具有收获率和Michaelis-Menten功能性反应的捕食系统的稳定性和Hopf分支  

Stability and Hopf Bifurcation of a Predator-prey System with Michaelis-Menten Functional Response and Harvesting

作　　者：张晓朋[1] 白玉真[1] 

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2011年第3期21-25,共5页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10771118);山东省高等学校科技计划资助项目(J10LA13)

摘　　要：研究一类具有收获率和Michaelis-Menten功能性反应的捕食系统的稳定性和Hopf分支.首先利用微分方程定性理论和构造合适的Dulac函数,对该系统的平衡点进行分析,得到边界平衡点和正平衡点全局渐近稳定的充分条件;其次研究时滞系统,以滞量为参量,得到边界平衡点和正平衡点处发生Hopf分支的充分条件.This paper is concerned with a predator-prey system with Michaelis-Menten functional response and harvesting terms.At first,the sufficient conditions are derived for global asymptotical stability of the boundary equilibrium point and positive equilibrium point by using qualitative analysis of differential equations and constructing suitable Dulac function.Then the time delay system is studied.By choosing time delay as a bifurcation parameter,the sufficient conditions for the existence of Hopf bifurcations at of the boundary equilibrium point and positive equilibrium point are given.

关 键 词：捕食系统 Michaelis-Menten功能性反应 全局渐近稳定 时滞 HOPF分支 

分 类 号：O175.1[理学—数学]