Revisiting the Memristor Concept within Basic Circuit Theory

TL;DR

This paper critically examines the memristor concept within circuit theory, clarifies misconceptions, and explores its applications and limitations, ultimately arguing it is not a fundamental circuit element and analyzing memristive behaviors through simulations.

Contribution

The paper provides a rigorous analysis of the memristor concept, clarifies its theoretical ambiguities, and demonstrates its limitations and applications in electrophysiology and circuit simulations.

Findings

The memristor is not a fundamental circuit element.

The flux linkage concept has ambiguities affecting memristor definitions.

Memristive systems often have non-single-valued or non-closed -q curves.

Abstract

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 non rigorous usage of the flux linkage concept. After concluding that the memristor is not a fourth basic circuit element, prompted by recent 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 $\varphi-q$ plane. We show that, contrary to what happens for the most basic memristor concept, for general memristive systems the $\varphi-q$ curve is not single-valued or not even closed.