具时滞的人类呼吸系统模型的稳定性与分支

沈启宏; 魏俊杰

具时滞的人类呼吸系统模型的稳定性与分支

沈启宏^1,2,
魏俊杰²

1.
迈阿密大学数学系,P.O.Box 249085,迈阿密美国;2.哈尔滨工业大学数学系,哈尔滨 150001

基金项目: 国家自然科学基金资助项目(19831030)

详细信息

作者简介:
沈启宏(1976- ),女,吉林省吉林市人,美国迈阿密大学博士(联系人.E-mail:sph11@yahoo.com).

中图分类号: O175.13
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- 被引次数: 0
出版历程
- 收稿日期: 2003-03-06
- 修回日期: 2004-07-15
- 刊出日期: 2004-11-15

Stability and Bifurcation of a Human Respiratory System Model With Time Delay

SHEN Qi-hong^1,2,
WEI Jun-jie²

1.
Department of Mathematics, University of Miami, P. O. Box 249085, Coral Gables, FL 331244-4250, U S A;

摘要

摘要: 研究了描述人类呼吸系统的具时滞的二维微分方程的平凡解的稳定性和Hopf分支．利用规范型理论和中心流形定理给出了关于分支周期解的稳定性及Hopf分支方向等的计算公式，且进行了数值模拟计算．
- 呼吸系统 /
- 时滞 /
- 稳定性 /
- 分支
Abstract: The stability and bifurcation of the trivial solution in the two-dimensional differental equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem. Furthermore, numerical simulation was carried out.
- respiratory system /
- time delay /
- stability /
- bifurcation

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参考文献(9)

[1]	刘正荣，李继彬.哈密顿系统与时滞微分方程的周期解[M].北京：科学出版社，1996.
[2]	Vielle B,Chauvet G.Delay equation analysis of human respiratory stability[J].Mathematical Biosciences,1998,152：105—122. doi: 10.1016/S0025-5564(98)10028-7
[3]	Vielle B,Chauvet G.Mathematical study of periodic breathing as an instability of the respiratory system[J].Mathematical Biosciences,1993,114：149. doi: 10.1016/0025-5564(93)90076-M
[4]	秦元勋，王联，刘永清，等.带有时滞的动力系统的运动的稳定性[M].北京：科学出版社，1989.
[5]	Hale J,Lunel S V.Introduction to Functional Differential Equations[M].New York:Springer-Verlag,1993.
[6]	Hassard B,Kazarinoff N，Wan Y H.Theory of Applications of Hopf Bifurcaftion[M].London Math,Soc Lect Notes Series,41.Cambridge：Cambridge University Press，1981.
[7]	Kazarinoff N,Wan Y H，Van den Driessche P.Hopf bifurcation and stability of periodic solutions of differential-difference and integro-differential equations[J].J Inst Math Appl,1978,21：461—477.[KG*2]. 裘宗燕.Mathematica数学软件系统的应用及其程序设计[M].北京：北京大学出版社，1996. doi: 10.1093/imamat/21.4.461
[9]	Glass L,Mackey M C.Pathological conditions resulting from instabilities in physiological control system[J].Ann NY Acad,Sci,1979,316：214. doi: 10.1111/j.1749-6632.1979.tb29471.x
[10]	Cooke K,Grossman Z.Discrete delay,distributed delay and stability switches[J].J Math Anal Appl,1982,86:592—627. doi: 10.1016/0022-247X(82)90243-8