The effect of delay feedback control on dynamics of a stochastic Internet congestion control model

This paper investigates a stochastic Internet congestion control model with distributed and constant delays driven by Gaussian white noise. We study the stochastic dynamics of the system at different delay feedback intensities. Firstly, by using center manifold theory and the stochastic averaging method, the system is reduced to the average Ito equation. Secondly, the stochastic bifurcation behavior of the system is investigated by using the Fokker-Planck-Kolmogorov equation corresponding to the average Ito equation. It is found that the stochastic P(D)-bifurcation occurs when the delay feedback intensity reaches the critical value. Finally, numerical simulations are given to validate the effectiveness of the theoretical analysis.