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Stability and Hopf bifurcation of a class of TCP/AQM networks

【摘要】:In this paper, the local dynamics around the equilibrium of a class of TCP/AQM networks with proportional feedback is investigated, and the effect of the communication delay on the stability is addressed. It is found that the internet system keeps stable if the delay is not large, and it exhibits good performance only for mediate delay in the stable interval, NOT the case as expected: the smaller the better. In addition, a Hopf bifurcation occurs after the equilibrium loses its stability, and the method of multiple scales (MMS) is used to calculate the bifurcated periodic solution, and to determine the direction of the bifurcation, and to determine the stability of the periodic motion resulted from the bifurcation. The method of multiple scales involves easy computation and yields prediction on the bifurcated periodic solution in very good agreement with the numerical results.

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