The stochastic stability and bifurcation behavior of an Internet congestion control model

Mathematical and Computer Modelling

Volumn 54, Issue 9-10, 2011, Pages 1954-1965

  Huang, Zaitang ^a,b   Yang, Qi Gui ^a   Cao, Junfei ^a  

^a SOUTH CHINA UNIVERSITY OF TECHNOLOGY   (China)

^b Engineering Research Center of Guangxi Liupao tea Germplasm Innovation Comprehensive Utilization   (China)

Author keywords

Internet congestion control model; Invariant measure; Lyapunov exponent; Stochastic bifurcation; Stochastic stability

Indexed keywords

INTERNET CONGESTION CONTROL; INVARIANT MEASURE; LYAPUNOV EXPONENT; STOCHASTIC BIFURCATION; STOCHASTIC STABILITY;

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; INTERNET; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; STABILITY CRITERIA; STOCHASTIC SYSTEMS; TELECOMMUNICATION NETWORKS;

STOCHASTIC MODELS;

EID: 80955177688     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.05.002     Document Type: Article

References (32)

1. Jacobson V. Congestion avoidance and control. ACM SIGCOMM Comput. Commun. Rev. 1998, 18:314-329.
2. X. Wang, Controlling bifurcation and chaos in Internet congestion control system, in: Proc. 4th World Cong. on Intelligent Control and Automation, Shanghai, China, 2002, p. 573.
3. Floyd S., Jacobson V. Random early detection gateways for congestion avoidance. IEEE Trans. Netw. 1993, 1:397-413.
4. Athuraliya S., Low S., Li V., Yin Q. REM: active queue management. IEEE Trans. Netw. 2001, 15:48-53.
5. Gibbens R., Kelly F. Resource pricing and the evolution of congestion control. Automatica 1999, 35:1969-1985.
6. Kunniyur S., Srikant R. Analysis and design of adaptive virtual queue algorithm for active queue management. ACM Comput. Commun. Rev. 2001, 31:123-134.
7. Ding D., Zhu J., Luo X. Hopf bifurcation analysis in a fluid flow model of Internet congestion control algorithm. Nonlinear Anal. 2009, 10:824-839.
8. V. Misra, W. Gong, D. Towsley, Fluid based analysis of an AQM routers supporting TCP flows with an application to RED, in: Proc. SIGCOMM, Stockholm, Sweden, 2000, pp. 151-160.
9. Li C., Chen G., Liao X. Hopf bifurcation in an Internet congestion control model. Chaos Solitons Fractals 2004, 19:853-862.
10. Kelly F. Models for a self-managed Internet. Philos. Trans. R. Soc. A 2000, 358:2335-2348.
11. Hollot C., Misra V., Towsley D., Gong W. Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Trans. Automat. Control 2002, 47:945-959.
12. Arnold L. Random Dynamical Systems 1998, Springer, New York.
13. Namachchivaya N. Stochastic bifurcation. Appl. Math. Comput. 1990, 38:101-159.
14. Zhu W. Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation 2003, Science Press, Beijing.
15. Kuske R., Papanicolaou G. The invariant density of a chaotic dynamical system with small noise. Physica D 1998, 120:255-272.
16. Huang D., Wang H. Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics. Chaos Solitons Fractals 2006, 27:1072-1079.
17. Nowakowski B., Lemarchand A. Thermal explosion near bifurcation stochastic features of ignition. Physica A 2002, 311:80-96.
18. Vinals J., Lepine F., Gaudreault M. Pitchfork and Hopf bifurcations in stochastic regulatory networks with delayed feedback. Biophys. J. 2009, 96:305a.
19. Hasegawa H. Stochastic bifurcation in FitzHugh-Nagumo ensembles subjected to additive and/or multiplicative noises. Physica D 2008, 237:137-155.
20. Xu W., He Q., Fang T., Rong H. Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise. Internat. J. Non-Linear Mech. 2004, 39:1473-1479.
21. He Q., Xu W., Rong H., Fang T. Stochastic bifurcation in Duffing-Van der Pol oscillators. Physica A 2004, 338:319-334.
22. Caraballo T., Langa J., Robinson J. A stochastic pitchfork bifurcation in a reaction-diffusion equation. R. Soc. Lond. 2001, 457:2041-2061.
23. Chueshov I. Monotone Random Systems Theory and Applications 2002, Springer-Verlag.
24. Crauel H., Gundlach M. Stochastic Dynamics 1998, Springer-Verlag.
25. Khasminskii R. On the principle of averaging for ItÔ stochastic differential equations. Kybernetika (Prague) 1968, 4:260-279.
26. H. Keller, Random Attractors and bifurcations of the stochastic Lorenz system. Technical Report 389, Institut für Dynamische Systeme, Universität Bremen, 1996.
27. Leung H. Stochastic Hopf bifurcation in a biased Van der Pol model. Physica A 1998, 254:146-155.
28. Bulsara A., Acebron J. Injection locking near a stochastic bifurcation: the DC SOUID as a case study. Physica A 2003, 325:220-229.
29. Liu X., Liew K. Maximal Lyapunov exponent of a co-dimension two bifurcation system excited by a white noise. Internat. J. Non-Linear Mech. 2005, 40:653-668.
30. Diks C., Wagener F. A bifurcation theory for a class of discrete time Markovian stochastic systems. Physica D 2008, 237:3297-3306.
31. Chu J., Ducrot A., Magal P., Ruan S. Hopf bifurcation in a size-structured population dynamic model with random growth. J. Differential Equations 2009, 247:956-1000.
32. Rella C., He X., Wang D., Zheng M. The stochastic bifurcation behavior of speculative financial markets. Physica A 2008, 387:3837-3846.