无线网络拥塞控制中流体流模型的Hopf分岔及其稳定性
doi: 10.3724/SP.J.1146.2009.00358
Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks
-
摘要: 该文对一个用于无线网络拥塞控制算法设计的具有通信时延的流体流模型进行Hopf分岔分析，以通信时延作为分岔参数，证明此模型Hopf分岔的存在性，并应用中心流形和规范型理论推导出确定 Hopf 分岔方向和分岔周期解稳定性的计算公式，数值仿真验证了结论的有效性。Abstract: 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. -
计量
- 文章访问数: 4044
- HTML全文浏览量: 100
- PDF下载量: 859
- 被引次数: 0
下载:
