Controlling Delay-induced Hopf bifurcation in Internet congestion control system

This paper focuses on Hopf bifurcation control in a dual model of Internet congestion control algorithms which is modeled as a delay differential equation (DDE). By choosing communication delay as a bifurcation parameter, it has been demonstrated that the system loses stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Therefore, a time-delayed feedback control method is applied to the system for delaying the onset of undesirable Hopf bifurcation. Theoretical analysis and numerical simulations confirm that the delayed feedback controller is efficient in controlling Hopf bifurcation in Internet congestion control system. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determinated by applying the center manifold theorem and the normal form theory.Comment: 20 pages, 8 figure

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, we 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. Discussion of stability of the periodic solutions involves the computation of Floquet exponents by considering the corresponding Poincare -Lindstedt series expansion. Finally, numerical simulations for verify the theoretical analysis are provided.Comment: 18 pages, 6 figure