一类微生物种群生态数学模型的Hopf分支

基金项目: 国家自然科学基金资助课题(19571081)

Hopf Bifurcation for a Ecological Mathematical Model on Microbe Populations

1.
Department of Mathematics, Southwest Nationalities College, Chengdu 610041, P R China;
2.
Center for Mathematical Sciences, CICA, Academia Sinica, Chengdu 610041, P R China

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O⁺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。
- 数学模型 /
- 定性理论 /
- 平衡点 /
- Hopf分支
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.
- mathematical model /
- qualitative theory /
- equilibrium points /
- Hopf bifurcation

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