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.
This work was jointly supported by the Science and Technology Plans of the Department of Education, Shandong Province under Grant J06P04, the Youth Framework Teacher Subsidize Item of Henan Province under Grant 20050181, and the Natural Science Foundation of Henan Province, China under Grant 0611055100.
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Cheng, Z., Qiu, J., Wang, G., Yu, B. (2007). Hybrid Control of Hopf Bifurcation for an Internet Congestion Model. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_11
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DOI: https://doi.org/10.1007/978-3-540-74205-0_11
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