具时滞和收获项的捕食-食饵系统Hopf分支分析
Hopf Bifurcation Analysis of Predator-Prey System with Time Delay and Harvest Terms
吕堂红 1王菲 1周林华1
作者信息
- 1. 长春理工大学 数学与统计学院,吉林 长春 130022
- 折叠
摘要
针对一类具有Leslie-Gower功能反应函数的捕食-食饵系统,以时滞τ1、τ2为分支参数,利用比较定理,分析系统边界平衡点的全局稳定性,并利用规范型理论以及对特征根实部正负的判断,剖析系统正平衡点的局部稳定性以及正平衡点处发生Hopf分支的条件和分支方向.最后根据全局分支理论,将局部Hopf分支的稳定性结论延拓至全局,并经数值模拟证实结果.
Abstract
For a class of predator-prey system with Leslie-Gower functional response function,the global stability of the equilibrium point of the system is analyzed by using the delays τ1,τ2 bifurcation parameter comparison theory,and the local stability of the posi-tive equilibrium point of the system,the conditions and branching direction of Hopf branching at the positive equilibrium point are analyzed by using the gauge theory and the judgment of the positive and negative real parts of the characteristic root.Finally,ac-cording to the global branching theory,the stability conclusion of local Hopf bifurcation is extended to the whole,and the correct-ness of the conclusion is verified by numerical simulation.
关键词
时滞/Leslie-Gower捕食-食饵系统/Hopf分支/稳定性/周期解Key words
time delays/Leslie-Gower predator-prey system/Hopf bifurcation/stability/periodic solutions引用本文复制引用
基金项目
国家自然科学基金(11426045)
吉林省自然科学基金(20180101229JC)
出版年
2024
国家科技期刊平台
NSTL
万方数据