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

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

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 pas...

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Main Authors: Wen-bo Zhao, Xiao-ke Sun, Huicheng Wang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/632564
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spelling doaj-cbdcd30d6416439a927234c63f788fc72020-11-24T22:40:34ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/632564632564Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access NetworkWen-bo Zhao0Xiao-ke Sun1Huicheng Wang2School of Physics and Information, Tianshui Normal University, Tianshui, Gansu 741000, ChinaSchool of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu 741000, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaWe 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.http://dx.doi.org/10.1155/2014/632564
collection DOAJ
language English
format Article
sources DOAJ
author Wen-bo Zhao
Xiao-ke Sun
Huicheng Wang
spellingShingle Wen-bo Zhao
Xiao-ke Sun
Huicheng Wang
Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
Abstract and Applied Analysis
author_facet Wen-bo Zhao
Xiao-ke Sun
Huicheng Wang
author_sort Wen-bo Zhao
title Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
title_short Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
title_full Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
title_fullStr Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
title_full_unstemmed Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network
title_sort hopf bifurcation and stability analysis of a congestion control model with delay in wireless access network
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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.
url http://dx.doi.org/10.1155/2014/632564
work_keys_str_mv AT wenbozhao hopfbifurcationandstabilityanalysisofacongestioncontrolmodelwithdelayinwirelessaccessnetwork
AT xiaokesun hopfbifurcationandstabilityanalysisofacongestioncontrolmodelwithdelayinwirelessaccessnetwork
AT huichengwang hopfbifurcationandstabilityanalysisofacongestioncontrolmodelwithdelayinwirelessaccessnetwork
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