Stability And Hopf Bifurcation Of A Congestion Control Model With Window Delay In Wireless Networks

Supported by the National Natural Science Foundation of China under Grant NO.1137-2282,a congestion control model with window delays (once a congestion loss is detected,the time is required to executive marking/dropping the packet) in a non-linear wireless access networks is studied and analyzed from the non-linear dynamics in this dissertation. By choosing the round trip delay as a bifurcation parameter, the simplified model and general model of congestion control are studied for local stability of equihbria in the congestion control model systems. The formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, the results show that the stability of the wireless network system is sensitive to time delay and the small delay can also lead to instability of the system. Numerical simulations is presented to verify the theoretical results.