All 2-terminal non-volatile memory devices based on resistance switching are memristors, regardless of the device material and physical operating mechanisms. They all exhibit a distinctive “fingerprint” characterized by a pinched hysteresis loop confined to the first and the third quadrants of the v–i plane whose contour shape in general changes with both the amplitude and frequency of any periodic “sine-wave-like” input voltage source, or current source. In particular, the pinched hysteresis loop shrinks and tends to a straight line as frequency increases. Though numerous examples of voltage vs. current pinched hysteresis loops have been published in many unrelated fields, such as biology, chemistry, physics, etc., and observed from many unrelated phenomena, such as gas discharge arcs, mercury lamps, power conversion devices, earthquake conductance variations, etc., we restrict our examples in this tutorial to solid-state and/or nano devices where copious examples of published pinched hysteresis loops abound. In particular, we sampled arbitrarily, one example from each year between the years 2000 and 2010, to demonstrate that the memristor is a device that does not depend on any particular material, or physical mechanism. For example, we have shown that spin-transfer magnetic tunnel junctions are examples of memristors. We have also demonstrated that both bipolar and unipolar resistance switching devices are memristors. The goal of this tutorial is to introduce some fundamental circuit-theoretic concepts and properties of the memristor that are relevant to the analysis and design of non-volatile nano memories where binary bits are stored as resistances manifested by the memristor’s continuum of equilibrium states. Simple pedagogical examples will be used to illustrate, clarify, and demystify various misconceptions among the uninitiated.

From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm's law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of 'pinched' hysteresis loops in the v-i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling 'Goldilocks zone', dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors.

As the limits of transistor technology are approached, feature size in integrated circuit transistors has been reduced very near to the minimum physically-realizable channel length, and it has become increasingly difficult to meet expectations outlined by Moore’s law. As one of the most promising devices to replace transistors, memristors have many excellent properties that can be leveraged to develop new types of neural and non-von Neumann computing systems, which are expected to revolutionize information-processing technology. This survey provides a comparative overview of research progress on memristors. Different memristor synaptic devices are classified according to stimulation patterns and the working mechanisms of these various synaptic devices are analyzed in detail. Crossbar-based memristors have demonstrated advantages in physically executing vector-matrix multiplication and enabling highly power-efficient and area-efficient neuromorphic system designs. The extensive uses of crossbar-based memristors cover in-memory logic, vector-matrix multiplication, and many other fundamental computing operations. Furthermore, memristor-based architectures for efficient neural network training and inference have been studied. However, memristors have non-ideal properties due to programming inaccuracies and device imperfections from fabrication, which lead to error or mismatch in computed results. To build reliable memristor-based designs, circuit-level, algorithm-level, and system-level solutions to memristor reliability issues are being studied. To this end, state-of-the-art realizations of memristor crossbars, crossbar-based designs, and peripheral circuitry are presented, which show both promising full-system inference accuracy and excellent power efficiency in multiple tasks. Memristor in-situ learning benefits from high energy efficiency and biologically-imitative characteristics, which are conducive to further realizing hardware acceleration of cognitive learning. At present, the learning and training processes of brain-like networks are complex, presenting great challenges for network design and implementation.

In this paper, a generic model of memristive systems, which can emulate the behavior of real memristive devices is proposed. Non-ideal pinched hysteresis loops are sometimes observed in real memristive devices. For example, the hysteresis loops may deviate from the origin over a broad range of amplitude A and frequency f of the input signal. This deviation from the ideal case is often caused by parasitic circuit elements exhibited by real memristive devices. In this paper, we propose a generic memristive circuit model by adding four parasitic circuit elements, namely, a small capacitance, a small inductance, a small DC current source, and a small DC voltage source, to the memristive device. The adequacy of this model is verified experimentally and numerically with two thermistors (NTC and PTC) memristors.

No isolated system may ever support complexity. Emergent phenomena may however appear in an open system, if, as established by the Edge of Chaos theory, some of its constitutive elements feature the capability to amplify infinitesimal fluctuations in energy, provided an external source supplies them with a sufficient amount of DC power, which is known to be a signature for locally-active behaviour. In particular, complex behaviours, including static and dynamic pattern formation, may emerge in arrays of identical diffusively-coupled cells, if and only if the basic unit is poised on a particular sub-domain of the Local Activity regime, referred to as Edge of Chaos, within which a quiet state hides in fact a high degree of excitability. Here we show, for the first time, that these counterintuitive phenomena may emerge in a basic memristor cellular neural network, consisting of two identical diffusively-coupled second-order cells. The proposed bio-inspired array represents the simplest ever-reported open system, which reproduces the shocking phenomenon, reported by Smale in 1974, when, while studying a model from cellular biology, he observed two identical reaction cells, “mathematically dead” on their own, pulsating together upon diffusive coupling. Impressively, the bio-inspired two-cell reaction-diffusion network contains only nine circuit elements, specifically two DC voltage sources, three linear resistors, two linear capacitors, and two functional niobium oxide (NbO) memristors from NaMLab. Applying the theory of Local Activity to an accurate model of the memristor oscillator, a comprehensive picture for its local and global dynamics may be drawn, providing a systematic method to tune the design parameters of the two-cell array to enable diffusion-driven instabilities therein.