  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.
