Bifurcations in predator–prey systems with nonmonotonic functional response

Abstract

We consider a predator–prey system with nonmonotonic functional response. The bifurcation analysis of the model shows that Hopf bifurcation can occur as the delay τ (taken as a parameter) crosses some critical values and the system has a Bogdanov–Takens singularity for any time delay value. Following the procedure of deriving normal form given by Faria and Magalhães, we compute the normal form for the Hopf bifurcation of the model, and study the stability of the bifurcating non-trivial periodic solutions. We also obtain a versal unfolding of the model at the Bogdanov–Takens singularity under certain conditions.