Hopf Bifurcation Analysis in a Dual Model of Internet Congestion Control Algorithm With Communication Delay

This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order Delay Differential Equation (DDE). By choosing communication delay as the bifurcation parameter, the authors demonstrate that the system loses its stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Moreover, the bifurcating periodic solution of system is calculated by means of perturbation methods.