南阳师范学院学报2017，Vol.16Issue(3)：12-15,4.
一类具有时滞和Michaelis-Menten型收获的捕食系统的稳定性与Hopf分支分析
Stability and Hopf bifurcation analysis in a predator-preysystem with time delay and Michaelis-Menten type predator harvesting
胡志1
作者信息
- 1. 兰州交通大学 数理学院,甘肃 兰州 730070
- 折叠
摘要
Abstract
In this paper,a predator-prey system with time delay and nonlinear Michaelis-Menten type harvesting is discussed.By using qualitative theory, stability theory and Hopf bifurcation theory of differential equation, the author studies the dynamic behavior of the model.The author analyzes the conditions to guarantee existence and uniqueness of the positive equilibrium and to make the positive equilibrium asymptotic stability for the system.The author derives the critical value of delay to still guarantee the positive equilibrium of system stable in the certain range but to exhibit Hopf bifurcation as the delay pass through it, when the delay is viewed as bifurcation parameter.关键词
时滞/Hopf分支/稳定性/捕食系统/Michaelis-Menten型收获Key words
delay/Hopf bifurcation/stability/predator-prey system/Michaelis-Menten type harvesting分类
数理科学引用本文复制引用
胡志..一类具有时滞和Michaelis-Menten型收获的捕食系统的稳定性与Hopf分支分析[J].南阳师范学院学报,2017,16(3):12-15,4.
