Oscillatory dynamics induced by time delay in an internet congestion control model with ring topology

In this paper, an n-dimensional congestion control model with ring topology is considered to study delay-induced oscillation via the Hopf bifurcation. The expression of the possible critical delay for the Hopf bifurcation is obtained by analyzing the linear part of the system around the equilibrium and verified by the numerical simulation. Based on the linear analysis, the method of multiple scales is employed to obtain the quantitative relation between the delay and the oscillation induced by it. The analytical results agree well with those obtained by the numerical method. Furthermore, the effects of other parameters are also studied. The discussions reveal that excessive transfer times may cause the oscillation and that increasing the link capacity can control the oscillatory dynamics.