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.

中文翻译：

---

回顾基础电路理论中的忆阻器概念

在本文中，我们将回顾电路理论中的忆阻器概念。我们从基本电路元件的定义开始，然后介绍忆阻器概念的原始表述，并总结有关其性质的一些争议。我们还指出了由于不严格使用通量链接概念而引起的歧义。在忆阻器不是第四基本电路元件之后，由于忆阻器文献的最新主张，我们研究了忆阻器概念在电生理学中的应用，意识到一种适合于解释所观察到的巨型鱿鱼轴突的感应行为的方法。在1960年代已经开发出了“时变电阻器”。我们还讨论了最近的忆阻器实现，其中磁通量起着直接作用，结论认为它不能严格地符合忆阻器的要求，因为它的$ vi $曲线不能精确地夹在原点上。最后，我们介绍一些忆阻器和忆阻系统的数值模拟，重点是$ \ varphi-q $平面中的行为。我们证明，与最基本的忆阻器概念相反，对于一般的忆阻系统，$ \ varphi-q $曲线不是单值的，甚至不是封闭的。