中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90506-090506.doi: 10.1088/1674-1056/20/9/090506

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Hopf bifurcation and uncontrolled stochastic traffic- induced chaos in an RED-AQM congestion control system

王德进1, 高志伟2, 王俊松3, 袁睿翕4   

  1. (1)Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China; (2)Department of Automation, Tianjin University, Tianjin 300072, China; (3)School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China; (4)School of Information Science, Tsinghua University, Beijing 100084, China
  • 收稿日期:2011-01-17 修回日期:2011-04-07 出版日期:2011-09-15 发布日期:2011-09-15

Hopf bifurcation and uncontrolled stochastic traffic- induced chaos in an RED-AQM congestion control system

Wang Jun-Song(王俊松)a)†, Yuan Rui-Xi(袁睿翕) b), Gao Zhi-Wei(高志伟)c), and Wang De-Jin(王德进) d)   

  1. a School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China; b School of Information Science, Tsinghua University, Beijing 100084, China; c Department of Automation, Tianjin University, Tianjin 300072, China; d Department of Automation, Tianjin University of Science and Technology, Tianjin 300222, China
  • Received:2011-01-17 Revised:2011-04-07 Online:2011-09-15 Published:2011-09-15

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摘要： We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results.

关键词: stability, Hopf bifurcation, chaos, stochastic traffic

Abstract: We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results.

Key words: stability, Hopf bifurcation, chaos, stochastic traffic

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
47.52.+j (Chaos in fluid dynamics)