Research On Hopf Bifurcation Control Of Internet Congestion Control System

With the rapid increase of Internet users and business, the Internet congestion phenomenon has become increasingly serious. The occurrence of Internet congestion has a serious influence on the performance of the entire network. The complexity and variability of the Internet environment increased a lot of problems for mathematical modeling of the Internet system and designing new congestion control algorithm. In recent years, the rapid development of wireless access network adds many new network structures and features to the Internet, if we continue to use the traditional TCP congestion control algorithm, it will bring many problems. Therefore, in order to make the Internet work better, it is very necessary that using and designing a suitable congestion control algorithm.This thesis mainly studies the problem of stability, bifurcation and bifurcation control of dual model with time-delay in the Internet congestion control system and fluid flow model in wireless access network. Bifurcation control principle is that adding a suitable controller to the original system, changing the bifurcation characteristics of the system and producing needed dynamic behavior. This paper presents a hybrid control method, which has been applied to the Internet congestion control system. Then according to the stability theory, the theory of bifurcation and bifurcation control theorem, we study of the complex dynamic phenomena in depth. The main content of the full text is as follows:(1) We study the problem of Hopf bifurcation of the dual model in the Internet congestion control system, and introduce the hybrid control method combined parameter adjustment with state feedback to the model. By adjusting the control parameters of hybrid control method, the method can delay or even eliminate the bifurcation behavior of the original system, and enlarge the stability range of the system. Finally, the experimental simulation results also show that the method can effectively control the Hopf bifurcation of the dual model.(2) We pay attention to the fluid flow model in wireless access network First of all, we do the simplification and analysis of the model. Then, the hybrid control method is added to the fluid flow model. Finally, according to the Routh-Hurwitz stability criterion, we study the stability and bifurcation behavior of the controlled system. Furthermore, by combining the normal form theory with center manifold theorem, the direction and stability of periodic solutions of the Hopf bifurcation in controlled system are discussed. The numerical simulation verifies that applying the hybrid control method to the Hopf bifurcation control of the fluid flow model in wireless access network is feasible.