The Dynamic Route Map tool can be utilized to investigate the response of a ReRAM device to DC stimuli. On the other hand, an analogue technique to explore the device behaviour under generic AC excitations is still unavailable. However, as recently shown, the Poincaré Map technique allows to explore the operating principles of the ReRAM cell under periodic inputs through numerical investigations. An alternative method, which enables some analytical derivation, may be adopted when the periodic inputs are in the form of pulse trains and the change they induce in the device state over each cycle is so small to allow its approximation with the respective time average. Employing this method, referred to as Time Average State Dynamic Route, we propose an analytical procedure to modulate the heights and widths of the pulses in each cycle of a generalised pulse train stimulus so as to endow a TaOx ReRAM device with a programmable number of oscillatory operating modes.