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-PreySystem with Harvest Terms, Two Time Delays and Allee Effect

作　　者：衣薪燃 吕堂红[1] YI Xinran;LV Tanghong(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022,China)

机构地区：[1]长春理工大学数学与统计学院,长春130022

出　　处：《吉林大学学报(理学版)》2025年第2期321-330,共10页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅科学研究项目(批准号:JJKH20240891KJ)。

摘　　要：针对自然界中生物种群对环境变化或种群间的相互作用无法做出即时反应的问题.通过引入两个时滞作为分支参数,分析相应的特征方程,并讨论系统在各平衡点处的局部稳定性和Hopf分支的存在性.首先,在两个时滞都等于τ时,用中心流形定理和规范型理论,得到决定Hopf分支方向及周期解稳定性的显式公式;其次,通过数值模拟验证理论分析的准确性.结果表明:当时滞超出临界值时,系统的稳定性发生改变并产生Hopf分支.在生物模型中引入时滞有助于进行更准确地预测种群动态.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 

分 类 号：O175.1[理学—数学]