Hou Ping, Wang Zhi-quan. Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks[J]. Journal of Electronics & Information Technology, 2010, 32(4): 983-987. doi: 10.3724/SP.J.1146.2009.00358
Citation:
Hou Ping, Wang Zhi-quan. Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks[J]. Journal of Electronics & Information Technology, 2010, 32(4): 983-987. doi: 10.3724/SP.J.1146.2009.00358
Hou Ping, Wang Zhi-quan. Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks[J]. Journal of Electronics & Information Technology, 2010, 32(4): 983-987. doi: 10.3724/SP.J.1146.2009.00358
Citation:
Hou Ping, Wang Zhi-quan. Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks[J]. Journal of Electronics & Information Technology, 2010, 32(4): 983-987. doi: 10.3724/SP.J.1146.2009.00358
This paper focuses on the Hopf bifurcation analysis of a fluid-flow model with time-delay for the congestion control algorithm in the wireless networks. By choosing the communication delay as a bifurcation parameter, the model exhibits of Hopf bifurcation are proved. The formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, a numerical simulation is presented to verify the theoretical results.
Li C, Chen G, and Liao X, et al.. Hopf bifurcation in anInternet congestion control model[J].Chaos, Solitons andFractals.2004, 19(4):853-862[2]Yang H and Tian Y. Hopf bifurcation in REM algorithmwith communication delay[J].Chaos, Solitons andFractals.2005, 25(5):1093-1105[3]Raina G and Heckmann O. TCP: Local stability and Hopfbifurcation[J].Performance Evaluation.2007, 64(3):266-275[4]Ding D, Zhu J, and Luo X. Hopf bifurcation analysis in afluid flow model of Internet congestion control algorithm[J].Nonlinear Analysis: Real World Applications.2009, 10(2):824-839[5]Zheng F and Nelson J. An H approach to congestion controldesign for AQM routers supporting TCP flows in wirelessaccess networks[J].Computer Networks.2007, 51(6):1684-1704[6]Hollot C V, Misra V, and Towsley D, et al.. Analysis anddesign of controllers for AQM routers supporting TCPflows[J].IEEE Transactions on Automatic Control.2002,47(6):945-959[7]Cooke K and Grossman Z. Discrete delay, distributed delayand stability switches [J].Mathematical Analysis andApplications.1982, 86(2):592-627[8]Hale J. Theory of Functional Differential Equations [M]. NewYork Heidelberg Berlin, Spring-Verlag, 1977, Chapter 11.[9]Hassard B D, Kazarinoff N D, and Wan Y H. Theory andapplications of Hopf bifurcation[M]. Cambridge, CambridgeUniversity Press, 1981, Chapter 3.