Stability and bifurcation analysis for a congestion control model with caputo fractional derivative and time delay
Min Xiao, Wei Xing Zheng, Yurong Song, Guo‐Ping Jiang · 2016
This paper proposes a delayed fractional-order model which is more accurate than the original integer-order model when depicting dual congestion control algorithms. Some sufficient conditions for the local stability are derived for the delayed fractional-order model of congestion control algorithms. Hopf bifurcation conditions are put forward for general delayed fractional-order systems. Then the existence of Hopf bifurcations is established for the delayed fractional-order congestion control model. The critical values of the delay are determined, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Finally, numerical simulations are carried out to illustrate the main results.