Impacts of Predation-Driven Allee Effect in a Predator-Prey Model.

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.