Hybrid control of Hopf bifurcation in a congestion control system of dual algorithm

This paper proposes a hybrid strategy to control Hopf bifurcations of a first-order dual model of congestion control algorithms. By choosing the gain parameter as the bifurcation parameter, it is proved that a Hopf bifurcation occurs when the gain parameter passes through a critical value. It is shown that the absence of controller results in the early instability of the model via the Hopf bifurcation. By applying a hybrid strategy and time-delayed feedback to the model, the onset of the Hopf bifurcation is postponed without changing the original equilibrium point. Numerical simulations are given to justify the validity of the hybrid strategy in bifurcation control.