一类食饵具有常数收获率和Holling第II类功能性反应的捕食者–食饵模型的分支分析

Bifurcation Analysis of a Predator-Prey Model with Constant Prey Harvesting Rate and Holling Type II Functional Response

本文研究一类食饵种群具有常数收获率且有Holling第Ⅱ类功能性反应的捕食者–食饵模型的平衡点和分支问题。首先给出系统模型平衡点的存在条件,然后主要讨论了平衡点的类型及稳定性和正平衡点的Hopf分支,且得出了产生Hopf分支的条件;最后,对该模型做了数值仿真模拟实验得到了相关结论。

In this paper, we study the equilibria and the bifurcation of a predator-prey model with constant prey harvesting rate and Holling type II functional response. Firstly, we analyze the existence condition of the equilibria of the system model. Then, we discuss the type and stability of the equilibria, Hopf bifurcation near positive equilibria and we obtain the conditions of Hopf bifurcation. Finally, the numerical simulation of the model is carried out and the relevant conclusions are obtained.