Since intraguild predation (IGP) is a ubiquitous and important community module in nature and Allee effect has strong impact on population dynamics, in this paper we propose a three-species IGP food web model consisted of the IG predator, IG prey and basal prey, in which the basal prey follows a logistic growth with strong Allee effect. We investigate the local and global dynamics of the model with emphasis on the impact of strong Allee effect. First, positivity and boundedness of solutions are studied. Then existence and stability of the boundary and interior equilibria are presented and the Hopf bifurcation curve at an interior equilibrium is given. The existence of a Hopf bifurcation curve indicates that if competition between the IG prey and IG predator for the basal resource lies below the curve then the interior equilibrium remains stable, while if it lies above the curve then the interior equilibrium loses its stability. In order to explore the impact of Allee effect, the parameter space is classified into sixteen different regions and, in each region, the number of interior equilibria is determined and the corresponding bifurcation diagrams on the Allee threshold are given. The extinction parameter regions of at least one species and the necessary coexistence parameter regions of all three species are provided. In addition, we explore possible dynamical patterns, i.e., the existence of multiple attractors. By theoretical analysis and numerical simulations, we show that the model can have one (i.e. extinction of all species), two (i.e. bi-stability) or three (i.e. tri-stability) attractors. It is also found by simulations that when there exists a unique stable interior equilibrium, the model may generate multiple attracting periodic orbits and the coexistence of all three species is enhanced as the competition between the IG prey and IG predator for the basal resource is close to the Hopf bifurcation curve from below. Our results indicate that the intraguild predation food web model exhibits rich and complex dynamic behaviors and strong Allee effect in the basal prey increases the extinction risk of not only the basal prey but also the IG prey or/and IG predator.

由于公会内部捕食（IGP）是自然界中普遍存在且重要的社区模块，而Allee效应对种群动态具有强烈影响，因此在本文中，我们提出了由IG捕食者，IG猎物和基础猎物组成的三物种IGP食物网模型，其中基础猎物遵循逻辑生长，并具有强大的阿利效应。我们调查模型的局部和全局动态，重点放在强大的Allee效应的影响上。首先，研究了溶液的正性和有界性。然后给出了边界和内部平衡的存在性和稳定性，并给出了内部平衡点的霍普夫分叉曲线。Hopf分叉曲线的存在表明，如果IG猎物和IG捕食者之间对基础资源的竞争位于曲线下方，则内部平衡保持稳定，如果它位于曲线上方，则内部平衡会失去稳定性。为了探究Allee效应的影响，将参数空间分为16个不同的区域，并在每个区域中确定内部平衡的数量，并给出Allee阈值的相应分叉图。提供了至少一种物种的消光参数区域和所有三种物种的必要的共存参数区域。此外，我们探索了可能的动力学模式，即多个吸引子的存在。通过理论分析和数值模拟，我们表明该模型可以具有一个（即所有物种灭绝），两个（即双稳定性）或三个（即三稳定性）吸引子。通过模拟还发现，当存在独特的稳定内部平衡时，该模型可能会产生多个吸引周期轨道，并且随着IG猎物和IG捕食者之间对基础资源的竞争从下方接近Hopf分叉曲线，这三个物种的共存性得到了增强。我们的研究结果表明，行会内部捕食食物网络模型表现出丰富而复杂的动态行为，而在基础猎物中强大的Allee效应不仅增加了基础猎物的灭绝风险，而且还增加了IG猎物或IG掠食者的灭绝风险。