Impacts of Predation-Driven Allee Effect in a Predator–Prey Model
Kaushik Kayal, Sudip Samanta, Joydev Chattopadhyay
Abstract
In the present work, we introduce one of the most significant biological factors — predator-driven Allee effect in a modified Leslie–Gower (LG) model. Our mathematical analyses include local stability analysis, Hopf bifurcation analysis, direction of Hopf bifurcation and Bogdanov–Tankens bifurcation around the coexisting equilibrium point. We also perform numerical simulations to validate our analytical results and to explore rich dynamics. Our results indicate that introducing predator-driven Allee effect not only destabilizes the system but also changes the characteristics of Hopf bifurcation from supercritical to subcritical. The system exhibits two types of bistability behavior between prey-free equilibrium and coexisting equilibrium, and prey-free equilibrium and limit cycle oscillation. Further, we explore an interesting result that the probability of extinction risk of prey population of modified LG system with predator-driven Allee effect is much higher in comparison to modified LG system when Allee term is absent. We have also demonstrated that predation-driven Allee effect increases extinction risk of prey population when the initial predator population size is large.