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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 628369, 12 pages
http://dx.doi.org/10.1155/2011/628369
Research Article

Dynamics of a Discrete Internet Congestion Control Model

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received 24 July 2011; Accepted 1 September 2011

Academic Editor: Carlo Piccardi

Copyright © 2011 Yingguo Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions is derived. Finally, some numerical simulations are given to verify the theoretical analysis.