In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

中文翻译：

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具有霍林 III 型功能响应和捕获效应的离散捕食者-猎物模型中的分岔与混沌

在本文中，我们研究了一个离散时间的捕食者 - 猎物模型，该模型具有 Holling III 型功能响应和两个物种的收获。详细的分岔分析，取决于一些参数，揭示了丰富的分岔结构，包括跨临界分岔、翻转分岔和 Neimark-Sacker 分岔。然而，也给出了保证平凡不动点和唯一正不动点全局渐近稳定性的一些充分条件。对于离散系统，建立了李-约克意义上的混沌存在。给出了广泛的数值模拟来支持分析结果。该系统表现出翻转分岔和 Neimark-Sacker 分岔，然后是大范围的密集混沌。进一步，