The condition of Hopf bifurcation occurrence for congestion control system in computer networks with communication delay

In this paper, we study a rate-based congestion control system with communication delay. We drive the condition on delay parameter under which Hopf bifurcation occurs. By taking delay as a bifurcation parameter and changing it, we find the critical value of delay such that the system passes the critical point and a periodic solution bifurcates from the equilibrium point. The model considered in this paper is a nonlinear delay differential equation which stands for a network with fixed communication delay. The simulation of a numerical example is given for justifying the theorical results.