Delay induced Hopf bifurcation in a simplified network congestion control model

This paper studies delay induced Hopf bifurcation in a simplified network congestion control model. It is shown that there exists a critical value of delay for the stability of the network. When the value of feedback delay passes through the critical value, the system will lose its stability and Hopf bifurcation will occur. The stability and direction of the bifurcating periodic solutions are determined by perturbation procedure. A numerical example is also worked out to verify the theoretical analysis.