Impact of double Allee effect on the dynamics and stability of a predator-prey model

In this paper, we investigated the complex dynamics of a discrete-time predator-prey model incorporating a double Allee effect in the prey population. We investigated the existence and stability of biologically meaningful fixed points, including extinction, prey-only, and coexistence equilibria. Through analytical and numerical bifurcation analysis, we demonstrated that the model underwent a Neimark-Sacker bifurcation as key parameters varied, leading to quasi-periodic oscillations that characterized realistic population cycles. Our results revealed that stronger Allee effects tend to destabilize the model, increasing extinction risks and promoting oscillatory dynamics, while higher predator mortality rates and saturation in predation response enhance stability. A comparative analysis with models lacking the Allee effect highlights its critical role in delaying equilibrium convergence and inducing instability at low population densities. These findings provide important insights for ecological conservation, particularly for species vulnerable to population depletion, and contribute to the theoretical understanding of predator-prey models with density-dependent growth constraints.