具Michaelis-Menten型收获项的双时滞捕食-食饵系统Hopf分支  

Hopf Bifurcation of Two Time Delays Predator-Prey System with Michaelis-Menten Harvesting Term

作　　者：王菲[1] 吕堂红[1] 周林华[1] WANG Fei;LÜ Tanghong;ZHOU Linhua(School of Science, 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：《中北大学学报（自然科学版）》2022年第1期25-34,共10页Journal of North University of China(Natural Science Edition)

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

摘　　要：以两个时滞τ_(1),τ_(2)为分支参数,分析了时滞对一类具有Michaelis-Menten型收获项的捕食-食饵系统动力学性质产生的影响.通过对特征方程的根进行研究并运用规范型理论,阐述了多种不同的时滞组合情形下,系统的正稳态性质以及正平衡点附近的Hopf分支的发生条件,利用中心流形定理最终得到确定Hopf分支方向的表达式,并进行了支持理论分析的数值模拟.结果表明,时滞影响了系统的动力学行为,使其动力学性质更加复杂.Taking two time delays as branching parameters,the influence of time delays on the dynamic properties of a predator-prey system with Michaelis-Menten harvesting term was analyzed.By studying the roots of the characteristic equation and using the gauge theory,the positive steady-state properties of the system and the occurrence conditions of Hopf bifurcation near the positive equilibrium point under various combinations of time delays were expounded.The expression for determining the Hopf bifurcation direction was finally obtained by using the central manifold theorem,and the numerical simulation supporting the theoretical analysis was carried out.The results show that the time delay affects the dynamic behavior of the system and makes its dynamic properties more complex.

关 键 词：双时滞 捕食-食饵系统 HOPF分支 稳定性 周期解 

分 类 号：O175.1[理学—数学]