一类微生物种群生态数学模型的Hopf分支  

Hopf Bifurcation for a Ecological Mathematical Model on Microbe Populations

作　　者：郭瑞海[1] 袁晓凤[2] 

机构地区：[1]西南民族学院数学系,成都610041 [2]中国科学院成都计算所数理室,成都610041

出　　处：《应用数学和力学》2000年第7期693-700,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金!资助课题 (195710 81)

摘　　要：讨论了一类具有二阶生长速率的微生物菌群生态数学模型·　运用常微分方程空间定性理论的手法 ,在四维相空间中对该模型进行了深入讨论 ,判定了平衡点的类型及稳定性 ,分析了正平衡点的存在及成为 0 + 吸引子的条件·　最后讨论了系统小扰动下产生Hopf分支的问题·The ecological Model of a class of the two microbe populations with second_order growth rate is studied. The methods of qualitative theory of ordinary differential equations are used in the four_dimension phase space. The qualitative property and stability of equilibrium points are 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.

关 键 词：生态数学模型 定性理论 HOPF分支 微生物 种群 

分 类 号：Q938.15[生物学—微生物学] O174.12[理学—数学]