Stability And Hopf Bifurcation Analysis Of A FAST TCP Model With State-dependent Delay

FAST TCP is a new congestion control protocol, which is based on queue delay and can be flexibly used to monitor the internet congestion packet loss and packet delay. Sup-ported by the National Natural Science Foundation of China under Grant NO.11372282, this dissertation is based on a continuous time state-dependent delay FAST TCP model to study the effect of round-trip delay on the stability and performance of the system. Delay value is fixed on the equibilibrium point in the course of studying. Taking μ as a round-trip delay times, the stability of the system is investigated. The time-delayed sys-tem is linearized at the equilibrium by employing formal linearization method with state dependent delay differential equations, which leads to the characteristic equation of the corresponding linearized system; Then equilibrium’s local asymptotic stability conditions can be obtained combine with Rouche theorem and the sufficient conditions of Hopf bifur-cation. The necessary and sufficient condition of Hopf bifurcation is discussed, next the property of the Hopf bifurcation such as the direction, stability and bifurcating periodic solutions are investigated combine with the center manifold theorem and the normal form theory; Finally, numerical simulations are illustrated to verify our theoretical prediction by employing the nonlinear dynamical software WinPP.The results show:stability can be analyzed by other parameters’s choosing conditions to study the dependent quantity of the delay to realize the system for the FAST TCP model with state-dependent delay. But the FAST TCP system should have very small round-trip delay, otherwise, the system will lose stability and produce periodic oscillation, causing performance deterioration.