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We explore the local dynamics, flip bifurcation, chaos control and existence of periodic point of the predator-prey model with Allee effect on the prey population in the interior of R∗ 2+. Numerical simulations not only exhibit our results with the theoretical analysis but also show the complex dynamical behaviors, such as the period-2, 8, 11, 17, 20 and 22 orbits. Further, maximum Lyapunov exponents as well as fractal dimensions are also computed numerically to show the presence of chaotic behavior in the model under consideration.