Revisiting the memristor concept within basic circuit theory. (14th August 2021) - Tellini, Bernardo; Bologna, Mauro; Chandía, Kristopher J.; Macucci, Massimo
Summary: In this paper, we revisit the memristor concept within circuit theory. We start from the definition of the basic circuit elements; then, we introduce the original formulation of the memristor concept and summarize some of the controversies on its nature. We also point out the ambiguities resulting from a nonrigorous usage of the flux linkage concept. After concluding that the memristor is not a fourth basic circuit element, prompted by claims in the memristor literature, we look into the application of the memristor concept to electrophysiology, realizing that an approach suitable to explain the observed inductive behavior of the giant squid axon had already been developed in the 1960s, with the introduction of "time‐variant resistors.' We also discuss a recent memristor implementation in which the magnetic flux plays a direct role, concluding that it cannot strictly qualify as a memristor, because its v ‐ i curve cannot exactly pinch at the origin. Finally, we present numerical simulations of a few memristors and memristive systems, focusing on the behavior in the φ ‐ q plane. We show that, contrary to what happens for the most basic memristor concept, for general memristive systems, the φ ‐ q curve is not single‐valued or not even closed. Abstract : We revisit the memristor concept, pointing out the nonrigorous usage of the flux linkage definition and that the memristor is not a fourth basic circuit element but rather an extension of the resistor concept. We also show that the inductive behavior of the giant squid axon was already developed in the 1960s, without resorting to memristors. Finally, we present simulations of a few memristive systems, showing that, in general, the φ ‐ q curve is not single‐valued or not even closed.