Hopf bifurcation control in the XCP for the Internet congestion control system

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 3, 2012, Pages 1466-1479

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

^a CHINA UNIVERSITY OF GEOSCIENCES   (China)

^b Boston University   (United States)

^c HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Bifurcation control; Hopf bifurcation; XCP system

Indexed keywords

AVERAGE QUEUE LENGTHS; BIFURCATION BEHAVIOR; BIFURCATION CONTROL; EXPLICIT CONTROL PROTOCOLS; HOPF BIFURCATION CONTROL; INTERNET CONGESTION CONTROL; TIME-DELAYED FEEDBACK; XCP SYSTEM;

COMPUTER SIMULATION; CONGESTION CONTROL (COMMUNICATION); CONTROL SYSTEMS; FEEDBACK CONTROL; INTERNET; INTERNET PROTOCOLS;

HOPF BIFURCATION;

EID: 84655167663     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.11.010     Document Type: Article

References (50)

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. V. Misra, W.B. Gong, and D. Towlsey Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED Proc. ACM SIGCOMM 2000 151 160
4. J.P. Hepanha, S. Bohacek, K. Obrxzka, and J. Lee Hybrid modeling of TCP congestion control Lect. Notes Comput. Sci. 2034 2001 291 304 (Pubitemid 33256425)
5. C.V. Hollot, V. Misra, D. Towsley, and W-B. Gong A control theoretic analysis of RED Proc. IEEE INFOCOM 2001
6. S.H. Low, F. Paganini, J. Wang, S. Adlakha, and J.C. Doyle Dynamics of TCP/RED and a scalable control Proc. IEEE INFOCOM 2002
7. D. Katabi, M. Handley, and C. Rohrs Congestion control for high bandwidth-delay product networks Proc. ACM SIGCOMM 2002
8. N. Dukkipati, M. Kobayashi, R. Zhang-Shen, N. McKeown, Processor sharing flows in the internet, in: Thirteenth International Workshop on Quality of Service, 2005.
9. S. Floyd, HighSpeed TCP for large congestion windows, (2003) RFC Editor 3649.
10. C. Jin, D.X. Wei, and S.H. Low FAST TCP: motivation, architecture, algorithms, performance Proc. IEEE INFOCOM 2004
11. T. Kelly Scalable TCP: improving performance in highspeed wide area networks Comput. Commun. Rev. 32 2 2003
12. A. Veres, and M. Boda The chaotic nature of TCP congestion control Proc. IEEE INFOCOM 3 2000 1715 1723 (Pubitemid 30584665)
13. L. Massoulie Stability of distributed congestion control with heterogeneous feedback delays IEEE Trans. Automat. Control 47 6 2002 895 902 (Pubitemid 34773017)
14. G. Walsh, H. Ye, and L. Bushnell Stability analysis of network control systems IEEE Control Syst. Technol. 10 3 2002 438 446 (Pubitemid 34630818)
15. F.P. Kelly Fairness and stability of end-to-end congestion control Eur. J. Cont. 9 2003 149 165
16. R. Srikant The Mathematics of Internet Congestion Control 2004 Birkhauser
17. P. Ranjan, and E.H. Abed Nonlinear instabilities in TCP-RED IEEE/ACM Trans. Netw. 12 6 2004 1079 1092 (Pubitemid 40085374)
18. R.J. La Instability of a tandem network and its propagation under RED IEEE Trans. Automat. Control 49 6 2004 1006 1011
19. 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
20. 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 (Pubitemid 37049870)
21. 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
22. Z. Chen, and P. Yu Hopf bifurcation control for an internet congestion model Int. J. Bifur. Chaos 15 2005 2643 2651 (Pubitemid 41392587)
23. P. Yu, and G.R. Chen Hopf bifurcation control using nonlinear feedback with polynomial functions Int. J. Bifur. Chaos 14 2004 1683 1704 (Pubitemid 40242133)
24. J. L, 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
25. H.Y. Yang, and Y.P. Tian Hopf bifurcation in REM algorithm with communication delay Chaos Solitons Fractals 25 5 2005 1093 1105
26. G. Raina Local bifurcation analysis for some dual congestion control algorithms IEEE Trans. Automat. Control 50 8 2005 1135 1146 (Pubitemid 41410112)
27. G. Raina, and O. Heckmann TCP: local stability and Hopf bifurcation Perform. Eval. 64 3 2007 266 275 (Pubitemid 44827303)
28. M. Liu, H. Zhang, and Lj. Trajkovi' c Stroboscopic model and bifurcations in TCP/RED Proc. IEEE ISCAS 2005 2060 2063
29. M. Liu, A. Marciello, M. di Bernardo, and Lj. Trajkovi' c Discontinuity-induced bifurcations in TCP/RED communication algorithms Proc. IEEE Int. Sym. Circuits and Systems 2006 2629 2632 (Pubitemid 47132090)
30. Z. Wang, and T. Chu Delay induced Hopf bifurcation in a simplified network congestion control model Chaos Solitons Fractals 28 1 2006 161 172 (Pubitemid 41491982)
31. S. Guo, X. Liao, and C. Li Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay Nonlinear Analysis: RWA 9 2008 1292 1309 (Pubitemid 351685780)
32. 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 Analysis: RWA 9 4 2008 1768 1793 (Pubitemid 351685814)
33. D. Ding, J. Zhu, and X. Luo Hopf bifurcation analysis in a fluid flow model of Internet congestion Nonlinear Analysis: RWA 10 2009 824 839
34. D. Ding, J. Zhu, X. Luo, and Y. Liu Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm Nonlinear Analysis: RWA 10 2009 2873 2883
35. F. Liu, Z.-H Guan, and H.O. Wang Controlling bifurcations and chaos in TCP-UDP-RED Nonlinear Analysis: RWA 11 2010 1491 1501
36. F. Liu, Z.-H Guan, and H.O. Wang Stability and Hopf bifurcation analysis in a TCP fluid model Nonlinear Analysis: RWA 12 2011 353 363
37. F. Liu, Z.-H. Guan, and H.O. Wang Controlling bifurcations and chaos in small-world networks Chin. Phys. B 17 2008 2405 2411
38. B. Rezaie, M.R. Jahed Motlagh, S. Khorsandi, and M. Analoui Hopf bifurcation analysis on an Internet congestion control system of arbitrary dimension with communication delay Nonlinear Analysis: RWA 11 2010 3842 3857
39. R.R. Chen, and K. Khorasani A robust adaptive congestion control strategy for large scale networks with differentiated services traffic Automatica 47 2011 26 38
40. S. Guo, H. Zheng, and Q. Liu Hopf bifurcation analysis for congestion control with heterogeneous delays Nonlinear Analysis: RWA 11 2010 3077 3090
41. Y.G. Zheng, and Z.H. Wang Stability and Hopf bifurcation of a class of TCP/AQM networks Nonlinear Analysis: RWA 11 2010 1552 1559
42. L.J. Pei, X.W. Mu, R.M. Wang, and J.P. Yang Dynamics of the Internet TCPRED congestion control system Nonlinear Analysis: RWA 12 2011 947 955
43. Z.-K. Gao, and N.-D. Jin A directed weighted complex network for characterizing chaotic dynamics from time series Nonlinear Analysis: RWA 13 2012 947 952
44. Z.T. Huang, Q.-G. Yang, and J.F. Cao The stochastic stability and bifurcation behavior of an Internet congestion control model Math. Comput. Model. 54 2011 1954 1965
45. K. Cooke, and Z. Grossman Discrete delay, distributed delay and stability switches J. Math. Anal. Appl. 86 1982 592 627
46. B.D. Hassard, N.D. Kazarinoff, and Y.-H. Wan Theory and Applications of Hopf Bifurcation 1981 Cambridge University Press
47. J. Awrejcewicz Bifurcation and Chaos in Simple Dynamical Systems 1989 World Scientific Singapore
48. J. Awrejcewicz Bifurcation and Chaos in Coupled Oscillators 1991 World Scientific Singapore
49. J. Awrejcewicz, and C.-H. Lamarque Bifurcation and Chaos in Nonsmooth Mechanical Systems 2003 World Scientific Singapore
50. J. Hale Theory of Functional Differential Equations 1977 Spring-Verlag Berlin