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

doi:10.1088/1674-1056/20/9/090506

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.

Keywords: stability Hopf bifurcation chaos stochastic traffic

Received: 17 January 2011
Revised: 07 April 2011
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	47.52.+j	(Chaos in fluid dynamics)

Cite this article:

Wang Jun-Song(王俊松), Yuan Rui-Xi(袁睿翕), Gao Zhi-Wei(高志伟), and Wang De-Jin(王德进) Hopf bifurcation and uncontrolled stochastic traffic- induced chaos in an RED-AQM congestion control system 2011 Chin. Phys. B 20 090506

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

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