Analysis of bifurcation and local stability of a discrete-time predator-prey model with weak multiple Allee effect and chaos control

This study investigates the dynamic behaviour and bifurcations of a two-dimensional discrete-time predator-prey model influenced by a weak multiple Allee effect on the prey. We examine the existence and local stability of the model's fixed points across all permissible parameter regions. Our bifurcation analysis reveals that the model can experience both Flip and Neimark-Sacker bifurcations. In addition, the system is shown to admit codimension-two resonance bifurcations, including the 1:2, 1:3, and 1:4 cases, under suitable critical parameter configurations. To support our theoretical findings, we provide numerical simulations, including bifurcation diagrams, phase portraits, and Lyapunov exponents. Additionally, we extend the OGY feedback control strategy to manage Flip and Neimark-Sacker bifurcations in the discrete-time predator-prey model.