Local Hopf bifurcation and global existence of periodic solutions in TCP system (Q605177)

Dynamics of the widely used Internet transmission control protocol (TCP) is described by a first order delayed ODE. Using normal form and center manifold theories, the authors investigate the stability of the positive equilibrium and the occurrence of Hopf bifurcation as the delay passes through its critical value. Results on the direction and stability of the local Hopf bifurcation are obtained. Global existence of periodic solutions is established on the base of \textit{J. Wu}'s results [Trans. Am. Math. Soc. 350, No.~12, 4799--4838 (1998; Zbl 0905.34034)].