互联网拥塞控制系统动力学行为分析及控制研究
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摘要
由于计算机和通信技术的不断进步,以TCP(Transmission Control Protocol)/IP(Internet Protocol)为基础的互联网逐步普及并得到了巨大的发展。然而随着网络规模的迅速扩大、用户数量的急剧增加和网络应用类型的不断丰富,网络拥塞现象也日益严重。网络拥塞的直接后果是整个网络性能的下降,包括数据包丢弃率增大、时间延迟增加,以及吞吐量下降等,严重时甚至导致网络崩溃。网络拥塞控制是改善网络性能、增加网络鲁棒性和提高服务质量(QoS)的主要手段。
当前互联网拥塞控制包括两方面:基于源端的TCP拥塞控制机制和基于链路端的队列管理机制。这两方面相互影响、相互作用,成为解决目前互联网拥塞问题的主要途径之一,形成了计算机网络、通信、自动控制等学科交叉的一个新的研究热点。
本文采用非线性动力学分析方法来研究互联网拥塞控制系统中存在的复杂非线性动力学现象,如分岔(bifurcation)、混沌(chaos)等,并用成熟的分岔、混沌控制方法来抑制互联网中的这些非线性现象。相对于传统的基于随机理论和排队论的方法,非线性动力学分析可以得到更加精确的结论,这对于互联网拥塞控制系统的建模、改进当前互联网拥塞控制算法和探索新的适合未来高带宽时延乘积网络的拥塞控制机制都非常关键,具有非常重要的理论意义和应用价值。本文主要研究内容和创新之处包括以下几个方面:
(1).提出一种简化互联网拥塞控制系统离散模型动力学行为控制方法。当源端既有TCP流又有UDP(User Datagram Protocol)流、链路端采用RED(Random Early Detection)算法时,分析了该模型的分岔、混沌现象,并采用标准和扩展时延反馈控制(Time-delayed Feedback Control, TDFC)方法来控制系统状态或者参数,从而达到稳定系统平均队列长度的混沌行为的目的。进一步,将该模型扩展到源端是TCP Westwood流、链路端采用RED算法,分析得到了TCP Westwood/RED拥塞控制的动力学模型,并利用该模型分析了系统在不同参数变化时存在倍周期分岔和混沌行为。
(2).提出互联网拥塞控制系统频闪(Stroboscopic)模型混沌行为控制的混合控制(hybrid control)方法。采用一种既包含状态反馈又包含参数摄动的混合控制策略来控制频闪模型的混沌轨道,将其稳定到不动点。而且,获得了包含两条拥塞链路的串联网络的拥塞控制系统频闪模型,并研究了两个瓶链路之间的相互影响,对其系统状态进行控制。结果表明,只要对关键节点进行控制,就可以稳定整个系统。
(3).证明互联网拥塞控制系统对偶(Dual)模型存在霍普夫分岔行为,并提出一种控制其分岔行为的控制方法。理论分析表明,当分岔参数(通信延迟)超过某一临界值,系统失去稳定性,并且发生霍普夫分岔。同时,利用摄动法(Perturbation Method, PM),确定了该分岔的方向和分岔周期解的稳定性。其次,采用时间延迟反馈的方法有效地推迟了系统霍普夫分岔的发生,扩大了系统的稳定区间。
(4).分析TCP/RED拥塞控制系统流体流模型(Fluid-Flow Model, FFM)当通信延迟变化时存在的霍普夫分岔现象,提出一种简单的控制器来扩大系统的稳定性。理论分析和仿真实验表明,当系统的通信延迟超过某一临界值,系统将出现霍普夫分岔行为,即系统状态由稳定的平衡点变为极限环。并且,霍普夫分岔的方向和周期解的稳定性可以通过中心流形定理(Center Manifold Theorem, CMT)和正规形理论(Normal Form Theory, NFT)来确定。进一步,通过在系统的一个状态变量上加入一种时间延迟反馈控制器,控制霍普夫分岔的发生,进而扩大系统对通信延迟的稳定性区间。
Since the rapid progress made in computer and communication technology, the TCP (Transmission Control Protocol) / IP (Internet Protocol)-based Internet has developed enormously. However, with the growing size, popularity and application of the Internet, congestion has become an increasing serious issue. Congestion can cause significant deterioration of network performance, including package drop probability, time delay and network throughput, and even cause the happening of congestion collapse. Network congestion control is the main method for improving the performance, increasing the robustness and strenghthening the quality of service of the whole network.
At present, the congestion control strategy of Internet consists of two parts: a source algorithm carried out by TCP at hosts and a link algorithm by AQM (Active Queue Management) schemes at routers. The combination of both parts has been the main approach to solve the Internet congestion control problem and is now considered a research hotspot which intercrosses several disciplines, such as computer networks, communication and automatic control.
In this dissertation, nonlinear dynamic analysis is applied to interpret the occurrence of nonlinear phenomenon (such as bifurcation and chaos) in Internet congestion control systems. Moreover, bifurcation and chaos control methods are used to eliminate nonlinear behavior in the Internet. Comparing traditional stochastic theory and queuing theory, the nonlinear dynamic analysis is expected to lead to more precise results. Thus it is important to model the Internet congestion control systems, improve the present congestion control scheme and explore new congestion control strategies for future high bandwidth-delay-product networks. Therefore, research of the Internet congestion control systems has very important theoretical significance and application values.
The main contents and contributions of this dissertation can be summarized as follows:
(1). Nonlinear dynamic behavior and its control problem in a discrete-time model of a simple Internet congestion control system are studied. It is shown that the system has complex dynamic behaviors, such as bifurcation and chaos, with TCP and UDP (User Data Protocol) flows at sources and RED (Random Early Detect) algorithm at router. Then, we apply standard and extended time-delayed feedback control (TDFC) approaches to control the system state or parameters in order to stabilize the chaotic behavior of average queue size of the system. Furthermore, this model is extended to systems with TCP Westwood flows and RED gateway. The existence of period-doubling bifurcation and chaotic behaviors is also indicated in the system with variation of parameters.
(2). The control of dynamic behavior in stroboscopic model of Internet congestion control system is studied. A hybrid control strategy using both state feedback and parameter perturbation is applied to control the chaotic orbits embedded in the stroboscopic model in order to stabilize it to an equilibrium point. Moreover, this model is extended to a network with two bottleneck links. The interaction of two bottleneck links is investigated. The result indicates that the whole network can be stabilized when a key node is controlled.
(3). The analysis and control of Hopf bifurcation in a Dual model of Internet congestion control system are studied. It is indicated that the model loses stability and a Hopf bifurcation occurs when bifurcation parameter (communication delay) passes through a critical value. Moreover, by using the perturbation method, we have analyzed the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Then a time-delayed feedback control strategy is applied to the system for postponing onset of undesirable Hopf bifurcation and increasing stability region of the system.
(4). The analysis and control of Hopf bifurcation in a Fluid-Flow model of Internet congestion control system are studied. Theoretical analysis and numerical simulations show that a Hopf bifurcation occurs in the system when communication delay passes through a critical value. This means that the state of system changes from an equilibrium point to a limit cycle. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions have also been investigated by applying the center manifold theorem and the normal form theory. Then a time-delay feedback controller is added to the system for controlling the Hopf bifurcation, which can increase stability region of the system.
当前互联网拥塞控制包括两方面:基于源端的TCP拥塞控制机制和基于链路端的队列管理机制。这两方面相互影响、相互作用,成为解决目前互联网拥塞问题的主要途径之一,形成了计算机网络、通信、自动控制等学科交叉的一个新的研究热点。
本文采用非线性动力学分析方法来研究互联网拥塞控制系统中存在的复杂非线性动力学现象,如分岔(bifurcation)、混沌(chaos)等,并用成熟的分岔、混沌控制方法来抑制互联网中的这些非线性现象。相对于传统的基于随机理论和排队论的方法,非线性动力学分析可以得到更加精确的结论,这对于互联网拥塞控制系统的建模、改进当前互联网拥塞控制算法和探索新的适合未来高带宽时延乘积网络的拥塞控制机制都非常关键,具有非常重要的理论意义和应用价值。本文主要研究内容和创新之处包括以下几个方面:
(1).提出一种简化互联网拥塞控制系统离散模型动力学行为控制方法。当源端既有TCP流又有UDP(User Datagram Protocol)流、链路端采用RED(Random Early Detection)算法时,分析了该模型的分岔、混沌现象,并采用标准和扩展时延反馈控制(Time-delayed Feedback Control, TDFC)方法来控制系统状态或者参数,从而达到稳定系统平均队列长度的混沌行为的目的。进一步,将该模型扩展到源端是TCP Westwood流、链路端采用RED算法,分析得到了TCP Westwood/RED拥塞控制的动力学模型,并利用该模型分析了系统在不同参数变化时存在倍周期分岔和混沌行为。
(2).提出互联网拥塞控制系统频闪(Stroboscopic)模型混沌行为控制的混合控制(hybrid control)方法。采用一种既包含状态反馈又包含参数摄动的混合控制策略来控制频闪模型的混沌轨道,将其稳定到不动点。而且,获得了包含两条拥塞链路的串联网络的拥塞控制系统频闪模型,并研究了两个瓶链路之间的相互影响,对其系统状态进行控制。结果表明,只要对关键节点进行控制,就可以稳定整个系统。
(3).证明互联网拥塞控制系统对偶(Dual)模型存在霍普夫分岔行为,并提出一种控制其分岔行为的控制方法。理论分析表明,当分岔参数(通信延迟)超过某一临界值,系统失去稳定性,并且发生霍普夫分岔。同时,利用摄动法(Perturbation Method, PM),确定了该分岔的方向和分岔周期解的稳定性。其次,采用时间延迟反馈的方法有效地推迟了系统霍普夫分岔的发生,扩大了系统的稳定区间。
(4).分析TCP/RED拥塞控制系统流体流模型(Fluid-Flow Model, FFM)当通信延迟变化时存在的霍普夫分岔现象,提出一种简单的控制器来扩大系统的稳定性。理论分析和仿真实验表明,当系统的通信延迟超过某一临界值,系统将出现霍普夫分岔行为,即系统状态由稳定的平衡点变为极限环。并且,霍普夫分岔的方向和周期解的稳定性可以通过中心流形定理(Center Manifold Theorem, CMT)和正规形理论(Normal Form Theory, NFT)来确定。进一步,通过在系统的一个状态变量上加入一种时间延迟反馈控制器,控制霍普夫分岔的发生,进而扩大系统对通信延迟的稳定性区间。
Since the rapid progress made in computer and communication technology, the TCP (Transmission Control Protocol) / IP (Internet Protocol)-based Internet has developed enormously. However, with the growing size, popularity and application of the Internet, congestion has become an increasing serious issue. Congestion can cause significant deterioration of network performance, including package drop probability, time delay and network throughput, and even cause the happening of congestion collapse. Network congestion control is the main method for improving the performance, increasing the robustness and strenghthening the quality of service of the whole network.
At present, the congestion control strategy of Internet consists of two parts: a source algorithm carried out by TCP at hosts and a link algorithm by AQM (Active Queue Management) schemes at routers. The combination of both parts has been the main approach to solve the Internet congestion control problem and is now considered a research hotspot which intercrosses several disciplines, such as computer networks, communication and automatic control.
In this dissertation, nonlinear dynamic analysis is applied to interpret the occurrence of nonlinear phenomenon (such as bifurcation and chaos) in Internet congestion control systems. Moreover, bifurcation and chaos control methods are used to eliminate nonlinear behavior in the Internet. Comparing traditional stochastic theory and queuing theory, the nonlinear dynamic analysis is expected to lead to more precise results. Thus it is important to model the Internet congestion control systems, improve the present congestion control scheme and explore new congestion control strategies for future high bandwidth-delay-product networks. Therefore, research of the Internet congestion control systems has very important theoretical significance and application values.
The main contents and contributions of this dissertation can be summarized as follows:
(1). Nonlinear dynamic behavior and its control problem in a discrete-time model of a simple Internet congestion control system are studied. It is shown that the system has complex dynamic behaviors, such as bifurcation and chaos, with TCP and UDP (User Data Protocol) flows at sources and RED (Random Early Detect) algorithm at router. Then, we apply standard and extended time-delayed feedback control (TDFC) approaches to control the system state or parameters in order to stabilize the chaotic behavior of average queue size of the system. Furthermore, this model is extended to systems with TCP Westwood flows and RED gateway. The existence of period-doubling bifurcation and chaotic behaviors is also indicated in the system with variation of parameters.
(2). The control of dynamic behavior in stroboscopic model of Internet congestion control system is studied. A hybrid control strategy using both state feedback and parameter perturbation is applied to control the chaotic orbits embedded in the stroboscopic model in order to stabilize it to an equilibrium point. Moreover, this model is extended to a network with two bottleneck links. The interaction of two bottleneck links is investigated. The result indicates that the whole network can be stabilized when a key node is controlled.
(3). The analysis and control of Hopf bifurcation in a Dual model of Internet congestion control system are studied. It is indicated that the model loses stability and a Hopf bifurcation occurs when bifurcation parameter (communication delay) passes through a critical value. Moreover, by using the perturbation method, we have analyzed the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Then a time-delayed feedback control strategy is applied to the system for postponing onset of undesirable Hopf bifurcation and increasing stability region of the system.
(4). The analysis and control of Hopf bifurcation in a Fluid-Flow model of Internet congestion control system are studied. Theoretical analysis and numerical simulations show that a Hopf bifurcation occurs in the system when communication delay passes through a critical value. This means that the state of system changes from an equilibrium point to a limit cycle. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions have also been investigated by applying the center manifold theorem and the normal form theory. Then a time-delay feedback controller is added to the system for controlling the Hopf bifurcation, which can increase stability region of the system.
引文
[1] Postel J., Transmission Control Protocol. RFC793. IETF. 1981
[2] Jacobson V., Congestion Avoidance and Control. ACM Computer Communication Review. 1988 18 (4): 314-329
[3] Jain R., Congestion control in computer networks: Issues and Trends. IEEE Network Magazine. 1990 4 (3): 24-30
[4]姜明, TCP协议的拥塞控制策略及改进. 2003. http://business.ccidnet.com/art/930/20030402/42351_1.html
[5]汪小帆,孙金生,王执铨,控制理论在Internet拥塞控制中的应用.控制与决策. 2002 17 (2): 129-134
[6] Kaplan D., Glass L., Understanding Nonlinear Dynamics. New York: Springer-Verlag. 1997
[7] Banerjee S., Ranjan P., Grebogi C., Bifurcations in two-dimensional piecewise smooth maps- theory and application in switching circuits. IEEE Trans. Circuits Syst. I. 2000 47 633-643
[8]刘秉正,彭建华,非线性动力学.北京:高等教育出版社. 2004
[9] Kalampoukas L., Congestion Management in High Speed Networks. Ph.D. University of California, Santa Cruz. 1997
[10] Tanenbaum A.S., Computer Networks. New Jersey: Prentice-hall. 1996
[11]章淼,吴建平,林闯,互联网端到端拥塞控制研究综述.软件学报. 2002 13 (3): 354-363
[12] Thompson K., Miller G.J., Wilder R., Wide-Area Internet traffic patterns and characteristics. IEEE Network. 1997 11 (6): 10-23
[13] Floyd S., Fall K., Promoting the use of end-to-end congestion control in the Internet.IEEE/ACM Transactions on Networking. 1999 7 (4): 458-472
[14]张曾科,计算机网络.北京:清华大学出版社. 2005
[15] Floyd S., Henderson T., The New Reno modification to TCP's fast recovery algorithm. RFC2582. IETF. 1999
[16] Mathis M., Mahdavi J., Floyd S. et.al, TCP selective acknowledgement options. RFC2018. IETF. 1996
[17] Brakmo L.S., Peterson L.L., TCP Vegas: end to end congestion avoidance on a global Internet. IEEE J. on Selected Areas in Communications. 1995 13 (8): 1465-1480
[18] Allman M., Paxson V., Stevens W., TCP congestion control. RFC2581. IETF. 1999
[19] Floyd S., A report on some recent developments in TCP congestion control. IEEE Communications Magazine. 2001 35 (4): 84-90
[20] Floyd S., High speed TCP for large congestion windows. RFC3649. IETF. 2003
[21] Kelly T., Scalable TCP: Improving performance in high speed wide area networks. 2003. http://www.lce.eng.cam.ac.uk/~ctk21/scalable/
[22] Wei D. X., Jin C., Low S. H., Hegde S., FAST TCP: Motivation, Architecture, Algorithms, Performance. IEEE/ACM Transactions on Networking. 2006 14 (6): 1246-1259
[23] Xu L., Harfoush K., Rhee I., Binary increase congestion control for fast long-distance networks. In Proc. IEEE INFOCOM 2004. Piscataway. 2004:2514-2524
[24] Leith D., Shorten R. , H-TCP: TCP for high-speed and long-distance networks. 2004. http://www.hamilton.ie/net/htcp3.pdf
[25] Rhee I., Xu L., CUBIC: A New TCP-Friendly High-Speed TCP Variants. In Proc. PFLDnet. Lyon. 2005
[26] Katabi D., Handley M., Rohrs C., Internet Congestion Control for Future High Bandwidth-Delay Product Environments. In Proc. ACM Sigcomm 2002. Pittsburgh. 2002
[27] Braden B., Clark D., Crowcroft J., et al., Recommendations on queue management and congestion avoidance in the Internet. RFC2309. IETF. 1998
[28] Floyd S., Jacobson V., Random early detection gateways for congestion avoidance. IEEE/ACM Transactions on Networking. 1993 1 (4): 393-413
[29] Christiansen M., Jeffay K., Ott D., et al., Tuning RED for Web traffic. ACMComputer Communication Review. 2000 30 (4): 139-150
[30] May M., Bolot J., Diot C., et al., Reasons not to deploy RED. In Proc. IWQoS'99. London. 1999 260-262
[31] Ott T.J., Lakshman T.V., Wong L.H., SRED: Stabilized RED. In Proc. IEEE INFOCOM'99. New York. 1999 1346-1355
[32] Aweya J., Ouellette M., Montuno D.Y. , A Control Theoretic Approach to Active Queue Management. Computer Networks 2001 36 (2-3): 203-235
[33] Floyd S., Gummadi R., Shenker S., Adaptive RED: An algorithm for increasing the robustness of RED's active queue management. 2001. http://www.icir.org/floyd
[34] Liu S., Basar T., Srikant R. , Exponential RED: A Stabilizing AQM Scheme for Low- and High-speed TCP Protocols. IEEE/ACM Trans. Networking. 2005 13 (5): 1068-1081
[35] Athuraliya S., Low S., Li V., et al., REM: Active queue management. IEEE Network Magazine. 2001 15 (3): 48-53
[36] Lakshmikantha A., Beck C.L., Srikant R., Robustness of Real and Virtual Queue-Based Active Queue Management Schemes IEEE/ACM Transactions on Networking 2005 13 (1): 81-93
[37] Kunniyur S., Srikant R., Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management. In Proc. ACM SIGCOMM 2001. San Diego. 2001:123-134
[38] Feng W., Kandlur D., Saha D., et al., BLUE: A New Class of Active Queue Management Algorithms. 1999. http://citeseer.ist.psu.edu/feng99blue.html
[39] Hollot C.V., Misra V., Towsley D., et al., On Designing Improved Controllers for AQM Routers Supporting TCP Flows. In Proc. IEEE INFOCOM 2001. Anchorage. 2001:1726-1734
[40] Mascolo S., Casetti C., Gerla M., et al., TCP westwood: Bandwidth estimation for enhanced transport over wireless links. In Proc. ACM Mobicom 2001. Rome, Italy. 2001:287-297
[41]蒋凯,一类网络拥塞控制系统非线性动力学分析与设计. [博士学位论文]上海.上海交通大学. 2005
[42]刘延柱,陈立群,非线性振动.北京:高等教育出版社. 2001
[43]陈予恕,非线性振动.北京:高等教育出版社. 2002
[44] Hassard B.D., KazarinoffN. D., Wan Y.H., Theory and application of Hopf bifurcation. Cambridge: Cambridge University Press. 1981
[45] Chen G., Moiola J.L., Wang H.O., Bifurcation control: theories, methods, and applications. International Journal of Bifurcation and Chaos. 2000 10 (3): 511-548
[46] Abed E.H., Fu J.H., Local feedback stabilization and bifurcation control 1. Hopf bifurcation. Systems & Control Letters 1986 7 (1): 11-17
[47] Abed E.H., Fu J.H., Local feedback stabilization and bifurcation control 2. Stationary bifurcation. Systems & Control Letters. 1987 8 (5): 467-473
[48] Abed E.H., Wang H.O., Chen R.C., Stabilization of period doubling bifurcations and implications for control of chaos. Physica D. 1994 70 (1): 154-164
[49] Kang W., Bifurcation control via state feedback for systems with a single uncontrollable mode. SIAM Journal on Control and Optimization. 2000 38 (5): 1428-1452
[50] Yabuno H., Bifurcation control of parametrically excited Duffing system by a combined linear-plus-nonlinear feedback control. Nonlinear Dynamics. 1997 12 (3): 263-274
[51] Wang H.O., Abed E.H., Bifurcation control of a chaotic system. Automatica. 1995 31 (9): 1213-1226
[52] Berns D.W., Moiola J.L., Chen G., Feedback control of limit cycle amplitudes from a frequency domain approach. Automatica. 1998 34 (12): 1567-1573
[53] Berns D.W., Moiola J.L., Chen G., Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1998 45 (7): 759-763
[54] Genesio R., Tesi A., Wang H.O., et al., Control of period doubling bifurcations using harmonic balance. In Proc. IEEE Conference on Decision and Control'93. San Antonio. 1993:492 - 497
[55] Tesi A., Abed E.H., Genesio R., et al., Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics. Automatica. 1996 32 (9): 1255-1271
[56] Brandt M.E., Chen G., Bifurcation control of two nonlinear models of cardiac activity.IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1997 44 (10): 1031-1034
[57] Chen G., Fang J.Q., Hong Y., et al., Controlling bifurcations: continuous-time systems. ACTA Physica China. 1999 8:416-422
[58] Chen G., Fang J.Q., Hong Y., et al., Controlling Hopf bifurcations: The discrete-time systems. Discrete Dynamics in Nature and Society. 2000 5 (1): 29-33
[59] Chen G., Lu J., Nicholas B., et al., Bifurcation dynamics in control system. International Journal of Bifurcation and Chaos. 1999 9 (1): 287-293
[60] Yap K.C., Chen G., Controlling bifurcations of discrete maps. Latin American Applied Research. 2001 31 (3): 157-162
[61] Kang W., Bifurcation and normal form of nonlinear control systems Parts I and II. SIAM Journal on Control and Optimization. 1998 36 (1): 193-232
[62]邹艳丽,非线性电路和复杂网络的混沌控制与同步研究. [博士学位论文]上海.上海交通大学. 2006
[63]关新平,范正平,陈彩莲,华长春,混沌控制及其在保密通信中的应用.北京:国防工业出版社. 2002
[64] Ott. E, Chaos in dynamical systems. (Second edition). Cambridge: Cambridge University Press. 2002
[65] Kolmogorov A.N., Preservation of conditionally periodic movements with small change in the Hamiltonian function. Doklady Akad Nauk SSSR. 1954 98:527-530
[66] Lorenz E., Deterministic non-periodic flows. Atmosphere Science. 1963 20 (1): 130-141
[67] Ruelle D., Takens F., On the nature of turbulence. Commun. math. Phys. 1971 20:167-192
[68] Li T.Y., Yorke J.A., Period Three Implies Chaos. Amer. Math. Monthly. 1975 82 (10): 985-992
[69] Feigenbaum M.J., Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. . 1978 19 (1): 25-52
[70] Feigenbaum M.J., The universal metric properties of nonlinear transformations. J. Stat. Phys. 1979 21 (4): 669-706
[71]罗晓曙,非线性系统中的混沌控制与同步及其应用研究. [博士学位论文]合肥.中国科学技术大学. 2003
[72]蒋品群,混沌系统和复杂网络系统的控制、同步和演化研究. [博士学位论文]合肥.中国科学技术大学. 2005
[73] Ott E., Grebogi C., Yorke J.A., Controlling chaos. Physical Review Letters. 1990 64 (11): 1196-1199
[74] Ditto W.L., Rauseo S.N., Spano M. L., Experimental control of chaos. Physical Review Letters. 1990 65 (26): 3211-3214
[75] Hubler A., Adaptive control of chaotic system. Hdvetica Physica Acta. 1989 62:343-346
[76] Fradkov A.L., Guzenko P., Pavlov A., Adaptive control of recurrent trajectories based on linearization of Poincare map. International Journal of Bifurcation and Chaos. 2000 10 (3): 621-637
[77] Epureanu B.I., Dowell E.H., System Identification for Ott-Grebogi-Yorke controller design. Phys. Rev. E. 1997 56 (5): 5327-5331
[78] Epureanu B.I., Dowell E.H., Optimal multi-dimensional OGY controller. Physica D. 2000 139 (1): 87-96
[79] Aston P.J., Bird C.M., Using control of chaos to refine approximations to periodic points. International Journal of Bifurcation and Chaos. 2000 10:227-235
[80] Huberman B.A., Lumer E., Dynamics of adaptive systems. IEEE Transactions on Circuits and Systems. 1990 37 (4): 547-550
[81] Sinha S., Ramaswamy R., Rao J., Adaptive control on nonlinear dynamics. Physica D. 1990 43 (1): 118-128
[82] Hu H.Y., An adaptive control scheme for recovering periodic motion of chaotic systems. Journal of Sound and Vibration. 1997 199 (2): 269-274
[83] Ramaswamy R., Sinha S., Gupte N., Targeting chaos through adaptive control. Phys. Rev. E. 1998 57 (3): 2507-2510
[84] Arecchi F.T., Boccaletti S., Adaptive strategies for recognition, nosie filtering, control, synchronization and targeting of chaos. Chaos. 1997 7 (4): 621-634
[85] Boccaletti S., Farini A., Arecchi F.T., Adaptive strategies for recognition, control, andsynchronization of chaos. Chaos, Solitons and Fractals. 1997 8 (9): 1431-1448
[86] Christini D.J., In V., Spano M.L., et al., Real-time experimental control of system in its chaotic and nonchaotic regimes. Phys. Rev. E. 1997 56 (4): 3749-3752
[87] Christini D.J., Kaplan D.T., Adaptive estimation and control method for unstable periodic dynamics in spike trains. Phys. Rev. E. 2000 61 (5): 5149-5153
[88] Pyragas K., Continuous control of chaos by self-controlling feedback. Physics Letters A. 1992 170 (6): 421-428
[89] Naumenko A.V., Loiko N.A., Turovets S.I., et al., Bias current impulsive feedback control of nonlinear dynamics in external cavity laser diodes. Electronics Letters. 1998 34 (2): 181-182
[90] Naumenko A.V., Loiko N.A., Turovets S.I., et al., Chaos control in external cavity laser diodes using electronic impulsive delayed feedback. International Journal of Bifurcation and Chaos. 1998 8 (9): 1791-1799
[91] Bleich M.E., Hochheiser D., Moloney J.V., et al., Controlling extended systems with spatially filtered, time-delayed feedback. Phys. Rev. E. 1997 55 (3): 2119-2126
[92] Hai W.H., Duan Y.W., Pan L.X., An analytical study for controlling unstable periodic motion in Magneto-elastic Chaos. Phys. Lett. A. 1997 234 (3): 198-204
[93] Hikihara T., Touno M., Kawagoshi T., Experimental stabilization of unstable periodic orbit in Magneto-elastic chaos by delayed feedback control. International Journal of Bifurcation and Chaos. 1997 7 (12): 2837-2846
[94] Brandt M.E., Shih H.T., Chen G., Linear time-delay feedback control of a Pathological rhythm in a cardiac conduction model. Phys. Rev. E. 1997 56 (2): 1334-1337
[95] Konishi K., Kokame H., Hirata K., Decentralized delayed-feedback control of an optimal velocity traffic model. The European Physical Journal B. 2000 15 (4): 715-722
[96] Konishi K., Kokame H., Hirata K., Coupled map car-following model and its delayed-feedback control. Phys. Rev. E. 1999 60 (4): 4000-4007
[97] Batlle C., Fossas E., Olivar G., Stabilization of periodic orbits of the buck converter by time-delayed feedback. Int. J. Circ. Theor. And Appl. 1999 27 (6): 617-631
[98] Bakker R., De Korte R.J., Schouten J.C., Neural networks for prediction and control of chaotic fluidized bed hydrodynamics: a first step. Fractals. 1997 5 (3): 523-530
[99] Dracopoulos D.C., Jones A.J., Adaptive neuro-genetic control of chaos applied to the attitude control problem. Neural Computing and Applications. 1997 6 (2): 102-115
[100] Greenwood D.P.A., Carrasco R.A., Neural networks for the adaptive control of disruptive nonlinear network traffic. IEE Proceedings Communications. 2000 147 (5): 285-291
[101] Tanaka K., Ikeda T., Wang H.O., A unified approach to controlling chaos via Arm LMI-based fuzzy control system design. IEEE Trans. Circuits Syst. I. 1998 45 (10): 1021-1040
[102] Udawatta L., Watanabe K., Kiguchi K., et al., Fuzzy-chaos hybrid controller for controlling of nonlinear systems. IEEE Transactions on Fuzzy Systems. 2002 10 (3): 401 - 411
[103] Arecchi F.T., Boccaletti S., The control of chaos: theoretical schemes and experimental realizations. International Journal of Bifurcation and Chaos. 1998 8 (8): 1643-1655
[104] Boccaletti S., Farini A., Arecchi F.T., The control of chaos: theory and applications. Physics Reports. 2000 329 (3): 103-197
[105] Andrievskii B.R., Fradkov A.L., Control of chaos: methods and applications I. methods. Automation and Remote Control 2003 64 (5): 673-713
[106] Andrievskii B.R., Fradkov A.L., Control of chaos: methods and applications II. applications. Automation and Remote Control 2004 65 (4): 505-533
[107]闫友彪,陈元琰,罗晓曙等, Internet拥塞控制研究的最新进展分析和展望.计算机应用研究. 2005 2:8-13
[108] Ranjan P., Abed E.H., La R.J., Nonlinear instabilities in TCP-RED. In Proc. IEEE INFOCOM 2002. New York. 2002:249 - 258
[109] Ranjan P., Abed E.H., La R.J., Nonlinear instabilities in TCP-RED. IEEE/ACM Trans. Networking. 2004 12 (6): 1079-1092
[110] Firoiu V., Borden M., A study of active queue management for congestion control. In Proc. IEEE INFOCOM 2000. Tel Aviv. 2000:1435-1444
[111] Mathis M., Semke J., Mahdavi J., et al., The macroscopic behavior of the TCP congestion avoidance algorithm. Computer Communication Review. 1997 27 (3): 67-82
[112] Plasser T., Ziegler T., Reichl P., On the nonlinearity of the RED drop function. In Proc. International Conference on Computer Communication (ICCC 2002). Mumbai, India. 2002 515-534
[113] Padhye J., Firoiu V., Towsley D., et al., Modeling TCP Reno performance: a simple model and its empirical validation. IEEE/ACM Trans. Networking. 2000 8 (2): 133-145
[114] Ranjan P., Abed E.H., Chaotic behavior in TCP-RED. In Proc. IEEE Conference on Decision and Control (CDC 2002). Las Vegas. 2002:540- 542
[115] Ranjan P., Abed E.H., Bifurcation analysis of TCP-RED dynamics. In Proc. American Control Conference (ACC 2002). Anchorage. 2002:2443-2448
[116] La R.J., Ranjan P., Abed E.H., Nonlinearity of TCP and instability with RED. In Proc. SPIE ITCom 2002 Boston. 2002:283-294
[117] La R.J., Ranjan P., Abed E.H., Nonlinear dynamics of mixed TCP and UDP traffic under RED. 2002. http://citeseer.ist.psu.edu/489676.html
[118] Ranjan P., La R.J., Abed E.H., Bifurcations of TCP and UDP traffic under RED. 2002. http://citeseer.ist.psu.edu/501895.html
[119] La R.J., Instability of a tandem network and its propagation under RED. IEEE Trans. Automatic Control. 2004 49 (6): 1006-1011
[120] Ranjan P., La R.J., Abed E.H., Washout filter-aided RED control. In Proc. American Control Conference (ACC 2004). Boston. 2004:2966 - 2971
[121] La R. J., Ranjan P., Abed E. H. , Feedback Control of Random Early Detection. In Proc. 40th Annual Allerton. Conference on Communication Control and Computing. Urbana. 2002:1377-1386
[122] Chen L., Wang X.F., Han Z.Z., Controlling bifurcation and chaos in Internet congestion control model. International Journal of Bifurcation and Chaos. 2004 14 (5): 1863-1876
[123] Zhang H., Liu M., Vukadinovic V., et al., Modeling TCP/RED: a dynamical approach. Complex Dynamics in Communication Networks. Berlin. Springer Verlag. 2005:251-278
[124] Liu M., Zhang H., Trajkovic Lj., Stroboscopic model and bifurcations in TCP/RED. In Proc. IEEE International Symposium on Circuits and Systems (ISCAS 2005). Kobe,Japan. 2005:2060 - 2063
[125] Liu M., Marciello A., Bernardo M. di, et al., Discontinuity-induced bifurcations in TCP/RED. In Proc. IEEE International Symposium on Circuits and Systems (ISCAS 2006). Kos, Greece. 2006:2629-2632
[126] Fall K., Floyd S., Simulation-based comparison of Tahoe, Reno and SACK TCP. ACM Computer Communication Review. 1996 26 (3): 5-21
[127] Low S.H., A duality model of TCP and queue management algorithms. IEEE/ACM Trans. Networking. 2003 11 (4): 525-536
[128] Athuraliya S., Low S.H., An empirical validation of a duality model of TCP and queuemanagement algorithms. In Proc. The 33nd conference on Winter simulation. Arlington. 2001:1269 - 1274
[129] Low S.H., Paganini F., Doyle J.C., Internet congestion control. IEEE Control Systems Magazine. 2002 22 (1): 28-43
[130] Paganini F., On the stability of optimization-based flow control. In Proc. American Control Conference (ACC 2001). Arlington. 2001 4689 - 4694
[131] Kelly F., Maulloo A., Tan D., Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Socity. 1998 49 (3): 237-252
[132] Gibbens R.J., Kelly F.P. , Resource pricing and the evolution of congestion control. Automatica. 1999 35 (12): 1969-1985
[133] Zhu L., Ansari N., Local Stability of a New Adaptive Queue Management (AQM) Scheme. IEEE Communications Letters. 2004 8 (6): 406-408
[134] Papachristodoulou A., Global stability analysis of a TCP/AQM protocol for arbitrary networks with delay. In Proc. 43rd IEEE Conference on Decision and Control (CDC 2004). Atlantis. 2004:1029-1034
[135] Voice T., A Global Stability Result For Primal Dual Congestion Control Algorithms With Routing. Computer Communication Review. 2004 34 (3): 35-41
[136] Alpcan T., Basar T., A Globally Stable Adaptive Congestion Control Scheme for Internet-Style Networks with Delay. IEEE/ACM Trans. Networking. 2005 13 (6): 1261-1274
[137] Paganin i F., Wang Z., Doyle J.C., et al. , Congestion Control for High Performance, Stability, and Fairness in General Networks. IEEE/ACM Trans. Networking. 2005 13 (1): 43-56
[138] Ying L., Dullerud G.E., Srikant R., Global Stability of Internet Congestion Controllers with Heterogeneous Delays. IEEE/ACM Trans. Networking. 2006 14 (3): 579-591
[139] Tian Y.P., Stability Analysis and Design of the Second-Order Congestion Control for Networks with Heterogeneous Delays. IEEE/ACM Trans. Networking. 2005 13 (5): 1082-1093
[140] Li C.G., Chen G., Liao X.F., et al., Hopf bifurcation in an Internet congestion control model. Chaos, Solitons and Fractals. 2004 19 (4): 853-862
[141] Yang H.Y., Tian Y.P., Hopf bifurcation in REM algorithm with communication delay. Chaos, Solitons and Fractals. 2005 25 (5): 1093-1105
[142] Raina G., Local Bifurcation Analysis of Some Dual Congestion Control Algorithms. IEEE Trans. Automatic Control. 2005 50 (8): 1135-1146
[143] Chen Z., Yu P., Hopf Bifurcation Control for an Internet Congestion Model. International Journal of Bifurcation and Chaos. 2005 15 (8): 2643-2651
[144] Misra V., Gong W.B., Towsley D., Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED. In Proc. ACM/SIGCOMM 2000. Santa Clara. 2000:151-160
[145] Hollot C.V., Misra V., Towsley D., et al., A control theoretic analysis of RED. In Proc. IEEE/INFOCOM 2001. Anchorage. 2001:1510-1519
[146] Hollot C.V., Chait Y. , Nonlinear Stability Analysis for a Class of TCP/AQM Networks In Proc. IEEE Conference on Decision and Control (CDC 2001). Orlando. 2001:2309-2314
[147] Hollot C.V., Misra V., Towsley D., et al., Analysis and Design of Controllers for AQM Routers Supporting TCP Flows. IEEE Trans. Automatic Control. 2002 47 (6): 945-959
[148] Ren F.Y., Li C., Wei B., A nonlinear control theoretic analysis to TCP-RED system. Computer Networks. 2005 49 (4): 580-592
[149] Tan L.S., Zhang W., Peng G., et al., Stability of TCP/RED Systems in AQM Routers. IEEE Trans. Automatic Control. 2006 51 (8): 1393-1398
[150] Bauso D., Giarre L., Neglia G., AQM stability in multiple bottleneck networks. In Proc. IEEE International Conference on Communication (ICC 2004). Paris. 2004:2267-2271
[151] Michiels W., Niculescu S.-I., Stability analysis of a Fluid Flow Model for TCP like Behavior. International Journal of Bifurcation and Chaos. 2005 15 (7): 2277-2282
[152] Michiels W., Melchor-Aguilar D., Niculescu S.-I., Stability analysis of some classes of TCP/AQM networks. International Journal of Control. 2006 79 (9): 1134-1144
[153] Chen J., Paganini F., Sanadidi M.Y., et al., Fluid-flow analysis of TCP Westwood with RED. Computer Networks. 2006 50 (9): 1302-1326
[154] Wang J.T., Tang A., Low S.H. , Local stability of FAST TCP. In Proc. 43rd IEEE Conference on Decision and Control (CDC 2004). Atlantis. 2004:1023-1028
[155] Mascolo S., Congestion control in high-speed communication networks using the Smith principle. Automatica. 1999 35 (12): 1921-1935
[156] Hespanha J.P., Bohacek S., Obraczka K., et al., Hybrid Modeling of TCP Congestion Control. Hybrid Systems: Computation and Control. Berlin. Springer-Verlag. 2001:291-304
[157] Kuusela P., Lassila J., Virtamo J., et al., Modeling RED with Idealized TCP Sources. In Proc. 9th IFIP Conference on Performance Modelling and Evaluation. of ATM and IP Networks (IFIP ATM & IP 2001). Budapest, Hungary 2001:155-166
[158] Kuusela P., Lassila P., Virtamo J. , Stability of TCP-RED Congestion Control. In Proc. ITC-17. Salvador da Bahia, Brazil. 2001:655-666
[159] Veres A., Boda M., The Chaotic Nature of TCP Congestion Control. In Proc. IEEE INFOCOM 2000. Tel-Aviv, Israel. 2000:1715-1723
[160] Chen L., Wang X.F., Han Z.Z., Controlling chaos in Internet congestion control model. Chaos, Solitons and Fractals. 2004 21 (1): 81-91
[161] Jiang K., Wang X.F., Xi Y.G. , A Robust RED Algorithm Based on Time-delayed Feedback Control. In Proc. 5th Asian Control Conference. Melbourne. 2004:707-712
[162] Socolar J.S., Sukow D.W., Gauthier D.J. , Stabilizing unstable periodic orbits in fastdynamic system. Phys. Rev. E. 1994 50 (4): 3245-3248
[163] Grieco L.A., Mascolo S., Westwood TCP and easy RED to improve Fairness in High Speed Network. In Proc. IFIP/IEEE Seventh International Workshop on Protocols For High-Speed Networks. Berlin, Germany. 2002:130-146
[164] Guckenheimer J., Holmes P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag. 1983
[165] Low S.H., Paganini F., Wang J., et al., Dynamics of TCP/RED and a scalable control. In Proc. IEEE INFOCOM 2002. New York. 2002:239-248
[166] Luo X.S., Chen G., Wang B.H., et al. , Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems. Chaos, Solitons and Fractals. 2003 18 (4): 775-783
[167] Johari R., Tan D. , End-to-end congestion control for the Internet: Delays and stability. IEEE/ACM Trans. Networking. 2001 9 (6): 818-832
[168] Massoulie L., Stability of distributed congestion control with heterogeneous feedback delays. IEEE Trans. Automatic Control. 2002 47 (6): 895–902
[169] Liu S., Basar T., Srikant R. , Controlling the Internet: A survey and some new results. In Proc. 42nd IEEE Conference on Decision and Control. Maui, Hawaii. 2003:3048-3057
[170] Sichitiu M.L., Bauer P.H., Asymptotic stability of congestion control systems with multiple sources. IEEE Trans. Automatic Control. 2006 51 (2): 292–298
[171] Ranjan P., La R.J., Abed E.H., Global stability conditions for rate control with arbitrary communication delay. IEEE/ACM Trans. Networking. 2006 14 (1): 94-107
[172] Wang X., Eun D.Y. , Local and global stability of TCP-newReno/RED with many flows. Computer communications. 2007 30 (5): 1091-1105
[173] Wang Z., Chu T., Delay induced Hopf bifurcation in a simplified network congestion control model. Chaos, Solitons and Fractals. 2006 28 (1): 161-172
[174] Guo S., Liao X., Li C., Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay. Nonlinear analysis: Real World Applications. 2007 (In Press)
[175] Guo S., Liao X., Li C., Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay. Nonlinear analysis: Real WorldApplications. 2007 (In Press)
[176] Wang H.L., Hu H.Y. , Remarks on the perturbations in solving the second-order delay differential equations. Nonlinear Dynamics. 2003 33 (4): 379-398
[177] He J.H., Periodic solutions and bifurcations of delay-differential equations. Phys. Lett. A. 2005 347 (4-6): 228-230
[178] Hu H.Y., Wang Z.H., Singular perturbation methods for nonlinear dynamic systems with time delay. Chaos, Solitons and Fractals. 2007 (In Press)
[179] Gopalsamy K., Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D. 1996 89 (1): 395-426
[180] Xiao M., Cao J. , Delayed feedback-based bifurcation control in an Internet congestion model. Journal of Mathematical Analysis and Applications. 2007 332 (2): 1010-1027
[181] Liu C., Tian Y., Eliminating oscillations in the Internet by time-delayed feedback control. Chaos, Solitons and Fractals. 2008 35 (5): 878-887
[182] Cooke K., Grossman Z. , Discrete. delay, distributed delay and stability switches. Journal of Mathematical Analysis and Applications. 1982 86:592-627
[183] Barabasi A.L., Albert R., Emergence of scaling in random networks. Science. 1999 286:509-512
[184] Wang H.L., Hu H.Y. , Bifurcation analysis of a delayed dynamic system via method of multiple scales and shooting technique. International Journal of Bifurcation and Chaos. 2005 15 (2): 425-450
[185] Wang Z.H., Hu H.Y., Anenergy analysis of nonlinear oscillators with time-delayed coupling. International Journal of Bifurcation and Chaos. 2006 16 (8): 2275-2292
[186] Wang Z.H., Hu H.Y., An energy analysis of the local dynamics of a delayed oscillator near a Hopf bifurcation. Nonlinear Dynamics. 2006 46 (1-2): 149-159
[187] Wang Z.H., Hu H.Y., Pseudo-oscillator analysis of scalar nonlinear dynamics with time delays neara Hopf bifurcation. International Journal of Bifurcation and Chaos. 2007 17 (8): (In Press)
[188] Gao F., Wang H.L., Wang Z.H., Hopf bifurcation of a nonlinear delayed system of machine tool vibration via pseudo-oscillator analysis. Nonlinear analysis: Real WorldApplications. 2007 8 (5): 1561-1568
[189] Hu H.Y., Wang Z.H., Singular perturbation methods for nonlinear dynamic systems with time delays. Chaos, Solitons and Fractals. 2007 (In Press)
[190]卢利琼,陈元琰,吴东等,高带宽时延乘积网络中的拥塞控制端算法研究.计算机应用研究. 2006 23 (3): 8-10
[2] Jacobson V., Congestion Avoidance and Control. ACM Computer Communication Review. 1988 18 (4): 314-329
[3] Jain R., Congestion control in computer networks: Issues and Trends. IEEE Network Magazine. 1990 4 (3): 24-30
[4]姜明, TCP协议的拥塞控制策略及改进. 2003. http://business.ccidnet.com/art/930/20030402/42351_1.html
[5]汪小帆,孙金生,王执铨,控制理论在Internet拥塞控制中的应用.控制与决策. 2002 17 (2): 129-134
[6] Kaplan D., Glass L., Understanding Nonlinear Dynamics. New York: Springer-Verlag. 1997
[7] Banerjee S., Ranjan P., Grebogi C., Bifurcations in two-dimensional piecewise smooth maps- theory and application in switching circuits. IEEE Trans. Circuits Syst. I. 2000 47 633-643
[8]刘秉正,彭建华,非线性动力学.北京:高等教育出版社. 2004
[9] Kalampoukas L., Congestion Management in High Speed Networks. Ph.D. University of California, Santa Cruz. 1997
[10] Tanenbaum A.S., Computer Networks. New Jersey: Prentice-hall. 1996
[11]章淼,吴建平,林闯,互联网端到端拥塞控制研究综述.软件学报. 2002 13 (3): 354-363
[12] Thompson K., Miller G.J., Wilder R., Wide-Area Internet traffic patterns and characteristics. IEEE Network. 1997 11 (6): 10-23
[13] Floyd S., Fall K., Promoting the use of end-to-end congestion control in the Internet.IEEE/ACM Transactions on Networking. 1999 7 (4): 458-472
[14]张曾科,计算机网络.北京:清华大学出版社. 2005
[15] Floyd S., Henderson T., The New Reno modification to TCP's fast recovery algorithm. RFC2582. IETF. 1999
[16] Mathis M., Mahdavi J., Floyd S. et.al, TCP selective acknowledgement options. RFC2018. IETF. 1996
[17] Brakmo L.S., Peterson L.L., TCP Vegas: end to end congestion avoidance on a global Internet. IEEE J. on Selected Areas in Communications. 1995 13 (8): 1465-1480
[18] Allman M., Paxson V., Stevens W., TCP congestion control. RFC2581. IETF. 1999
[19] Floyd S., A report on some recent developments in TCP congestion control. IEEE Communications Magazine. 2001 35 (4): 84-90
[20] Floyd S., High speed TCP for large congestion windows. RFC3649. IETF. 2003
[21] Kelly T., Scalable TCP: Improving performance in high speed wide area networks. 2003. http://www.lce.eng.cam.ac.uk/~ctk21/scalable/
[22] Wei D. X., Jin C., Low S. H., Hegde S., FAST TCP: Motivation, Architecture, Algorithms, Performance. IEEE/ACM Transactions on Networking. 2006 14 (6): 1246-1259
[23] Xu L., Harfoush K., Rhee I., Binary increase congestion control for fast long-distance networks. In Proc. IEEE INFOCOM 2004. Piscataway. 2004:2514-2524
[24] Leith D., Shorten R. , H-TCP: TCP for high-speed and long-distance networks. 2004. http://www.hamilton.ie/net/htcp3.pdf
[25] Rhee I., Xu L., CUBIC: A New TCP-Friendly High-Speed TCP Variants. In Proc. PFLDnet. Lyon. 2005
[26] Katabi D., Handley M., Rohrs C., Internet Congestion Control for Future High Bandwidth-Delay Product Environments. In Proc. ACM Sigcomm 2002. Pittsburgh. 2002
[27] Braden B., Clark D., Crowcroft J., et al., Recommendations on queue management and congestion avoidance in the Internet. RFC2309. IETF. 1998
[28] Floyd S., Jacobson V., Random early detection gateways for congestion avoidance. IEEE/ACM Transactions on Networking. 1993 1 (4): 393-413
[29] Christiansen M., Jeffay K., Ott D., et al., Tuning RED for Web traffic. ACMComputer Communication Review. 2000 30 (4): 139-150
[30] May M., Bolot J., Diot C., et al., Reasons not to deploy RED. In Proc. IWQoS'99. London. 1999 260-262
[31] Ott T.J., Lakshman T.V., Wong L.H., SRED: Stabilized RED. In Proc. IEEE INFOCOM'99. New York. 1999 1346-1355
[32] Aweya J., Ouellette M., Montuno D.Y. , A Control Theoretic Approach to Active Queue Management. Computer Networks 2001 36 (2-3): 203-235
[33] Floyd S., Gummadi R., Shenker S., Adaptive RED: An algorithm for increasing the robustness of RED's active queue management. 2001. http://www.icir.org/floyd
[34] Liu S., Basar T., Srikant R. , Exponential RED: A Stabilizing AQM Scheme for Low- and High-speed TCP Protocols. IEEE/ACM Trans. Networking. 2005 13 (5): 1068-1081
[35] Athuraliya S., Low S., Li V., et al., REM: Active queue management. IEEE Network Magazine. 2001 15 (3): 48-53
[36] Lakshmikantha A., Beck C.L., Srikant R., Robustness of Real and Virtual Queue-Based Active Queue Management Schemes IEEE/ACM Transactions on Networking 2005 13 (1): 81-93
[37] Kunniyur S., Srikant R., Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management. In Proc. ACM SIGCOMM 2001. San Diego. 2001:123-134
[38] Feng W., Kandlur D., Saha D., et al., BLUE: A New Class of Active Queue Management Algorithms. 1999. http://citeseer.ist.psu.edu/feng99blue.html
[39] Hollot C.V., Misra V., Towsley D., et al., On Designing Improved Controllers for AQM Routers Supporting TCP Flows. In Proc. IEEE INFOCOM 2001. Anchorage. 2001:1726-1734
[40] Mascolo S., Casetti C., Gerla M., et al., TCP westwood: Bandwidth estimation for enhanced transport over wireless links. In Proc. ACM Mobicom 2001. Rome, Italy. 2001:287-297
[41]蒋凯,一类网络拥塞控制系统非线性动力学分析与设计. [博士学位论文]上海.上海交通大学. 2005
[42]刘延柱,陈立群,非线性振动.北京:高等教育出版社. 2001
[43]陈予恕,非线性振动.北京:高等教育出版社. 2002
[44] Hassard B.D., KazarinoffN. D., Wan Y.H., Theory and application of Hopf bifurcation. Cambridge: Cambridge University Press. 1981
[45] Chen G., Moiola J.L., Wang H.O., Bifurcation control: theories, methods, and applications. International Journal of Bifurcation and Chaos. 2000 10 (3): 511-548
[46] Abed E.H., Fu J.H., Local feedback stabilization and bifurcation control 1. Hopf bifurcation. Systems & Control Letters 1986 7 (1): 11-17
[47] Abed E.H., Fu J.H., Local feedback stabilization and bifurcation control 2. Stationary bifurcation. Systems & Control Letters. 1987 8 (5): 467-473
[48] Abed E.H., Wang H.O., Chen R.C., Stabilization of period doubling bifurcations and implications for control of chaos. Physica D. 1994 70 (1): 154-164
[49] Kang W., Bifurcation control via state feedback for systems with a single uncontrollable mode. SIAM Journal on Control and Optimization. 2000 38 (5): 1428-1452
[50] Yabuno H., Bifurcation control of parametrically excited Duffing system by a combined linear-plus-nonlinear feedback control. Nonlinear Dynamics. 1997 12 (3): 263-274
[51] Wang H.O., Abed E.H., Bifurcation control of a chaotic system. Automatica. 1995 31 (9): 1213-1226
[52] Berns D.W., Moiola J.L., Chen G., Feedback control of limit cycle amplitudes from a frequency domain approach. Automatica. 1998 34 (12): 1567-1573
[53] Berns D.W., Moiola J.L., Chen G., Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1998 45 (7): 759-763
[54] Genesio R., Tesi A., Wang H.O., et al., Control of period doubling bifurcations using harmonic balance. In Proc. IEEE Conference on Decision and Control'93. San Antonio. 1993:492 - 497
[55] Tesi A., Abed E.H., Genesio R., et al., Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics. Automatica. 1996 32 (9): 1255-1271
[56] Brandt M.E., Chen G., Bifurcation control of two nonlinear models of cardiac activity.IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1997 44 (10): 1031-1034
[57] Chen G., Fang J.Q., Hong Y., et al., Controlling bifurcations: continuous-time systems. ACTA Physica China. 1999 8:416-422
[58] Chen G., Fang J.Q., Hong Y., et al., Controlling Hopf bifurcations: The discrete-time systems. Discrete Dynamics in Nature and Society. 2000 5 (1): 29-33
[59] Chen G., Lu J., Nicholas B., et al., Bifurcation dynamics in control system. International Journal of Bifurcation and Chaos. 1999 9 (1): 287-293
[60] Yap K.C., Chen G., Controlling bifurcations of discrete maps. Latin American Applied Research. 2001 31 (3): 157-162
[61] Kang W., Bifurcation and normal form of nonlinear control systems Parts I and II. SIAM Journal on Control and Optimization. 1998 36 (1): 193-232
[62]邹艳丽,非线性电路和复杂网络的混沌控制与同步研究. [博士学位论文]上海.上海交通大学. 2006
[63]关新平,范正平,陈彩莲,华长春,混沌控制及其在保密通信中的应用.北京:国防工业出版社. 2002
[64] Ott. E, Chaos in dynamical systems. (Second edition). Cambridge: Cambridge University Press. 2002
[65] Kolmogorov A.N., Preservation of conditionally periodic movements with small change in the Hamiltonian function. Doklady Akad Nauk SSSR. 1954 98:527-530
[66] Lorenz E., Deterministic non-periodic flows. Atmosphere Science. 1963 20 (1): 130-141
[67] Ruelle D., Takens F., On the nature of turbulence. Commun. math. Phys. 1971 20:167-192
[68] Li T.Y., Yorke J.A., Period Three Implies Chaos. Amer. Math. Monthly. 1975 82 (10): 985-992
[69] Feigenbaum M.J., Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. . 1978 19 (1): 25-52
[70] Feigenbaum M.J., The universal metric properties of nonlinear transformations. J. Stat. Phys. 1979 21 (4): 669-706
[71]罗晓曙,非线性系统中的混沌控制与同步及其应用研究. [博士学位论文]合肥.中国科学技术大学. 2003
[72]蒋品群,混沌系统和复杂网络系统的控制、同步和演化研究. [博士学位论文]合肥.中国科学技术大学. 2005
[73] Ott E., Grebogi C., Yorke J.A., Controlling chaos. Physical Review Letters. 1990 64 (11): 1196-1199
[74] Ditto W.L., Rauseo S.N., Spano M. L., Experimental control of chaos. Physical Review Letters. 1990 65 (26): 3211-3214
[75] Hubler A., Adaptive control of chaotic system. Hdvetica Physica Acta. 1989 62:343-346
[76] Fradkov A.L., Guzenko P., Pavlov A., Adaptive control of recurrent trajectories based on linearization of Poincare map. International Journal of Bifurcation and Chaos. 2000 10 (3): 621-637
[77] Epureanu B.I., Dowell E.H., System Identification for Ott-Grebogi-Yorke controller design. Phys. Rev. E. 1997 56 (5): 5327-5331
[78] Epureanu B.I., Dowell E.H., Optimal multi-dimensional OGY controller. Physica D. 2000 139 (1): 87-96
[79] Aston P.J., Bird C.M., Using control of chaos to refine approximations to periodic points. International Journal of Bifurcation and Chaos. 2000 10:227-235
[80] Huberman B.A., Lumer E., Dynamics of adaptive systems. IEEE Transactions on Circuits and Systems. 1990 37 (4): 547-550
[81] Sinha S., Ramaswamy R., Rao J., Adaptive control on nonlinear dynamics. Physica D. 1990 43 (1): 118-128
[82] Hu H.Y., An adaptive control scheme for recovering periodic motion of chaotic systems. Journal of Sound and Vibration. 1997 199 (2): 269-274
[83] Ramaswamy R., Sinha S., Gupte N., Targeting chaos through adaptive control. Phys. Rev. E. 1998 57 (3): 2507-2510
[84] Arecchi F.T., Boccaletti S., Adaptive strategies for recognition, nosie filtering, control, synchronization and targeting of chaos. Chaos. 1997 7 (4): 621-634
[85] Boccaletti S., Farini A., Arecchi F.T., Adaptive strategies for recognition, control, andsynchronization of chaos. Chaos, Solitons and Fractals. 1997 8 (9): 1431-1448
[86] Christini D.J., In V., Spano M.L., et al., Real-time experimental control of system in its chaotic and nonchaotic regimes. Phys. Rev. E. 1997 56 (4): 3749-3752
[87] Christini D.J., Kaplan D.T., Adaptive estimation and control method for unstable periodic dynamics in spike trains. Phys. Rev. E. 2000 61 (5): 5149-5153
[88] Pyragas K., Continuous control of chaos by self-controlling feedback. Physics Letters A. 1992 170 (6): 421-428
[89] Naumenko A.V., Loiko N.A., Turovets S.I., et al., Bias current impulsive feedback control of nonlinear dynamics in external cavity laser diodes. Electronics Letters. 1998 34 (2): 181-182
[90] Naumenko A.V., Loiko N.A., Turovets S.I., et al., Chaos control in external cavity laser diodes using electronic impulsive delayed feedback. International Journal of Bifurcation and Chaos. 1998 8 (9): 1791-1799
[91] Bleich M.E., Hochheiser D., Moloney J.V., et al., Controlling extended systems with spatially filtered, time-delayed feedback. Phys. Rev. E. 1997 55 (3): 2119-2126
[92] Hai W.H., Duan Y.W., Pan L.X., An analytical study for controlling unstable periodic motion in Magneto-elastic Chaos. Phys. Lett. A. 1997 234 (3): 198-204
[93] Hikihara T., Touno M., Kawagoshi T., Experimental stabilization of unstable periodic orbit in Magneto-elastic chaos by delayed feedback control. International Journal of Bifurcation and Chaos. 1997 7 (12): 2837-2846
[94] Brandt M.E., Shih H.T., Chen G., Linear time-delay feedback control of a Pathological rhythm in a cardiac conduction model. Phys. Rev. E. 1997 56 (2): 1334-1337
[95] Konishi K., Kokame H., Hirata K., Decentralized delayed-feedback control of an optimal velocity traffic model. The European Physical Journal B. 2000 15 (4): 715-722
[96] Konishi K., Kokame H., Hirata K., Coupled map car-following model and its delayed-feedback control. Phys. Rev. E. 1999 60 (4): 4000-4007
[97] Batlle C., Fossas E., Olivar G., Stabilization of periodic orbits of the buck converter by time-delayed feedback. Int. J. Circ. Theor. And Appl. 1999 27 (6): 617-631
[98] Bakker R., De Korte R.J., Schouten J.C., Neural networks for prediction and control of chaotic fluidized bed hydrodynamics: a first step. Fractals. 1997 5 (3): 523-530
[99] Dracopoulos D.C., Jones A.J., Adaptive neuro-genetic control of chaos applied to the attitude control problem. Neural Computing and Applications. 1997 6 (2): 102-115
[100] Greenwood D.P.A., Carrasco R.A., Neural networks for the adaptive control of disruptive nonlinear network traffic. IEE Proceedings Communications. 2000 147 (5): 285-291
[101] Tanaka K., Ikeda T., Wang H.O., A unified approach to controlling chaos via Arm LMI-based fuzzy control system design. IEEE Trans. Circuits Syst. I. 1998 45 (10): 1021-1040
[102] Udawatta L., Watanabe K., Kiguchi K., et al., Fuzzy-chaos hybrid controller for controlling of nonlinear systems. IEEE Transactions on Fuzzy Systems. 2002 10 (3): 401 - 411
[103] Arecchi F.T., Boccaletti S., The control of chaos: theoretical schemes and experimental realizations. International Journal of Bifurcation and Chaos. 1998 8 (8): 1643-1655
[104] Boccaletti S., Farini A., Arecchi F.T., The control of chaos: theory and applications. Physics Reports. 2000 329 (3): 103-197
[105] Andrievskii B.R., Fradkov A.L., Control of chaos: methods and applications I. methods. Automation and Remote Control 2003 64 (5): 673-713
[106] Andrievskii B.R., Fradkov A.L., Control of chaos: methods and applications II. applications. Automation and Remote Control 2004 65 (4): 505-533
[107]闫友彪,陈元琰,罗晓曙等, Internet拥塞控制研究的最新进展分析和展望.计算机应用研究. 2005 2:8-13
[108] Ranjan P., Abed E.H., La R.J., Nonlinear instabilities in TCP-RED. In Proc. IEEE INFOCOM 2002. New York. 2002:249 - 258
[109] Ranjan P., Abed E.H., La R.J., Nonlinear instabilities in TCP-RED. IEEE/ACM Trans. Networking. 2004 12 (6): 1079-1092
[110] Firoiu V., Borden M., A study of active queue management for congestion control. In Proc. IEEE INFOCOM 2000. Tel Aviv. 2000:1435-1444
[111] Mathis M., Semke J., Mahdavi J., et al., The macroscopic behavior of the TCP congestion avoidance algorithm. Computer Communication Review. 1997 27 (3): 67-82
[112] Plasser T., Ziegler T., Reichl P., On the nonlinearity of the RED drop function. In Proc. International Conference on Computer Communication (ICCC 2002). Mumbai, India. 2002 515-534
[113] Padhye J., Firoiu V., Towsley D., et al., Modeling TCP Reno performance: a simple model and its empirical validation. IEEE/ACM Trans. Networking. 2000 8 (2): 133-145
[114] Ranjan P., Abed E.H., Chaotic behavior in TCP-RED. In Proc. IEEE Conference on Decision and Control (CDC 2002). Las Vegas. 2002:540- 542
[115] Ranjan P., Abed E.H., Bifurcation analysis of TCP-RED dynamics. In Proc. American Control Conference (ACC 2002). Anchorage. 2002:2443-2448
[116] La R.J., Ranjan P., Abed E.H., Nonlinearity of TCP and instability with RED. In Proc. SPIE ITCom 2002 Boston. 2002:283-294
[117] La R.J., Ranjan P., Abed E.H., Nonlinear dynamics of mixed TCP and UDP traffic under RED. 2002. http://citeseer.ist.psu.edu/489676.html
[118] Ranjan P., La R.J., Abed E.H., Bifurcations of TCP and UDP traffic under RED. 2002. http://citeseer.ist.psu.edu/501895.html
[119] La R.J., Instability of a tandem network and its propagation under RED. IEEE Trans. Automatic Control. 2004 49 (6): 1006-1011
[120] Ranjan P., La R.J., Abed E.H., Washout filter-aided RED control. In Proc. American Control Conference (ACC 2004). Boston. 2004:2966 - 2971
[121] La R. J., Ranjan P., Abed E. H. , Feedback Control of Random Early Detection. In Proc. 40th Annual Allerton. Conference on Communication Control and Computing. Urbana. 2002:1377-1386
[122] Chen L., Wang X.F., Han Z.Z., Controlling bifurcation and chaos in Internet congestion control model. International Journal of Bifurcation and Chaos. 2004 14 (5): 1863-1876
[123] Zhang H., Liu M., Vukadinovic V., et al., Modeling TCP/RED: a dynamical approach. Complex Dynamics in Communication Networks. Berlin. Springer Verlag. 2005:251-278
[124] Liu M., Zhang H., Trajkovic Lj., Stroboscopic model and bifurcations in TCP/RED. In Proc. IEEE International Symposium on Circuits and Systems (ISCAS 2005). Kobe,Japan. 2005:2060 - 2063
[125] Liu M., Marciello A., Bernardo M. di, et al., Discontinuity-induced bifurcations in TCP/RED. In Proc. IEEE International Symposium on Circuits and Systems (ISCAS 2006). Kos, Greece. 2006:2629-2632
[126] Fall K., Floyd S., Simulation-based comparison of Tahoe, Reno and SACK TCP. ACM Computer Communication Review. 1996 26 (3): 5-21
[127] Low S.H., A duality model of TCP and queue management algorithms. IEEE/ACM Trans. Networking. 2003 11 (4): 525-536
[128] Athuraliya S., Low S.H., An empirical validation of a duality model of TCP and queuemanagement algorithms. In Proc. The 33nd conference on Winter simulation. Arlington. 2001:1269 - 1274
[129] Low S.H., Paganini F., Doyle J.C., Internet congestion control. IEEE Control Systems Magazine. 2002 22 (1): 28-43
[130] Paganini F., On the stability of optimization-based flow control. In Proc. American Control Conference (ACC 2001). Arlington. 2001 4689 - 4694
[131] Kelly F., Maulloo A., Tan D., Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Socity. 1998 49 (3): 237-252
[132] Gibbens R.J., Kelly F.P. , Resource pricing and the evolution of congestion control. Automatica. 1999 35 (12): 1969-1985
[133] Zhu L., Ansari N., Local Stability of a New Adaptive Queue Management (AQM) Scheme. IEEE Communications Letters. 2004 8 (6): 406-408
[134] Papachristodoulou A., Global stability analysis of a TCP/AQM protocol for arbitrary networks with delay. In Proc. 43rd IEEE Conference on Decision and Control (CDC 2004). Atlantis. 2004:1029-1034
[135] Voice T., A Global Stability Result For Primal Dual Congestion Control Algorithms With Routing. Computer Communication Review. 2004 34 (3): 35-41
[136] Alpcan T., Basar T., A Globally Stable Adaptive Congestion Control Scheme for Internet-Style Networks with Delay. IEEE/ACM Trans. Networking. 2005 13 (6): 1261-1274
[137] Paganin i F., Wang Z., Doyle J.C., et al. , Congestion Control for High Performance, Stability, and Fairness in General Networks. IEEE/ACM Trans. Networking. 2005 13 (1): 43-56
[138] Ying L., Dullerud G.E., Srikant R., Global Stability of Internet Congestion Controllers with Heterogeneous Delays. IEEE/ACM Trans. Networking. 2006 14 (3): 579-591
[139] Tian Y.P., Stability Analysis and Design of the Second-Order Congestion Control for Networks with Heterogeneous Delays. IEEE/ACM Trans. Networking. 2005 13 (5): 1082-1093
[140] Li C.G., Chen G., Liao X.F., et al., Hopf bifurcation in an Internet congestion control model. Chaos, Solitons and Fractals. 2004 19 (4): 853-862
[141] Yang H.Y., Tian Y.P., Hopf bifurcation in REM algorithm with communication delay. Chaos, Solitons and Fractals. 2005 25 (5): 1093-1105
[142] Raina G., Local Bifurcation Analysis of Some Dual Congestion Control Algorithms. IEEE Trans. Automatic Control. 2005 50 (8): 1135-1146
[143] Chen Z., Yu P., Hopf Bifurcation Control for an Internet Congestion Model. International Journal of Bifurcation and Chaos. 2005 15 (8): 2643-2651
[144] Misra V., Gong W.B., Towsley D., Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED. In Proc. ACM/SIGCOMM 2000. Santa Clara. 2000:151-160
[145] Hollot C.V., Misra V., Towsley D., et al., A control theoretic analysis of RED. In Proc. IEEE/INFOCOM 2001. Anchorage. 2001:1510-1519
[146] Hollot C.V., Chait Y. , Nonlinear Stability Analysis for a Class of TCP/AQM Networks In Proc. IEEE Conference on Decision and Control (CDC 2001). Orlando. 2001:2309-2314
[147] Hollot C.V., Misra V., Towsley D., et al., Analysis and Design of Controllers for AQM Routers Supporting TCP Flows. IEEE Trans. Automatic Control. 2002 47 (6): 945-959
[148] Ren F.Y., Li C., Wei B., A nonlinear control theoretic analysis to TCP-RED system. Computer Networks. 2005 49 (4): 580-592
[149] Tan L.S., Zhang W., Peng G., et al., Stability of TCP/RED Systems in AQM Routers. IEEE Trans. Automatic Control. 2006 51 (8): 1393-1398
[150] Bauso D., Giarre L., Neglia G., AQM stability in multiple bottleneck networks. In Proc. IEEE International Conference on Communication (ICC 2004). Paris. 2004:2267-2271
[151] Michiels W., Niculescu S.-I., Stability analysis of a Fluid Flow Model for TCP like Behavior. International Journal of Bifurcation and Chaos. 2005 15 (7): 2277-2282
[152] Michiels W., Melchor-Aguilar D., Niculescu S.-I., Stability analysis of some classes of TCP/AQM networks. International Journal of Control. 2006 79 (9): 1134-1144
[153] Chen J., Paganini F., Sanadidi M.Y., et al., Fluid-flow analysis of TCP Westwood with RED. Computer Networks. 2006 50 (9): 1302-1326
[154] Wang J.T., Tang A., Low S.H. , Local stability of FAST TCP. In Proc. 43rd IEEE Conference on Decision and Control (CDC 2004). Atlantis. 2004:1023-1028
[155] Mascolo S., Congestion control in high-speed communication networks using the Smith principle. Automatica. 1999 35 (12): 1921-1935
[156] Hespanha J.P., Bohacek S., Obraczka K., et al., Hybrid Modeling of TCP Congestion Control. Hybrid Systems: Computation and Control. Berlin. Springer-Verlag. 2001:291-304
[157] Kuusela P., Lassila J., Virtamo J., et al., Modeling RED with Idealized TCP Sources. In Proc. 9th IFIP Conference on Performance Modelling and Evaluation. of ATM and IP Networks (IFIP ATM & IP 2001). Budapest, Hungary 2001:155-166
[158] Kuusela P., Lassila P., Virtamo J. , Stability of TCP-RED Congestion Control. In Proc. ITC-17. Salvador da Bahia, Brazil. 2001:655-666
[159] Veres A., Boda M., The Chaotic Nature of TCP Congestion Control. In Proc. IEEE INFOCOM 2000. Tel-Aviv, Israel. 2000:1715-1723
[160] Chen L., Wang X.F., Han Z.Z., Controlling chaos in Internet congestion control model. Chaos, Solitons and Fractals. 2004 21 (1): 81-91
[161] Jiang K., Wang X.F., Xi Y.G. , A Robust RED Algorithm Based on Time-delayed Feedback Control. In Proc. 5th Asian Control Conference. Melbourne. 2004:707-712
[162] Socolar J.S., Sukow D.W., Gauthier D.J. , Stabilizing unstable periodic orbits in fastdynamic system. Phys. Rev. E. 1994 50 (4): 3245-3248
[163] Grieco L.A., Mascolo S., Westwood TCP and easy RED to improve Fairness in High Speed Network. In Proc. IFIP/IEEE Seventh International Workshop on Protocols For High-Speed Networks. Berlin, Germany. 2002:130-146
[164] Guckenheimer J., Holmes P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag. 1983
[165] Low S.H., Paganini F., Wang J., et al., Dynamics of TCP/RED and a scalable control. In Proc. IEEE INFOCOM 2002. New York. 2002:239-248
[166] Luo X.S., Chen G., Wang B.H., et al. , Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems. Chaos, Solitons and Fractals. 2003 18 (4): 775-783
[167] Johari R., Tan D. , End-to-end congestion control for the Internet: Delays and stability. IEEE/ACM Trans. Networking. 2001 9 (6): 818-832
[168] Massoulie L., Stability of distributed congestion control with heterogeneous feedback delays. IEEE Trans. Automatic Control. 2002 47 (6): 895–902
[169] Liu S., Basar T., Srikant R. , Controlling the Internet: A survey and some new results. In Proc. 42nd IEEE Conference on Decision and Control. Maui, Hawaii. 2003:3048-3057
[170] Sichitiu M.L., Bauer P.H., Asymptotic stability of congestion control systems with multiple sources. IEEE Trans. Automatic Control. 2006 51 (2): 292–298
[171] Ranjan P., La R.J., Abed E.H., Global stability conditions for rate control with arbitrary communication delay. IEEE/ACM Trans. Networking. 2006 14 (1): 94-107
[172] Wang X., Eun D.Y. , Local and global stability of TCP-newReno/RED with many flows. Computer communications. 2007 30 (5): 1091-1105
[173] Wang Z., Chu T., Delay induced Hopf bifurcation in a simplified network congestion control model. Chaos, Solitons and Fractals. 2006 28 (1): 161-172
[174] Guo S., Liao X., Li C., Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay. Nonlinear analysis: Real World Applications. 2007 (In Press)
[175] Guo S., Liao X., Li C., Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay. Nonlinear analysis: Real WorldApplications. 2007 (In Press)
[176] Wang H.L., Hu H.Y. , Remarks on the perturbations in solving the second-order delay differential equations. Nonlinear Dynamics. 2003 33 (4): 379-398
[177] He J.H., Periodic solutions and bifurcations of delay-differential equations. Phys. Lett. A. 2005 347 (4-6): 228-230
[178] Hu H.Y., Wang Z.H., Singular perturbation methods for nonlinear dynamic systems with time delay. Chaos, Solitons and Fractals. 2007 (In Press)
[179] Gopalsamy K., Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D. 1996 89 (1): 395-426
[180] Xiao M., Cao J. , Delayed feedback-based bifurcation control in an Internet congestion model. Journal of Mathematical Analysis and Applications. 2007 332 (2): 1010-1027
[181] Liu C., Tian Y., Eliminating oscillations in the Internet by time-delayed feedback control. Chaos, Solitons and Fractals. 2008 35 (5): 878-887
[182] Cooke K., Grossman Z. , Discrete. delay, distributed delay and stability switches. Journal of Mathematical Analysis and Applications. 1982 86:592-627
[183] Barabasi A.L., Albert R., Emergence of scaling in random networks. Science. 1999 286:509-512
[184] Wang H.L., Hu H.Y. , Bifurcation analysis of a delayed dynamic system via method of multiple scales and shooting technique. International Journal of Bifurcation and Chaos. 2005 15 (2): 425-450
[185] Wang Z.H., Hu H.Y., Anenergy analysis of nonlinear oscillators with time-delayed coupling. International Journal of Bifurcation and Chaos. 2006 16 (8): 2275-2292
[186] Wang Z.H., Hu H.Y., An energy analysis of the local dynamics of a delayed oscillator near a Hopf bifurcation. Nonlinear Dynamics. 2006 46 (1-2): 149-159
[187] Wang Z.H., Hu H.Y., Pseudo-oscillator analysis of scalar nonlinear dynamics with time delays neara Hopf bifurcation. International Journal of Bifurcation and Chaos. 2007 17 (8): (In Press)
[188] Gao F., Wang H.L., Wang Z.H., Hopf bifurcation of a nonlinear delayed system of machine tool vibration via pseudo-oscillator analysis. Nonlinear analysis: Real WorldApplications. 2007 8 (5): 1561-1568
[189] Hu H.Y., Wang Z.H., Singular perturbation methods for nonlinear dynamic systems with time delays. Chaos, Solitons and Fractals. 2007 (In Press)
[190]卢利琼,陈元琰,吴东等,高带宽时延乘积网络中的拥塞控制端算法研究.计算机应用研究. 2006 23 (3): 8-10
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