Control of Bifurcation in Internet Model with Time-Delay
Applied and Computational Mathematics
Volume 5, Issue 5, October 2016, Pages: 186-192
Received: Sep. 1, 2016; Accepted: Sep. 13, 2016; Published: Oct. 8, 2016
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Authors
Mohammad Darvishi, Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran
Haji Mohammad Mohammadinejad, Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran
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Abstract
In this paper we study the Hopf bifurcation control problem of a Internet Model with Time-delay. The stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply Proportional - Derivative (PD) controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulation results and figures confirm that the control strategy is efficient in controlling the Hopf bifurcation.
Keywords
Hopf Bifurcation, Bifurcation Control, PD Controller
To cite this article
Mohammad Darvishi, Haji Mohammad Mohammadinejad, Control of Bifurcation in Internet Model with Time-Delay, Applied and Computational Mathematics. Vol. 5, No. 5, 2016, pp. 186-192. doi: 10.11648/j.acm.20160505.11
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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