一类捕食食饵微分经济系统的稳定性与Hopf分支（英文）  

STABILITY AND HOPF BIFURCATION OF A PREDATOR-PREY BIOLOGICAL ECONOMIC SYSTEM

作　　者：刘炜[1] 李必文[1] 李震威 汪淦[1] LIU Wei LI Bi-wen LI Zhen-wei WANG Gan(School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, Chin)

机构地区：[1]湖北师范学院数学与统计学院,湖北黄石435002

出　　处：《数学杂志》2016年第6期1160-1172,共13页Journal of Mathematics

基　　金：Supported by the Research Project of Hubei Provincial Department of Education of China under Grant(T201412)

摘　　要：本文主要研究了一个带有对捕食者进行捕获的微分代数经济系统的稳定性和Hopf分支问题.利用了动力系统和微分代数系统中的稳定性理论和分支理论的方法,得到了稳定性和Hopf分支稳定性的相关结论.本文对Ratio-Dependent捕食食饵模型进行了一定程度的完善,并且选取经济效益μ为分支参数进行研究,最后利用Matlab进行数值模拟,这样使得到的结论更符合现实意义.In this paper,we mainly study the Hopf-bifurcation and the stability of differentialalgebraic biological economic system with predator harvesting.By using the method of stability thoery and Hopf bifurcation theorem dynamical systems and differential algebraic system,we find some related conclusions about stability and Hopf-bifurcation.We have improved the ratio-dependent predator-prey system,take economic effect μ as the bifurcation parameter and make a numerical simulation by using Matlab at last,so the conclusions are made more practical.

关 键 词：稳定性 经济系统 HOPF分支 捕获 

分 类 号：O29[理学—应用数学] O193[理学—数学]