Dynamics of a modified Leslie–Gower model with dual Allee effects under unilateral and bilateral control

This paper establishes unilateral and bilateral impulsive control frameworks based on a modified Leslie–Gower model with dual Allee effects. The existence and orbital stability of order-1 and order-2 periodic solutions are proved by differential equation geometric theory. Numerical simulations are performed to validate the theoretical results, and bifurcation diagrams reveal parameter-dependent dynamical properties. Unilateral control can prevent prey extinction caused by the Allee effect or suppress excessive prey growth, thereby avoiding predator outbreaks and the resulting prey loss. In contrast, bilateral control precisely keeps prey and predator populations within reasonable ecological thresholds, and achieves stable population persistence as well as sustainable utilization of ecological resources.