具有避难所和双时滞的捕食系统的Hopf分支  

Hopf bifurcation of predator-prey system system with two time delays including prey refuge

作　　者：于智博 吕堂红[1] 周林华[1] YU Zhi-bo;LYU Tang-hong;ZHOU Lin-hua(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,吉林长春130022

出　　处：《陕西理工大学学报（自然科学版）》2022年第6期60-69,共10页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(11426045);吉林省自然科学基金学科布局项目(20180101229JC)。

摘　　要：研究一类受到时滞影响的捕食系统的Hopf分支问题。分析了模型在正平衡点附近存在Hopf分支的条件,以时滞τ_(1)=τ_(2)=τ为分支参数,利用中心流型定理和规范型理论计算出决定Hopf分支方向的公式。The Hopf bifurcation problem for a predator-prey system with time delay is studied.The conditions for the existence of Hopf bifurcation near the positive equilibrium point are analyzed.With the time delay as the bifurcation parameter,based on the central flow regime theorem and the normal form theory,the calculation formulas related to Hopf bifurcation are obtained.

关 键 词：时滞 HOPF分支 稳定性 周期解 

分 类 号：O175.1[理学—数学]