HOPF BIFURCATION FOR A ECOLOGICAL MATHEMATICAL MODEL ON MICROBE POPULATIONS

作     者：郭瑞海 袁晓凤 

作者机构：Department of Mathematics Southwest Nationalities College Chengdu P R China Center for Mathematical Sciences CICA Academia Sinica Chengdu P R China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2000年第21卷第7期

页      面：767-774页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：theNationalScienceFoundationofChina !(1 95 71 0 81 ) 

主　　题：mathematical model qualitative theory equilibrium points Hopf bifurcation 

摘      要：The ecological model of a class of the two microbe populations with second-order growth rate was studied. The methods of qualitative theory of ordinary differential equations were used in the four-dimension phase space. The qualitative property and stability of equilibrium points were analysed. The conditions under which the positive equilibrium point exists and becomes and O+ attractor are obtained. The problems on Hopf bifurcation are discussed in detail when small perturbation occurs.