A Reliable Algorithm for the Characterization of the Nonlinear Dynamics of FAST TCP Networks

In this study, we investigate a class of Fast Transmission Control Protocol (FAST TCP) network with a delayed state feedback mechanism in terms of nonlinear dynamics, including local stability and periodic bifurcation. First, we successfully addressed the local stability of the system by employing the $\tau $ -decomposition strategy and provided an explicit expression for the delay stability interval. Second, we apply the normal form theory and the central manifold theorem to study the bifurcation solutions in depth and clarify the direction of the Hopf bifurcation as well as the stability of the bifurcation periodic solutions. In addition, the explicit bifurcation parameters are intuitively given by us using a symbolic arithmetic tools. Finally, by presenting a numerical example, we verify the accuracy of the theoretical analysis and demonstrate that the method is highly accurate and effective. These findings provide important theoretical support for deepening the understanding of the dynamic properties of time-lagged state feedback mechanisms in FAST TCP networks and the optimization of network control systems.