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 $\mathbb{R}^*{_+^2}$. Nu-merical 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.

中文翻译：

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具有翻转分叉和混沌控制的离散捕食-被捕食模型

我们研究了在$ \ mathbb {R} ^ * {_ + ^ 2} $内部的具有Allee效应的捕食者—猎物模型的局部动力学，翻转分叉，混沌控制和周期点的存在。数值模拟不仅显示了我们的理论分析结果，而且还显示了复杂的动力学行为，例如周期2、8、11、17、20和22轨道。此外，最大的李雅普诺夫指数和分形维数也被数值计算，以显示所考虑的模型中存在混沌行为。