On the predator–prey system with strong Allee effect in prey

Abstract

In this thesis, we conduct a global bifurcation analysis of a general class of predator–prey models incorporating a strong Allee effect in the prey population. We highlight the existence of a heteroclinic loop connecting two saddle points and investigate the occurrence of Hopf bifurcation. Depending on parameter ranges, we also prove the existence, uniqueness, or nonexistence of a limit cycle. For a unique critical parameter value, a threshold curve separates regions of overexploitation (prey extinction) and coexistence (successful predator invasion) in the space of initial conditions. To illustrate our theoretical results, we provide several numerical examples. This work is primarily based on the article by Jinfeng Wang, Junping Shi, and Junjie Wei entitled *Predator–prey system with strong Allee effect in prey*.