Bifurcation analysis and control in exponential RED algorithm

This paper investigates a nonlinear Internet congestion model with a single link and two sources. We pay much attention to the Hopf bifurcation through the variation of the gain parameter. Firstly, by analyzing the associated characteristic equation, we obtain the condition of the existence of the Hopf bifurcation. Then, a state feedback controller is proposed to control the Hopf bifurcation, and the theoretical analysis shows that the stability domain can be extended under the small control force. Furthermore, the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Finally, we firstly apply the software package DDE-BIFTOOL to Internet congestion systems, and numerical simulations are presented to justify the validity of our theoretical analysis.