Controlling Delay-induced Hopf bifurcation in Internet congestion control system

TL;DR

This paper investigates controlling Hopf bifurcation caused by delays in Internet congestion control systems using delayed feedback, with theoretical and numerical validation of the control method's effectiveness.

Contribution

It introduces a delayed feedback control approach to delay Hopf bifurcation in delay differential equation models of Internet congestion control, supported by theoretical analysis.

Findings

Delayed feedback control delays Hopf bifurcation onset

The control method stabilizes the system beyond critical delays

The bifurcation direction and stability are analytically determined

Abstract

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.