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This paper focuses on Hopf bifurcation control in a dual model of Internetcongestion control algorithms which is modeled as a delay differential equation(DDE). By choosing communication delay as a bifurcation parameter, it has beendemonstrated that the system loses stability and a Hopf bifurcation occurs whencommunication delay passes through a critical value. Therefore, a time-delayedfeedback control method is applied to the system for delaying the onset ofundesirable Hopf bifurcation. Theoretical analysis and numerical simulationsconfirm that the delayed feedback controller is efficient in controlling Hopfbifurcation in Internet congestion control system. Moreover, the direction ofthe Hopf bifurcation and the stability of the bifurcating periodic solutionsare determinated by applying the center manifold theorem and the normal formtheory.

Controlling Delay-induced Hopf bifurcation in Internet congestion control system