具有非线性收获的捕食-食饵模型的建立及分析

Establishment and analysis of a predator-prey model considering nonlinear harvesting

本文建立并分析了具有非线性收获函数的捕食-食饵模型。首先,讨论了平衡点的存在性,分析结果表明系统始终存在1个灭绝平衡点,且存在2个边界平衡点和1个正平衡点共存的现象;其次,对不同类型平衡点的稳定性进行了分析,发现了系统会出现鞍结点分支、Hopf分支等复杂的动力学行为。数值模拟结果表明,随着收获强度的改变,捕食者的规模会趋于灭绝、常数或者周期性震荡。这就表明在实际中可通过调节收获强度这一措施来实现控制捕食者数目的目的。本文的理论研究结果可进一步丰富有关具有非线性收获的捕食-食饵模型的研究,为合理收获策略的制定提供理论依据。

In this paper,a predator-prey model with nonlinear harvest function is established and analyzed.Firstly,we give the conditions for the existence of equilibria.The results of analysis show that this system has an extinction equilibrium,two boundary equilibria and a positive equilibrium.Then we focus on the dynamic behavior of this system and it is found that this system has complex dynamic behaviors such as saddle-node bifurcation and Hopf bifurcation.Furthermore,the numerical results show that the size of predators may go to extinct,constant or periodic oscillations,which depends on the intensity of harvest.This means that the number of predators can be controlled in practice by adjusting the intensity of harvest.The theoretical results of this paper can further enrich the research of predator-prey models,and provide theoretical basis for the formulation of rational harvesting strategies.