Stability and Hopf bifurcation analysis in a TCP fluid model

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 1, 2011, Pages 353-363

  Liu, Feng ^a,b   Guan, Zhi Hong ^b   Wang, Hua O ^c  

^a CHINA UNIVERSITY OF GEOSCIENCES   (China)

^b HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c BOSTON UNIVERSITY   (United States)

Author keywords

Congestion control; Hopf bifurcation; Stability; TCP fluid model

Indexed keywords

BIFURCATING PERIODIC SOLUTIONS; BIFURCATION BEHAVIOR; CENTER MANIFOLD THEOREM; COMPLEX BEHAVIOR; CONGESTION CONTROL; FLUID MODELS; HOPF BIFURCATION ANALYSIS; INTERNET CONGESTION CONTROL; NORMAL FORM THEORY; NUMERICAL SIMULATION; PARAMETER CONDITIONS; TCP FLUID MODEL;

FLUIDS; MATHEMATICAL MODELS; PLASMA FLOW; STABILITY; TRANSMISSION CONTROL PROTOCOL;

HOPF BIFURCATION;

EID: 77958011053     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.06.021     Document Type: Article

References (28)

1. V. Jacobson Congestion avoidance and control ACM SIGCOMM Comput. Commun. Rev. 18 4 1998 314 329
2. S. Floyd, and V. Jacobson Random early detection gateways for congestion avoidance IEEE/ACM Trans. Netw. 1 4 1993 397 413
3. J.P. Hepanha, S. Bohacek, K. Obrxzka, and J. Lee Hybrid modeling of TCP congestion control Lect. Notes Comput. Sci. 2034 2001 291 304
4. L. Massoulie Stability of distributed congestion control with heterogeneous feedback delays IEEE Trans. Automat. Control 47 6 2002 895 902
5. A. Veres, M. Boda, The chaotic nature of TCP congestion control, in: Proc. IEEE INFOCOM, vol. 3, 2000, pp. 17151723.
6. P. Ranjan, and E.H. Abed Nonlinear instabilities in TCP-RED Proc. IEEE Infocom. 2 2002 185 191
7. S.H. Low, F. Paganini, J. Wang, S. Adlakha, J.C. Doyle, Dynamics of TCP/RED and a scalable control, in: Proceedings of IEEE INFOCOM, 2002.
8. F.P. Kelly Fairness and stability of end-to-end congestion control Eur. J. Control 9 2003 149 165
9. R. Srikant The Mathematics of Internet Congestion Control 2004 Birkhauser
10. R.J. La Instability of a tandem network and its propagation under RED IEEE Trans. Automat. Control 49 6 2004 1006 1011
11. C. Li, G. Chen, X. Liao, and J. Yu Hopf bifurcation in an internet congestion control model Chaos Solitons Fractals 19 4 2004 853 862
12. Z. Chen, and P. Yu Hopf bifurcation control for an internet congestion model Int. J. Bifur. Chaos 15 2005 2643 2651
13. H.Y. Yang, and Y.P. Tian Hopf bifurcation in REM algorithm with communication delay Chaos Solitons Fractals 25 5 2005 1093 1105
14. G. Raina Local bifurcation analysis for some dual congestion control algorithms IEEE Trans. Automat. Control 50 8 2005 1135 1146
15. G. Raina, and O. Heckmann TCP: local stability and Hopf bifurcation Perform. Eval. 64 3 2007 266 275
16. Z. Wang, and T. Chu Delay induced Hopf bifurcation in a simplified network congestion control model Chaos Solitons Fractals 28 1 2006 161 172
17. S. Guo, X. Liao, and C. Li Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay Nonlinear Anal.: RWA 9 2008 1292 1309
18. S. Guo, X. Liao, Q. Liu, and C. Li Necessary and sufficient conditions for Hopf bifurcation in an exponential RED algorithm with communication delay Nonlinear Anal.: RWA 9 4 2008 1768 1793
19. D. Ding, J. Zhu, and X. Luo Hopf bifurcation analysis in a fluid flow model of Internet congestion Nonlinear Anal.: RWA 10 2009 824 839
20. D. Ding, J. Zhu, X. Luo, and Y. Liu Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm Nonlinear Anal.: RWA 10 2009 2873 2883
21. F. Liu, Z.-H Guan, and H.O. Wang Controlling bifurcations and chaos in TCP-UDP-RED Nonlinear Anal.: RWA 11 2010 1491 1501
22. F. Liu, Z.-H. Guan, and H.O. Wang Controlling bifurcations and chaos in Small-world networks Chin. Phys. B 17 2008 2405 2411
23. G. Walsh, H. Ye, and L. Bushnell Stability analysis of network control systems IEEE Control Syst. Technol. 10 3 2002 438 446
24. P. Yu Bifurcation dynamics in control systems G. Chen, D.J. Hill, X. Yu, Bifurcation Control: Theory and Applications 2003 Springer-Verlag New York 99 126
25. P. Yu Bifurcation, limit cycle and chaos of nonlinear dynamical systems J. Sun, A. Luo, Bifurcation and Chaos in Complex Systems vol. 1 2006 Elsevier New York 1 125
26. J. Lv, X. Yu, G. Chen, and D. Cheng Characterizing the synchronization of small world dynamical networks IEEE Trans. Circuits Syst. Part I 51 4 2004 787 796
27. J.K. Hale, and L.S. Verduyn Introduction to Functional Differential Equations 1993 Springer-Verlag New York
28. B.D. Hassard, N.D. Kazarinoff, and Y.-H. Wan Theory and Applications of Hopf Bifurcation 1981 Cambridge University Press