【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·更多还原

【Abstract】 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.更多还原