Hybrid Control of Hopf Bifurcation for an Internet Congestion Model

Authors:
Zunshui Cheng;Jianlong Qiu;Guangbin Wang;Bin Yu
Affiliations:
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China and Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Mathematics, Linyi Normal University, Linyi, Shandong 276005, China and Department of Mathematics, Southeast University, Nanjing 210096, China;School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China;School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Venue:
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Year:
2009

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Abstract

In this paper, the problem of Hopf bifurcation control for an Internet congestion model with time delays is considered by using a new hybrid control strategy, in which state feedback and parameter perturbation are used. It is well known that for the system without control, as the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a hybrid control strategy is proposed and the onset of an inherent bifurcation is delayed (advanced) when such bifurcation is undesired (desired). Furthermore, the dynamic behaviors of the controlled system can also be changed by choosing appropriate control parameters. Numerical simulation results confirm that the new control strategy is efficient in controlling Hopf bifurcation.