Very recently, a deep numerical investigation of resistance switching phenomena in a TaOxReRAM cell from Forschungszentrum Jülich, based on a predictive physics-based model, uncovered the capability of the nano-device to exhibit one of two possible steady-state oscillatory behaviours, depending upon the initial condition, under specific AC periodic triangular wave stimuli. In these circumstances, however, one of the two oscillations in the device memory state, was found to hit cyclically the lower bound in the existence domain of the model solution. Out of a thorough numerical exploration of the model, guided by system-theoretic considerations based upon the Time Average State Dynamic Route tool, this paper shows that it is indeed possible to shape the parameters of an AC periodic pulse train excitation signal so that each of the two locally-stable oscillatory response solutions for the memory state of the ReRAM cell lie well within the range of admissible values.