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This study introduces a simple memristor cellular neural network structure, a minimalist configuration with only two cells, designed to concurrently address two logic problems. The unique attribute of this system lies in its adaptability, where the nature of the implemented logic gate, be it AND, OR, and XOR, is determined exclusively by the initial states of the memristors. The memristors' state, alterable through current flow, allows for dynamic manipulation, enabling the setting of initial conditions and consequently, a change in the circuit's functionality. To optimize the parameters of this dynamic system, contemporary machine learning techniques are employed, specifically gradient descent optimization. Through a case study, the potential of leveraging intricate circuit dynamics is exemplified to expand the spectrum of problems solvable with a defined number of neurons. This work not only underscores the significance of adaptability in logical circuits but also demonstrates the efficacy of memristive elements in enhancing problem‐solving capabilities. [ABSTRACT FROM AUTHOR]

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The multidisciplinary field of memristors calls for the necessity for theoretically‐inclined researchers and experimenters to join forces, merging complementary expertise and technical know‐how, to develop and implement rigorous and systematic techniques to design variability‐aware memristor‐based circuits and systems. The availability of a predictive physics‐based model for a memristor is a necessary requirement before commencing these investigations. An interesting dynamic phenomenon, occurring ubiquitously in non‐volatile memristors, is fading memory. The latter may be defined as the appearance of a unique steady‐state behavior, irrespective of the choice of the initial condition from an admissible range of values, for each stimulus from a certain family, for example, the DC or the purely‐AC periodic input class. This paper first provides experimental evidence for the emergence of fading memory effects in the response of a TaOx redox‐based random access memory cell to inputs from both of these classes. Leveraging the predictive capability of a physics‐based device model, called JART VCM v1, a thorough system‐theoretic analysis, revolving around the Dynamic Route Map graphic tool, is presented. This analysis allows to gain a better understanding of the mechanisms, underlying the emergence of history erase effects, and to identify the main factors, that modulate this nonlinear phenomenon, toward future potential applications. [ABSTRACT FROM AUTHOR]

This manuscript provides a comprehensive tutorial on the operating principles of a bio-inspired Cellular Nonlinear Network, leveraging the local activity of NbO x memristors to apply a spike-based computing paradigm, which is expected to deliver such a separation between the steady-state phases of its capacitively-coupled oscillators, relative to a reference cell, as to unveal the classification of the nodes of the associated graphs into the least number of groups, according to the rules of a non-deterministic polynomial-hard combinatorial optimization problem, known as vertex coloring. Besides providing the theoretical foundations of the bio-inspired signal-processing paradigm, implemented by the proposed Memristor Oscillatory Network, and presenting pedagogical examples, illustrating how the phase dynamics of the memristive computing engine enables to solve the graph coloring problem, the paper further presents strategies to compensate for an imbalance in the number of couplings per oscillator, to counteract the intrinsic variability observed in the electrical behaviours of memristor samples from the same batch, and to prevent the impasse appearing when the array attains a steady-state corresponding to a local minimum of the optimization goal. The proposed Memristor Cellular Nonlinear Network, endowed with ad hoc circuitry for the implementation of these control strategies, is found to classify the vertices of a wide set of graphs in a number of color groups lower than the cardinality of the set of colors identified by traditional either software or hardware competitor systems. Given that, under nominal operating conditions, a biological system, such as the brain, is naturally capable to optimise energy consumption in problem-solving activities, the capability of locally-active memristor nanotechnologies to enable the circuit implementation of bio-inspired signal processing paradigms is expected to pave the way toward electronics with higher time and energy efficiency than state-of-the-art purely-CMOS hardware. [ABSTRACT FROM AUTHOR]

Log-domain filters use the large-signal exponential current-voltage relationship of the bipolar junction transistor to convert signals to logarithmic form, where they are processed, and to map them back to the linear domain after processing. Due to their internally nonlinear nature, application of standard linear circuit design techniques to such networks can give rise to unexpected externally nonlinear behavior. Methods of nonlinear dynamics are used here to explain the undesired nonlinearities recently observed in a differential first-order log-domain integrator and to investigate the input/output behavior of the corresponding low-pass filter. The nonlinear behavior of a floating-capacitor differential second-order log-domain bandpass filter is also investigated and explained. Index Terms--Analog circuits, log-domain circuits, nonlinear circuits, nonlinear oscillations, translincar circuits, stability.

Memristors are promising nanoelectronic devices for the implementation of future AI-driven sensor-processor electronic systems, which are essential for the ongoing digitalization of our world. Accurate and computationally cost-effective models for the manufactured memristors are essential for the design of such systems, especially for the simulation of large circuits. In this brief we address the simplification of the JART memristor model, a generic physics-based model of Valence Change Mechanism (VCM) memristors which accurately describes the dynamic behavior of fabricated memristor devices. Furthermore, the proposed model and simplification methodology have the potential to capture the dynamics of a wide range of memristor devices. Importantly, the implicit description of the current through the memristor is replaced by an explicit mathematical relationship. The proper reproduction of memristor dynamics, verified by applying the system-theoretic Dynamic Route Map (DRM) graphical analysis tool, applicable to first-order systems, can be observed through the proposed simplified model and enables the time-efficient simulation of large arrays of VCM devices. [ABSTRACT FROM AUTHOR]

Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state volatile memory devices, which, biased through appropriate DC sources, may enter a local activity domain, and, most importantly, the associated stable yet excitable sub-domain, referred to as edge of chaos, which is where the seed of complexity is actually planted, is of great appeal to the neuromorphic engineering community. This paper applies fundamentals from the theory of local activity to an accurate model of a niobium oxide volatile resistance switching memory to derive the conditions necessary to bias the device in the local activity regime. This allows to partition the entire design parameter space into three domains, where the threshold switch is locally passive (LP), locally active but unstable, and both locally active and stable, respectively. The final part of the article is devoted to point out the extent by which the response of the volatile memristor to quasi-static excitations may differ from its dynamics under DC stress. Reporting experimental measurements, which validate the theoretical predictions, this work clearly demonstrates how invaluable is non-linear system theory for the acquirement of a comprehensive picture of the dynamics of highly non-linear devices, which is an essential prerequisite for a conscious and systematic approach to the design of robust neuromorphic electronics. Given that, as recently proved, the potassium and sodium ion channels in biological axon membranes are locally active memristors, the physical realization of novel artificial neural networks, capable to reproduce the functionalities of the human brain more closely than state-of-the-art purely CMOS hardware architectures, should not leave aside the adoption of resistance switching memories, which, under the appropriate provision of energy, are capable to amplify the small signal, such as the niobium dioxide micro-scale device from NaMLab, chosen as object of theoretical and experimental study in this work. [ABSTRACT FROM AUTHOR]

A special subset of two-terminal elements providing pinched hysteresis loops in the voltage-current plane with the lobe area increasing with the frequency is analysed. These devices are identified as non-memristive systems and the sufficient condition for their hysteresis loop to be pinched at the origin is derived. It turns out that the analysed behaviour can be observed only for just one concrete initial state of the device. This knowledge is conclusive for understanding why such devices cannot be regarded as memristors. [ABSTRACT FROM AUTHOR]

The memristor represents the key circuit element for the development of the constitutive blocks of future non-volatile memory architectures and neuromorphic systems. However, resistance switching memories offer a plethora of further opportunities for the electronics of the future. By virtue of the compatibility between the well-established CMOS technology and the fabrication process of most memristors, the exploitation of the peculiar dynamic behaviour of resistance switching memories, which, in general, differ depending upon their material composition, may allow the development of new circuits, which, processing information in unconventional forms, may extend and/or complement the functionalities of state-of-the-art electronic systems. Further, the attractive capability of real-world non-volatile memristors to store and process information in the same physical nanoscale location open the fascinating opportunity to improve the low throughput of Von Neumann computing machines, due to the limited bandwidth of the bus transferring data between the memory and the central processing unit. Finally, the extreme sensitivity of their electrical behaviour to small changes in their initial condition/input and the intrinsic stochastic variability in their switching dynamics may be harnessed to develop innovative bio-signal sensors as well as new cryptographic circuits and systems. The derivation of accurate mathematical models for the electrical behaviour of real-world memristor nano-devices, and their later circuit- and system-theoretic investigation aimed at drawing a comprehensive picture of their peculiar nonlinear dynamic behaviour under the set of inputs and initial conditions expected of the application of interest are fundamental steps towards their conscious future use in integrated circuit design. With this in mind, the present paper adopts a powerful theoretic tool known as Dynamic Route Map to analyse some of the most reliable physics-based models of real-world resistance switching memories to reveal how a particular dynamic phenomenon, known as fading memory, and recently discovered in a tantalum oxide non-volatile memristor device fabricated at Hewlett Packard Labs, is ubiquitous at nanoscale. The physical mechanisms behind the emergence of history-erase effects in non-volatile memristor nano-devices is explained thoroughly for both the DC and the AC periodic excitation scenarios. [ABSTRACT FROM AUTHOR]

We demonstrate the direct biosensing of the Ebola VP40 matrix protein, using a memristor mode of a liquid-integrated nanodevice, based on a large array of honeycomb-shaped silicon nanowires. To shed more light on the principle of biodetection using memristors, we engineered the opening of the current-minima voltage gap V by involving the third gap-control electrode (gate voltage, V) into the system. The primary role of V is to mimic the presence of the charged species of the desired sign at the active area of the sensor. We further showed the advantages of biodetection with an initially opened controlled gap ( V ≠ 0), which allows the detection of the lowest concentrations of the biomolecules carrying arbitrary positive or negative charges; this feature was not present in previous configurations. We compared the bio-memristor performance, in terms of its detection range and sensitivity, to that of the already-known field-effect transistor (FET) mode by operating the same device. To our knowledge, this is the first demonstration of Ebola matrix protein detection using a nanoscaled electrical sensor. [ABSTRACT FROM AUTHOR]

According to the axiomatic definition of the memristor from 1971, its properties are unambiguously determined by the memristance versus charge (or flux) map. The original model of the 'HP memristor' introduces this map via a linear function that represents this memristor as a variable resistor whose resistance is linearly dependent on the amount of charge flowing through. However, some analog applications require nonlinear, frequently exponential or logarithmic dependence of the resistance on an external controlling variable. The memristor with nonlinear memristance versus charge map is analyzed in the paper. The results are specified for the exponential type of this nonlinearity, which may be useful for future applications. Analytic formulae of the area of the pinched hysteresis loop of such a memristor are derived for harmonic excitation. It is also shown that the current flowing through such a memristor, which is driven by a voltage of arbitrary waveform, conforms to the Abel differential equation, and its closed-form solution is found. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Part I has provided theoretical insights on the concept of local fading memory and analyzed a purely mathematical memristor model that, under dc and ac periodic stimuli, experiences memory loss in each of the basins of attraction of two locally stable state-space attractors. This brief designs the first ever real memristor with bistable stationary dc and ac behavior. A rigorous theoretical analysis unveils the key mechanisms behind the emergence of nonunique asymptotic dynamics in this novel electronic circuit, falling into the class of extended memristors. [ABSTRACT FROM PUBLISHER]

It has been recently shown that a current-controlled extended memristor may exhibit bistable steady-state behavior under dc as well as ac periodic stimuli. This brief employs standard techniques from the nonlinear dynamics theory as well as circuit and system theoretic concepts to explain the origin of the asymptotic bistable behavior, which is the signature of a local fading memory capability. Part II derives the first real memristor featuring similar complex dynamics. [ABSTRACT FROM PUBLISHER]

SUMMARY A number of resistive switching memories exhibit activation-based dynamical behavior, which makes them suitable for neuromorphic and programmable analog filtering applications. Because the Boundary Condition Memristor (BCM) model accounts for tunable activation thresholds only at the on and off boundary states, it is not quantitatively accurate in the description of these kinds of memristors and in the investigation of their circuit applications. This paper introduces the Generalized Boundary Condition Memristor (GBCM) model, preserving the features of the BCM model while allowing, further, an ad-hoc tuning of activation-based dynamics, which enables an appropriate modulation of the conditions under which memristors may operate as storage elements or data processors. A simple circuit implementation of the novel model is presented, and time-efficient simulations confirming the improvement in modeling accuracy over the BCM model are shown. As a proof-of-concept for the suitability of the GBCM model in the exploration of the full potential of memristors in neuromorphic circuits and programmable analog filters, this paper adopts it to model fundamental synaptic rules governing the mechanisms of learning in neural systems and to gain some insight into key issues in the design of a couple of filters. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose a whole class of memristor circuits. Each element from the class consists of the cascade connection between a static nonlinear two-port and a dynamic one-port. The class may be divided into two subclasses depending on the input variable (voltage or current). Within each of these subclasses, two further sets of memristor circuits may be distinguished according to which output voltage and current of the two-port represents one of the system states. The simplest memristor circuits make only use of purely passive elementary components from circuit theory, an absolute novelty in this field of research. Thus they are suitable circuit primers for the introduction of the topic of memristors to undergraduate students. A sample circuit is built using discrete devices and its memristive nature is validated experimentally. In case the one-port is purely passive, the proposed circuits feature volatile memristive behavior. Allowing active devices into the dynamic one-port, non-volatile dynamics may also emerge, as proved through concepts from the theory of nonlinear dynamics. Given the generality of the proposed class, the topology of the emulators may be adjusted so as to induce a large variety of dynamical behaviors, which may be exploited to accomplish new signal processing tasks, which conventional circuits are unable to perform. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This work presents a continuous and differentiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in software. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable functions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable approximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal candidates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit simulator. [ABSTRACT FROM AUTHOR]

The peculiar features of the memristor, a fundamental passive two-terminal element characterized by a nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential application, ultra-dense nonvolatile memories, much research has been lately devoted to their use in chaotic neural networks for the emulation of brain activity. In the studies on neuromorphic circuits, it is common to characterize each memristor with a theoretical model based upon a single-valued odd-symmetric charge-flux nonlinearity. Memristive nano-films exhibit different dynamics depending on the way they behave at boundaries. We recently developed a mathematical model, applicable to memristive nano-structures of various nature, offering the opportunity to tune the boundary conditions so as to capture a wide gamut of distinct nonlinear behaviors. However, in general the proposed model exhibits a multivalued charge-flux nonlinearity dependent on input and initial state condition. In this paper, we first derive the necessary and sufficient set of boundary conditions under which single-valuedness is observed in this nonlinearity for any input/state initial condition combination. Then, after proving that, under such boundary conditions, the asymmetrical nonlinearities of memristors with opposite orientation are the odd-symmetric function of the other, we devise a pair of suitable memristor arrangements with odd-symmetric charge-flux characteristics. This analysis is confirmed by showing how a chaotic neural circuit employing one of such arrangements behaves similarly to its counterpart with the theoretically-modeled memristor. [ABSTRACT FROM AUTHOR]

SUMMARY A topologically simple memristive-based oscillatory network showing a wide plethora of dynamical behaviors may be a good candidate for the realization of innovative oscillatory associative and dynamic memories for the recognition of spatial-temporal synchronization states. The design of such pattern recognition systems may not leave aside a preliminary thorough investigation of the nonlinear dynamics of the network and its basic components. In a synchronization scenario with almost-sinusoidal oscillations, each of the memristive elements used in the cells of the network under consideration features an unusual current-voltage behavior. This manuscript models the linear circuitry and the memristive element in each cell so as to capture the observed dynamics and then presents an analytical study explaining the quantitative dependence of memristive current-voltage behavior on excitation amplitude-angular frequency ratio and on initial condition on the system state. This work leads to the first rigorous classification of all possible current-voltage characteristics for a sine-wave voltage-driven memristive element. This analytical study shall pave way towards a better understanding of the complex and still unexplored dynamical properties of this nonlinear device, whose distinct features could improve the capabilities of future-generation pattern recognition systems. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]