Stability and Hopf bifurcation analysis in a TCP fluid model

Abstract In this paper the Hopf bifurcation behavior of a TCP fluid model of Internet congestion control system is investigated. The parameter condition that the Hopf bifurcation occurs is deduced. The stability and direction of the bifurcating periodic solutions are analyzed by applying the normal form theory and the center manifold theorem. Numerical simulations demonstrate the complex behavior of the system and verify the theoretical analysis.

[1]  Xiaofeng Liao,et al.  Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay , 2008 .

[2]  Hong-yong Yang,et al.  Hopf bifurcation in REM algorithm with communication delay , 2005 .

[3]  Jie Zhu,et al.  Hopf bifurcation analysis in a fluid flow model of Internet congestion control algorithm , 2009 .

[4]  Andras Veres,et al.  The chaotic nature of TCP congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[5]  Hua O. Wang,et al.  Controlling bifurcations and chaos in TCP–UDP–RED , 2010 .

[6]  Jian-Qiao Sun,et al.  Bifurcation and chaos in complex systems , 2006 .

[7]  Van Jacobson,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

[8]  Eyad H. Abed,et al.  Nonlinear instabilities in TCP-RED , 2002, IEEE/ACM Transactions on Networking.

[9]  Guanrong Chen,et al.  Bifurcation Dynamics in Control Systems , 1999 .

[10]  Fernando Paganini,et al.  Dynamics of TCP/RED and a scalable control , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[11]  Chuandong Li,et al.  Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay , 2008 .

[12]  Linda Bushnell,et al.  Stability analysis of networked control systems , 2002, IEEE Trans. Control. Syst. Technol..

[13]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Wang Hua,et al.  Controlling bifurcations and chaos in discrete small-world networks , 2008 .

[15]  Zhen Chen,et al.  Hopf bifurcation Control for an Internet Congestion Model , 2005, Int. J. Bifurc. Chaos.

[16]  Jie Zhu,et al.  Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm , 2009 .

[17]  Richard J. La.  Instability of a Tandem network and its propagation under RED , 2004, IEEE Trans. Autom. Control..

[18]  Guanrong Chen,et al.  Hopf bifurcation in an Internet congestion control model , 2004 .

[19]  Tianguang Chu,et al.  Delay induced Hopf bifurcation in a simplified network congestion control model , 2006 .

[20]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[21]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[22]  Gaurav Raina,et al.  Local bifurcation analysis of some dual congestion control algorithms , 2005, IEEE Transactions on Automatic Control.

[23]  Xinghuo Yu,et al.  Bifurcation Control: Theory and Applications , 2003 .

[24]  João Pedro Hespanha,et al.  Hybrid Modeling of TCP Congestion Control , 2001, HSCC.

[25]  Pei Yu.  Chapter 1 Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems , 2006 .

[26]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[27]  Frank Kelly,et al.  Fairness and Stability of End-to-End Congestion Control , 2003, Eur. J. Control.

[28]  Laurent Massoulié,et al.  Stability of distributed congestion control with heterogeneous feedback delays , 2002, IEEE Trans. Autom. Control..

[29]  Oliver Heckmann,et al.  TCP: Local stability and Hopf bifurcation , 2007, Perform. Evaluation.