Many important factors in ecological communities are related to the interplay between predation and competition. Intraguild predation or IGP is a mixture of predation and competition which is a very basic three-dimensional system in food webs where two species are related to predator–prey relationship and are also competing for a shared prey. On the other hand, Allee effect is also a very important ecological factor which causes significant changes to the system dynamics. In this work, we consider a intraguild predation model in which predator is specialist, the growth of shared prey population is subjected to additive Allee effect and there is Holling-Type III functional response between IG prey and IG predator. We analyze the impact of Allee effect on the global dynamics of the system with the prior knowledge of the dynamics of the model without Allee effect. Our theoretical and numerical analyses suggest that: (1) Trivial equilibrium point is always locally asymptotically stable and it may be globally stable also. Hence, all the populations may go to extinction depending upon initial conditions; (2) Bistability is observed between unique interior equilibrium point and trivial equilibrium point or between boundary equilibrium point and trivial equilibrium point; (3) Multiple interior equilibrium points exist under certain parameters range. We also provide here a comprehensive study of bifurcation analysis by considering Allee effect as one of the bifurcation parameters. We observed that Allee effect can generate all possible bifurcations such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov–Taken bifurcation and Bautin bifurcation. Finally, we compared our model with the IGP model without Allee effect for better understanding the impact of Allee effect on the system dynamics.

中文翻译：

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加性 Allee 效应对具有专家捕食者的公会内捕食模型动力学的影响

生态群落中的许多重要因素都与捕食和竞争之间的相互作用有关。Intraguild 捕食或 IGP 是捕食和竞争的混合体，它是食物网中非常基本的 3 维系统，其中两个物种与捕食者 - 猎物关系相关，并且也在竞争共享的猎物。另一方面，阿利效应也是一个非常重要的生态因素，它会引起系统动力学的显着变化。在这项工作中，我们考虑了一个内部捕食模型，其中捕食者是专家，共享猎物种群的增长受到加性 Allee 效应的影响，IG 猎物和 IG 捕食者之间存在 Holling-III 型功能反应。我们利用没有 Allee 效应的模型动力学的先验知识分析 Allee 效应对系统全局动力学的影响。我们的理论和数值分析表明：（1）平凡平衡点总是局部渐近稳定的，也可能是全局稳定的。因此，根据初始条件，所有种群都可能灭绝；(2)在唯一内部平衡点和平凡平衡点之间或在边界平衡点和平凡平衡点之间观察到双稳态；(3)在一定的参数范围内存在多个内部平衡点。我们还通过将 Allee 效应视为分岔参数之一，对分岔分析进行了全面研究。我们观察到 Allee 效应可以产生所有可能的分岔，例如跨临界分岔、鞍节点分岔、Hopf 分岔、Bogdanov-Taken 分岔和 Bautin 分岔。最后，我们将我们的模型与没有 Allee 效应的 IGP 模型进行了比较，以更好地了解 Allee 效应对系统动力学的影响。