具有Michaelis-Menten响应函数的3种群捕食模型  

A three species predator model with Michaelis-Menten functional response

作　　者：张群英[1] 周桦[1] 侯燕[1] 林支桂[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2004年第2期6-9,21,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10171088)

摘　　要：考虑一个具有Michaelis-Menten响应函数的3种群食物链的方程组正解的动力学行为,利用李雅普诺夫函数研究其局部稳定性与全局稳定性.主要结果为:在第1种群的净出生率足够大以及第3种群的净死亡率既不太大也不太小的情况下,方程组惟一的正平衡解是全局渐近稳定的.This paper deals with the behavior of positive solution for a system describing a three species food chain with Michaelis-Menten functional response. Local stability and global stability are established by Lyapunov function. Result shows that the unique positive equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small.

关 键 词：响应函数 捕食者 全局稳定性 

分 类 号：O175.26[理学—数学]