标题： 具有阿利效应的Bazykin-Berezovskaya捕食-食饵模型在经济框架下的几何分析 显示英文标题

标题： A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework

摘要： 我们研究了一种快速-慢速版本的带有阿利效应的Bazykin-Berezovskaya捕食者-猎物模型，该模型在两个时间尺度上演化，通过几何奇异摄动理论（GSPT）的视角进行分析。我们所考虑的系统形式非常规。我们完全刻画了其动力学特性，并提供了明确的阈值量来区分多种可能的渐近行为。此外，我们提出了数值结果以说明我们的发现。最后，我们在经济框架和捕食者-猎物模型背景下，对这些结果的实际意义进行了评论。 显示英文摘要

摘要： We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models.