The State Change Per Cycle Map: a novel system-theoretic analysis tool for periodically-driven ReRAM cells

Memristive devices are the subject of extensive studies nowadays. While the Dynamic Route Map is a powerful tool for analyzing the response of first-order memristors under DC stimuli, the development of an equivalent tool for investigating the response of these devices to AC stimuli is still an open question. Recently, Pershin and Slipko introduced a graphic method, which we name Time Average State Dynamic Route (TA-SDR), applicable to study first-order memristors subject to periodic rectangular pulse train-based stimuli. In this paper we introduce an alternative investigation tool, referred to as State Change Per Cycle Map (SCPCM), which is applicable in these very same scenarios. The novel analysis technique, inspired by the work of the French mathematician Henri Poincaré, reduces the investigation of a first-order non-autonomous continuous-time system to a simpler study of a first-order discrete-time map. A State Change Per Cycle Map defines precisely how the stimulus modulates each of the admissible device memory states over one input cycle. It is derivable either by means of numerical simulations, where a model for the ReRAM cell is available, or experimentally, in the case where the device memory state is accessible. While the predictive capability of a TA-SDR is limited to those case studies, where the AC periodic voltage signal applied across the device induces negligible changes in the respective memory state over each cycle, the conclusions drawn by analyzing a SCPCM have general validity, irrespective of the properties of the stimulus. The advantages of the novel analysis method for periodically driven ReRAM cells over the classical TA-SDR tool are highlighted through a number of case studies, some of which reveal the interesting capability of the ReRAM cell to display multiple oscillatory operating modes upon periodic stimulation via trains with a suitable number of SET and RESET pulses per period.