Chaos Control and Bifurcations in a Modified Discrete Prey–Predator Model with Weak Multiple Allee Effect

This study explores the local dynamics of a discrete-time prey–predator model, which has been modified to include a weak multiple Allee effect on the prey population. The investigation encompasses topological categorization, bifurcation analysis, and chaos control. The analysis reveals that the model exhibits flip bifurcation and Neimark–Sacker bifurcation within a narrow vicinity of the coexistence equilibrium point, as demonstrated through bifurcation theory. Furthermore, the direction of these bifurcations is elucidated. To stabilize chaos resulting from the bifurcation, the OGY method is employed. Numerical simulations are conducted to validate the theoretical findings, with maximum Lyapunov exponents indicating the probability of chaos in the model.