Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

中文翻译：

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具有非线性增长率和 Allee 效应对第一物种的 Holling-II Amensalism 系统的全局动力学

值得关注的是具有非线性增长率的双物种 Holling-II 无门系统的全局动态。研究了平凡平衡、半平凡平衡、内部平衡和无限奇点的存在和稳定性。在不同的参数下，存在两个稳定的平衡，这意味着该模型并不总是全局渐近稳定的。结合所有可能平衡的存在及其稳定性、鞍连接和闭合轨道，我们推导出了跨临界分岔和鞍节点分岔的一些条件。此外，执行模型的全局动力学。接下来，我们将 Allee 效应结合到第一个物种上，并对模型的平衡和分岔讨论进行了新的分析。最后，通过几个数值例子来验证我们的理论结果。