Abstract and Applied Analysis

Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

Wen-bo Zhao, Xiao-ke Sun, and Huicheng Wang

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Abstract

We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 632564, 12 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048250

Digital Object Identifier
doi:10.1155/2014/632564

Mathematical Reviews number (MathSciNet)
MR3200795

Zentralblatt MATH identifier
07022784

Citation

Zhao, Wen-bo; Sun, Xiao-ke; Wang, Huicheng. Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 632564, 12 pages. doi:10.1155/2014/632564. https://projecteuclid.org/euclid.aaa/1425048250


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