Global analysis in a predator-prey system with nonmonotonic functional response

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 dependi ng on all parameters indicates that it exhibits numerous kinds of bifurcati on phenomena, including the saddle-node bifurcation, the supercritical and subcritical Hopf bifurcations, and the homoclinic bifurcation. It is shown that there are different parameter values for which the model has a limit c ycle or a homoclinic loop, or exhibits the so-called paradox of enrichment phenomenon. Moreover, a limit cycle cannot coexist with a homoclinic loop f or all parameters. In the generic case, the model has the bifurcation of cu sp type of codimension 2 (i.e., Bogdanov-Takens bifurcation) but for some s pecific parameter values it has a multiple focus of multiplicity at least 2 .