This work introduces a discrete time model for a simplified TCP network with RED control. It is argued that by sampling the state space at certain instants, the dynamics of the system can be described explicitly as a discrete time feedback control system. This system is used to analyze the operating point of TCP-RED and its stability with respect to various controller and system parameters. With the help of bifurcation diagrams, it is numerically shown that non-trivial (not due to the discontinuity in the system or the control law) instabilities in the system are possible due to the presence of a strong nonlinearity in the characteristics of TCP throughput of a sender as a function of drop probability at the gateway. Some of the bifurcations observed in the system are the period-doubling sequence and border collisions leading to a change in the system periodicity and chaos. Analytical techniques are provided to help in the understanding of this kind of anomalous behavior. An explicit stability condition in terms of different parameters is given.