Allee效应下捕食者食饵模型的Hopf分支

Hopf Bifurcation of Predator-Prey Model with Allee Effect

摘要: 为了修正传统捕食者食饵模型的缺陷，解释小种群灭绝机制，提升模型解释和预测能力，本文在高鹤等人的研究基础上建立了一个具有Allee效应的捕食者食饵模型。通过求解模型的平衡点，分析三个边界平衡点以及正平衡点的稳定性和Hopf分支的存在性，利用数值模拟验证理论分析的结果，探索Allee效应对种群动态行为的影响。

Abstract: To address the shortcomings of traditional predator-prey models, explain the mechanism of small population extinction, and enhance the explanatory and predictive capabilities of the models, this paper establishes a predator-prey model with Allee effect based on the research of Gao He et al. By solving the equilibrium points of the model, analyzing the stability of the three boundary equilibrium points and the positive equilibrium point, as well as the existence of Hopf bifurcation, numerical simulations are used to verify the theoretical analysis results, and the influence of Allee effect on the dynamic behavior of the population is explored.