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This paper presents a circuit-theoretic analysis of a NbO 2 -Mott memristor fabricated at Hewlett-Packard Labs. It investigates mechanisms behind the origin of complexity based on local activity, which characterizes the behavior of this outstanding nanodevice. We propose an accurate, particularly simplified version of a recently introduced physical model suitable for large-scale circuit simulations. Following the concept of local activity, we then conduct a small-signal circuit-theoretic derivation of the impedance and associated small-signal equivalent circuit elements to analyze device stability and frequency response. Finally, our analysis reveals locally active operating regions, as well as regions where the device dynamics are positioned on the edge of chaos. The latter regions are crucial for designing bio-inspired computing systems.

We present and experimentally validate two minimal compact memristive models for spiking neuronal signal generation using commercially available low-cost components. The first neuron model is called the Memristive Integrate-and-Fire (MIF) model, for neuronal signaling with two voltage levels: the spike-peak, and the rest-potential. The second model MIF2 is also presented, which promotes local adaptation by accounting for a third refractory voltage level during hyperpolarization. We show both compact models are minimal in terms of the number of circuit elements and integration area. Using the MIF and MIF2 models, we postulate the design of a memristive solid-state brain with an estimation of its surface area and power consumption. Analytical projections show that a memristive solid-state brain could be realized within (i) the surface area of the median human brain, 2,400cm², (ii) the same volume of the median human brain, and (iii) a total power budget of approximately 20 W using a 3.5 nm technology. Distinct from the past decade of memristive neuron literature, our benchmarks are attained using generic commercially available memristors that are reproducible using off-the-shelf components. We expect this work can promote more experimental demonstrations of memristive circuits that do not rely on prohibitively expensive fabrication processes.

This chapter presents the mathematical investigation of the emergence of static patterns in a Reaction–Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) structure via the application of the theory of local activity. The proposed RD-MCNN has a planar grid structure, which consists of identical memristive cells, and the couplings are established in a purely resistive fashion. The single cell has a compact design being composed of a locally active memristor in parallel with a capacitor, besides the bias circuitry, namely a DC voltage source and its series resistor. We first introduce the mathematical model of the locally active memristor and then study the main characteristics of its AC equivalent circuit. Later on, we perform a stability analysis to obtain the stability criteria for the single cell. Consequently, we apply the theory of local activity to extract the parameter space associated with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the necessary calculations parametrically. The corresponding parameter space domains are represented in terms of intrinsic cell characteristics such as the DC operating point, the capacitance, and the coupling resistance. Finally, we simulate the proposed RD-MCNN structure where we demonstrate the emergence of pattern formation for various values of the design parameters.

In this work, we explore pattern formation dynamics across a diffusively coupled Memristor Cellular Nonlinear Network (MCNN), which is composed of identical cells with locally active memristors. We bias the cells on the edge-of-chaos, introduce a systematic design procedure to induce complexity in the array, and extract the element values analytically in a parametric form. In order to enhance the stability and speed of the numerical simulations, we apply a simple variable transformation to a core memristor model while we include the additional effect of parasitic resistors to investigate the locally active dynamics of a VO2 device. We first take a close look at the effect of the linear coupling resistor on pattern formation, and later study how nonlinearly-resistive coupling, based upon tangent hyperbolic law, affect the emergence of complex patterns. Simulation results reveal that a variety of static patterns with different characteristics can emerge across the proposed MCNN.

Memristor Cellular Nonlinear Networks (M-CNNs) have been recently introduced as a functional upgrade of standard CNNs, empowered by the potential of memristors to perform storage and computing functionalities in the same area. This paper exploits the diverse features of M-CNNs, which are equipped with threshold-based binary resistance switching devices, introducing two state-of-the-art image processing M-CNNs: a) the multi-tasking CORNER-EDGE M-CNN, which performs corner or edge detection depending on the initial states of the memristors within the network; b) the memcomputing STORE-EDGE M-CNN, which outputs the edges of a binary input image, that is simultaneously stored in the memristors of the cellular array.

The peculiar combined capability of nonvolatile resistance switching memories to store and process data within a common nanoscale physical medium allows to implement disruptive mem-computing paradigms in hybrid circuits leveraging the compatibility of CMOS and memristive technologies. This may pave the way toward the future development of minaturized, lightweight, ultra-dense, high-speed and low-power universal memcomputers with sensing functionality on board. Since the availability of technical products of this kind would respond to the current demands of the Internet-of-Things industry, it is timely to investigate the functionalities and limitations of memristive memcomputing structures, such as those arranged in cellular bio-inspired architectures. The adoption of memristors in circuit design brings new life to nonlinear system theory, since standard analysis and synthesis techniques from linear system theory are no longer applicable for the investigation of highly-nonlinear electronic systems. This paper demonstrates how the use of standard and novel concepts from nonlinear system theory allow to design a Memristor Cellular Nonlinear Network for the execution of pixel-wise logical boolean functions on binary images, and the concurrent storage of input or output data into the memristive memory bank, providing clear evidence for the truly mem-computing character of its memristor-centered signal processing paradigm.