System Of Global Qualitative Analysis

In this paper ,a predator-prey system with nonmonotonic functional response is considered.Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The bifurcation analysis of the model depending on all parameter indication that it exhibits numerous kinds of bifurcation phenomena,including the saddle-node bifurcation,the supercritical and subcritical Hopf bifurcation, and the lioinoclinic bifurcation.In the generic case,the model has the bifurcation of cusp type ol'codimension 2 (i.e..Bogdanov-Taken bifurcation)but for some specific parameter values it has a multiple focus of multiplicity at least 2. And,we give the global analysis.