摘要
对于高维微生物种群生态模型,如果能掌握其性态,对研究复杂的生物代谢过程有着重要的意义。文中运用常微分方程相空间定性理论对一类八维微生物数学模型进行了讨论,判定了平衡点的类型及其稳定性,得到了正平衡点的存在及成为O+吸引子的条件,还讨论了系统Hop f分支的存在性。在某些条件下,这四种微生物菌群在达到一定的数量时能够持续的共存。
The understanding of the developing patterns of the ecological model of the multi-dimension microbe has considerable meaning in studying the complicated course of biologic metabolism. Guided by the theory of phase space and qualitative theory of ordinary differential equations a mathematical model is presented and discussed of a class of eight dimension microbe in terms of their qualitative properties and stability of equilibrium points. The conditions under which the positive equilibrium point exists and becomes O^＋ attractor are obtained. The existence of Hopf bifurcation is also discussed. We notice that when the population of the four species of microbe increases to a certain number, they continue to exist under some conditions.
出处
《桂林电子工业学院学报》
2005年第5期66-69,共4页
Journal of Guilin Institute of Electronic Technology
关键词
平衡点
定性理论
HOPF分支
equilibrium points, qualitative theory, hopf bifurcation
