Abstract—This work develops a discrete-time dynamical feedback system model for a simpliﬁed TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. The dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as system parameters are varied. These bifurcations, which involve the emergence of oscillatory and/or chaotic behavior, shed light on the parametric sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the TCP throughput characteristic as a function of drop probability at the gateway. Among the bifurcations observed in the system are period doubling and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally.