一类基于Allee效应的捕食者–食饵模型的动力学研究

Global Dynamics in a Predator-Prey Model with Allee Effect

摘要: 近年来，关于捕食–食饵模型的动力学分析作为一个重要课题，吸引了许多学者的广泛研究。通过对Allee效应的研究，可以发现种群自身适应度与种群自身的生长密度等其他方面的正相关关系。本文从数学和生物学的角度出发，建立了带有Allee效应和具有Holling IV功能反应的捕食者–食饵模型。针对模型，对其有界性、解的性质、平衡点的存在性以及其局部稳定性和分支进行了分析。

Abstract: In recent years, the dynamical analysis of predator-prey models has emerged as a significant topic, garnering extensive research attention from scholars worldwide. Through the study of the Allee effect, it has been observed that there is a positive correlation between a population’s fitness and its growth density, among other factors. This paper constructs a predator-prey model incorporating the Allee effect and featuring the Holling type IV functional response from both mathematical and biological perspectives. The analysis of the model includes its boundedness, the properties of solutions, the existence of equilibrium points, as well as the local stability and Hopf bifurcation.