The multidisciplinary field of memristors calls for the necessity for theoretically-inclined researchers and experimenters to join forces, merging complementary expertise and technical know-how, to develop and implement rigorous and systematic techniques to design variability-aware memristor-based circuits and systems. The availability of a predictive physics-based model for a memristor is a necessary requirement before commencing these investigations. An interesting dynamic phenomenon, occurring ubiquitously in non-volatile memristors, is fading memory. The latter may be defined as the appearance of a unique steady-state behavior, irrespective of the choice of the initial condition from an admissible range of values, for each stimulus from a certain family, for example, the DC or the purely-AC periodic input class. This paper first provides experimental evidence for the emergence of fading memory effects in the response of a TaO_x redox-based random access memory cell to inputs from both of these classes. Leveraging the predictive capability of a physics-based device model, called JART VCM v1, a thorough system-theoretic analysis, revolving around the Dynamic Route Map graphic tool, is presented. This analysis allows to gain a better understanding of the mechanisms, underlying the emergence of history erase effects, and to identify the main factors, that modulate this nonlinear phenomenon, toward future potential applications.