If it’s pinched it’s a memristor

Abstract

This paper presents an in-depth review of the memristor from a rigorous circuit-theoretic perspective, independent of the material the device is made of. From an experimental perspective, a memristor is best defined as any two-terminal device that exhibits a pinched hysteresis loop in the voltage–current plane when driven by any periodic voltage or current signal that elicits a periodic response of the same frequency. This definition greatly broadens the scope of memristive devices to encompass even non-semiconductor devices, both organic and inorganic, from many unrelated disciplines, including biology, botany, brain science, etc. For pedagogical reasons, the broad terrain of memristors is partitioned into three classes of increasing generality, dubbed Ideal Memristors, Generic Memristors, and Extended Memristors. Each class is distinguished from the others via unique fingerprints and signatures. This paper clarifies many confusing issues, such as non-volatility, dc V–I curves, high-frequency v–i curves, local activity, as well as nonlinear dynamical and bifurcation phenomena that are the hallmarks of memristive devices. Above all, this paper addresses several fundamental issues and questions that many memristor researchers do not comprehend but are afraid to ask.