一类微生物种群生态数学模型的Hopf分支

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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

[1]	袁晓凤,刘世泽,郭瑞海等. 厌氧消化过程三种群微生物生态数学模型的定性分析[J]. 四川大学学报(自然科学版),1997,34(3):373～376.
[2]	梅茨基 B.B, 斯捷巴诺夫 B.B. 微分方程定性理论[M].(王柔怀译)北京: 科学出版社,1959,201～230.
[3]	刘世泽. n维空间奇点的拓扑分类[J]. 数学进展,1965,8(3):217～242.
[4]	Hartman P. Ordinary Differential Equation[M]. Baston: Birkhauser,1982,228～250.
[5]	李继彬,冯贝叶. 稳定性、分支与混沌[M]. 昆明: 云南科技出版社,1995,85～127.
[6]	Wiggins S. Introduction to Applied Nonlinear Dynamical System and Chaos[M]. New York: Springer-verlag,1990,193～284.
[7]	Liu Zhenrong, Jing Zhujun. Qualitative analysis for a third-order differential equation in a model of chemical systems[J]. Syst Scie Math Scie,1992,5(4):299～309.