吉林大学学报（理学版）2025，Vol.63Issue(2)：321-330,10.DOI:10.13413/j.cnki.jdxblxb.2024201
具有收获项和双时滞及Allee效应影响的Lotka-Volterra捕食-食饵系统的Hopf分支分析
Hopf Bifurcation Analysis of Lotka-Volterra Predator-Prey System with Harvest Terms,Two Time Delays and Allee Effect
摘要
Abstract
Aiming at the problem that organism populations in nature were not able to react quickly to environmental changes or interactions amongst populations.By introducing two time delays as branching parameters,we analyzed the corresponding characteristic equations and discussed the local stability of the system at each equilibrium point and the existence of Hopf bifurcation.Firstly,we obtained explicit formulas that determined the direction of Hopf bifurcation and the stability of periodic solutions when two time delays equal toτby using the central manifold theorem and canonical type theory.Secondly,numerical simulation was used to verify the accuracy of theoretical analysis.The results show that the stability of the system changes and a Hopf bifurcation is generated when the time delay surpasses a critical value.Time delay is introduced into biological models can help predict population dynamics more accurately.关键词
双时滞/Allee效应/Lotka-Volterra捕食-食饵系统/Hopf分支/周期解Key words
two time delays/Allee effect/Lotka-Volterra predator-prey system/Hopf bifurcation/periodic solution分类
数理科学引用本文复制引用
衣薪燃,吕堂红..具有收获项和双时滞及Allee效应影响的Lotka-Volterra捕食-食饵系统的Hopf分支分析[J].吉林大学学报（理学版）,2025,63(2):321-330,10.基金项目
吉林省教育厅科学研究项目(批准号:JJKH20240891KJ). （批准号:JJKH20240891KJ）
