渭南师范学院学报2025，Vol.40Issue(8)：69-77,9.
一类捕食者-食饵三种群模型的稳定性和Hopf分支
Stability and Hopf Bifurcation of a Predators-Prey Three Population Model
摘要
Abstract
The predation model of two predators on one prey in an ecosystem exhibits rich dynamic characteristics.By considering that one of the two predators has a ratio-dependent relationship and Holling type Ⅱ functional response to prey predation,a three-dimensional competitive predator-prey ecological model is established.Applying the qualitative and stability theory of differential equations,bifurcation theory,and numerical simulation methods,the intrinsic growth rate of the ratio-dependent predator is selected as the threshold parameter to derive the existence and stability conditions of the model's boundary equilibria and internal equilibria.The conditions for the occurrence of Hopf bifurcation in the model are obtained and numerical simulations demonstrate the existence of multi-stability phenomena in the model,with the theoretical conclusions validated through numerical methods.关键词
两种捕食者-一种食饵模型/Holling Ⅱ功能函数/稳定性/Hopf分支Key words
two predator-one prey model/Holling Ⅱ functional function/stability/Hopf bifurcation分类
数理科学引用本文复制引用
邱光明,孟新友..一类捕食者-食饵三种群模型的稳定性和Hopf分支[J].渭南师范学院学报,2025,40(8):69-77,9.基金项目
国家自然科学基金地区项目:基于时变时滞的复杂生态-传染病模型的动力学研究(12161054) （12161054）
