一类具有常数收获率的捕食者–食饵模型的分支分析
Bifurcation Analysis of a Predator-Prey Model with Constant Prey Harvesting
DOI: 10.12677/DSC.2019.83020, PDF,    国家自然科学基金支持
作者: 邹桂华, 刘宣亮：华南理工大学数学学院，广东 广州
关键词: 捕食者–食饵模型；收获率；Hopf分支；Bogdanov-Takens分支；Predator-Prey Model； Harvesting Rate； Hopf Bifurcation； Bogdanov-Takens Bifurcation
摘要: 本文研究一类食饵种群具有常数收获率的捕食者–食饵模型的分支问题。利用常微分方程的定性与分支理论，分析了模型平衡点的存在条件，主要讨论了正平衡点的Hopf分支和Bogdanov-Takens分支，并得出了相应分支产生的条件及其结论。
Abstract: In this paper, we study the bifurcation of a predator-prey model with constant prey harvesting rate. By using the qualitative and bifurcation theory of ordinary differential equations, we analyze the existence conditions of equilibria, and discuss the Hopf and Bogdanov-Takens bifurcations near positive equilibria, respectively. The conditions and conclusions of corresponding bifurcations are obtained.
文章引用：邹桂华, 刘宣亮. 一类具有常数收获率的捕食者–食饵模型的分支分析[J]. 动力系统与控制, 2019, 8(3): 181-190. https://doi.org/10.12677/DSC.2019.83020

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