Stability and Hopf bifurcation analysis of TCP with a RED-like queue management policy

We analyse a non-linear fluid model of TCP coupled with a Random Early Detection (RED)-like queue management policy. We first show that the conditions for local stability, as parameters vary, will be violated via a Hopf bifurcation. Thus, a stable equilibrium would give rise to limit cycles. To identify the type of the Hopf bifurcation, and to determine the stability of the bifurcating limit cycles, we apply the theory of normal forms and the center manifold analysis. Some numerical computations accompany our theoretical work.