Multiple Bifurcations in a Delayed Predator–Prey System with Nonmonotonic Functional Response

A delayed predator–prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhães. The bifurcation analysis of the model indicates that there is a Bogdanov–Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov–Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values.