  This paper focuses on Hopf bifurcation control in a dual model of Internet
congestion control algorithms which is modeled as a delay differential equation
(DDE). By choosing communication delay as a bifurcation parameter, it has been
demonstrated that the system loses stability and a Hopf bifurcation occurs when
communication delay passes through a critical value. Therefore, a time-delayed
feedback control method is applied to the system for delaying the onset of
undesirable Hopf bifurcation. Theoretical analysis and numerical simulations
confirm that the delayed feedback controller is efficient in controlling Hopf
bifurcation in Internet congestion control system. Moreover, the direction of
the Hopf bifurcation and the stability of the bifurcating periodic solutions
are determinated by applying the center manifold theorem and the normal form
theory.
