In this paper, we use a semidiscretization method to derive a discrete predator–prey model with Holling type II, whose continuous version is stated in [F. Wu and Y. J. Jiao, Stability and Hopf bifurcation of a predator-prey model, Bound. Value Probl. 129 (2019) 1–11]. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Then we obtain the sufficient conditions for the occurrence of the transcritical bifurcation and Neimark–Sacker bifurcation and the stability of the closed orbits bifurcated by using the Center Manifold theorem and bifurcation theory. Finally, we present numerical simulations to verify corresponding theoretical results and reveal some new dynamics.

中文翻译：

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具有 Holling-II 功能响应的离散捕食者-猎物模型的动力学

在本文中，我们使用半离散化方法推导出 Holling 类型 II 的离散捕食者 - 猎物模型，其连续版本在 [F. Wu 和 YJ Jiao，捕食者-猎物模型的稳定性和 Hopf 分岔，边界。价值问题 129（2019）1-11]。首先，利用关键引理研究系统不动点的存在性和局部稳定性。然后我们利用中心流形定理和分岔理论得到了跨临界分岔和内马克-萨克分岔发生的充分条件以及分岔闭合轨道的稳定性。最后，我们提出数值模拟来验证相应的理论结果并揭示一些新的动力学。