一类TCP系统的局部Hopf分支和周期解的全局存在性

徐昌进; 唐先华; 廖茂

doi:10.3879/j.issn.1000-0887.2010.06.012

一类TCP系统的局部Hopf分支和周期解的全局存在性

doi: 10.3879/j.issn.1000-0887.2010.06.012

中南大学数学与计算科学学院,长沙 410083;2.湖南工程学院理学院, 湖南湘潭 411004;3.南华大学数理学院,湖南衡阳 421001

基金项目: 国家自然科学基金资助项目(10771215);湖南工程学院科研启动基金(0744)的资助

详细信息

作者简介:
徐昌进(1970- ),男,湖南怀化人,讲师,博士生(E-mail:xcj403@126.com);唐先华(1963- ),男,湖南衡南人,教授,博士生导师(联系人.E-mail:tangxh@mai.lcsu.edu.cn).

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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-04-09
- 刊出日期: 2010-06-15

Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System

School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;

摘要

摘要: 研究了一类一阶非线性时滞微分方程描述的TCP系统的动力学行为．通过分析其相应的特征超越方程，得到了当时滞通过一系列临界值时，在正平衡点处Hopf分支产生．利用中心流形和规范型理论，得到了确定Hopf分支方向和稳定性的具体计算表达式．运用Wu的方法，得到了全局Hopf分支存在的条件．
- TCP系统 /
- 稳定性 /
- 局部Hopf分支 /
- 全局Hopf分支 /
- 周期解
Abstract: The dynamics of a TCP system described by a firs-torder non linear delay differential equations was investigated. Byanalyzing the associated characteristic tran scendental equation, the result thata sequence of Hopf bifurcations occurat the positive equilibrium as the delay passesth rough a sequence of critical values was obtained. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were derived by using the normal form theory and center manifold theory. Global existence of periodic solutions was also established by using the method of Wu [Trans Amer Math Soc, 1998, 350(12):4799-38].
- TCP system /
- stability /
- local Hopf bifurcation /
- global Hopf bifurcation /
- periodic solution

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参考文献(13)

[1]	Hollot C V， Misra V， Towlsey D， Gong W B. A control theoretic analysis of RED[C]Proceedings of IEEE INFOCOM. Anchorage，Alaska，2001.
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[3]	Hollot C V, Misra V, Towlsey D, Gong W B. On designing improved controller for AQM routes supporting TCP flows[C]Proceedings of IEEE INFOCOM. Anchorage, Alaska, 2001.
[4]	Kunniyur S, Srikant R. Analysis and design of an adaptive virtual queue(AVQ) algorithm for active queue management[C]Proceedings of ACM SIGCOMM. New York, USA, 2001.
[5]	Low S H, Paganin F, Doyle J C. Dynamics of TCP/RED and a scalable control[J].IEEE INFOCOM, 2002, 2(2): 1-10.
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[7]	Srikant R. Models and Methods for Analyzing Internet Congestion Control Algorithms[C]Abdallah C T, Chiasson J, Tarbouriech S.Advances in Communication Control Networks. Princeton, NJ: Springer-Verlag, 2004, 416-419.
[8]	Kelly F P. Fairness and stability of end-to-end congestion control[J]. Eur J Control, 2003, 9: 149-165.
[9]	RUAN Shi-gui, WEI Jun-jie. On the zero of some transcendential functions with applications to stability of delay differential equations with two delays[J]. Dyn Contin Discrete Impuls Syst, Ser A, 2003, 10(6): 863-874.
[10]	Kuang Y. Delay Differential Equations With Applications in Population Dynamics[M]. Boston: Academic Press, INC, 1993.
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[12]	Hassard B, Kazarino D, Wan Y. Theory and Applications of Hopf Bifurcation[M]. Cambridge: Cambridge University Press, 1981.
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一类TCP系统的局部Hopf分支和周期解的全局存在性

doi: 10.3879/j.issn.1000-0887.2010.06.012

作者简介:
徐昌进(1970- ),男,湖南怀化人,讲师,博士生(E-mail:xcj403@126.com);唐先华(1963- ),男,湖南衡南人,教授,博士生导师(联系人.E-mail:tangxh@mai.lcsu.edu.cn).

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Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System

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留言板

一类TCP系统的局部Hopf分支和周期解的全局存在性

doi: 10.3879/j.issn.1000-0887.2010.06.012

作者简介: 徐昌进(1970- ),男,湖南怀化人,讲师,博士生(E-mail:xcj403@126.com);唐先华(1963- ),男,湖南衡南人,教授,博士生导师(联系人.E-mail:tangxh@mai.lcsu.edu.cn).

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出版历程

Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System

计量

出版历程

目录

作者简介:
徐昌进(1970- ),男,湖南怀化人,讲师,博士生(E-mail:xcj403@126.com);唐先华(1963- ),男,湖南衡南人,教授,博士生导师(联系人.E-mail:tangxh@mai.lcsu.edu.cn).