As conventional computers based on von Neumann architecture approach their physical and performance limits, unconventional computing paradigms such as Cellular Neural Networks (CellNNs) have emerged as promising platforms for real-time, massively parallel analog computation. However, conventional analog CellNNs suffer from scalability and power constraints due to large cell hardware overhead. This work investigates the integration of memristor-based crossbar arrays into CellNN architectures to address these limitations by exploiting their analog tunability, high density, and low power operation. A 1-Transistor-1-Memristor (1T1R) crossbar is proposed for implementing the coupling weights defining the CellNN gene. Device nonlinearity, asymmetry and stochastic variability are incorporated using the physics-based JART VCM memristor model, enabling accurate mapping of target weights onto memristor conductances through numerical optimization and differential-pair encoding. Simulations of edge detection tasks confirm high functional accuracy and robustness, while Monte Carlo analysis reveals variability’s impact, underscoring the need for variability-aware design of reliable memristor-CNN hardware.

Memristive devices are promising enablers for computing-in-memory architectures, offering reduced latency and energy consumption compared to conventional designs. Among these, the memristive device-based Cellular Nonlinear Network (M-CNN) provides a compact framework for universal computing, including image processing and neuromorphic computing. In this work, we investigate the use of IGZO-based devices exhibiting gradual switching as core elements of M-CNN cells. A simulation approach based on measured I-V-characteristics is developed to evaluate device–circuit interactions. We first analyze the limitations of the conventional M-CNN cell core, where asymmetric I-V-characteristics restrict voltage levels and accelerate device degradation. To address these issues, we propose a symmetrized cell that mitigates asymmetry, intrinsically limits cell voltage, and supports differential readout. The results demonstrate that gradual switching enables reliable distinction of input current levels while ensuring stable operation and reduced power consumption, thus paving the way for robust IGZO-based M-CNN implementations.

Image encryption is a robust method to secure information transmission over public, unprotected networks. Thanks to their complex dynamics, chaotic systems are gaining interest for encryption scheme development. This paper presents a novel method to generate pseudorandom sequences designing a compact and cost-effective circuit that mimics the dynamics of the logistic map. This hardware platform employs a standard microcontroller to turn the raw chaotic time series into balanced binary sequences, made mutually-orthogonal one to the other through cross-correlation calculations. The resulting binary codes passed all statistical tests in the Institute of Standards and Technology (NIST) SP 800-22 suite, with success rates up to 99.6%. Here, we discuss the integration of the proposed hardware platform into an image encryption system aimed at securing clinical communications. We exploited the unique properties of the chaotic codes to implement a DNA-inspired image encryption algorithm. Robustness was evaluated against four clinical images of skin ulcers, one for each severity class (Wound Bed Preparation standard). An automated data classification procedure confirmed that the encryption and decryption processes do not degrade the diagnostic content of the images. Six security and robustness tests were also passed successfully. We thus present an economic hardware solution, amenable to integration into standard communication platforms, delivering security and enabling novel data protection methods in clinical environments.

In this work, we introduce a high speed and area efficient Cellular Nonlinear Network (CNN) cell, featuring two circuit variants that utilize threshold switches. The threshold switch (TS) model employed represents a current-controlled nanoscale negative differential resistance (NDR) device which exhibits an S-shaped DC I-V curve as a fingerprint. The proposed cell can be considered as the dual of the standard isolated CNN cell where the bistable cell characteristics, originating from the N-shaped voltage-controlled resistor, is implemented through the S-shaped current-controlled TSs. Similarly, the dynamics induced by the parallel capacitor accompanying the nonlinear resistor in the standard cell version are implemented through the internal inductive dynamics of the TSs, resulting in area and speed efficiency. The proposed CNN cell employs a DC voltage source, two bias resistors and 2 TSs, and essentially, features a differential-mode operation which helps to endow it with a symmetric DC I-V characteristic, as is the case for the standard CNN cell. The differential-mode approach further introduces design flexibility as the cell DC I-V characteristic can be adjusted by tuning circuit parameters. We demonstrate the functionality of the proposed cell by implementing image processing tasks ranging from edge detection and thresholding to logic AND and OR operations.

The symmetry-breaking phenomenon, appearing, under suitable conditions, when identical reaction cells, quiet on their own, are let interact via diffusion processes, is dubbedTuring Instability. Its local form exposes the local destabilization, which allows two multistable cells lose stability at one of its locallyasymptotically-stableoperating points. While the globalTuring Instabilityand its mechanisms have been recently explained in (Ascoli et al., 2022), its local form and an experimental demonstration of these complex effects on a physical memristive medium have not been reported yet. This paper investigates a local form ofTuring Instabilityin a two-cell array, when one of the possiblelocally asymptotically-stableandlocally-activestatic solutions loses stability, when let interact with an identical reaction cell via diffusion processes, resulting in the emergence of two different static solutions after transients fade away. In order to study its mechanisms, this paper first introduces a current-controlled Chua Corsage Memristor (CCM), and demonstrates the operating point destabilization in a single current-controlled CCM-based cell. Adding a dissipative resistor and a capacitor to the current-controlled CCM, preliminarily poised on anedge of chaosoperating point, gives birth to two unstable circuits, inducing a local quiescent bi-stability and a local oscillation, respectively. The mechanisms behind a local form ofTuring Instability, appearing in a current-controlled CCM-based two-cell array, have been elucidated, and the bifurcation, spawning symmetry-breaking effects, locally, across the cellular network, has been identified. Both numerical and experimental results confirm the correctness of the theoretical analysis.

We investigate multistability, noise-induced transitions, and stochastic resonance in a second-order nonlinear oscillator incorporating a nonvolatile memristive device. The memristor provides a programmable nonlinear conductance, enabling bistable dynamics with two asymptotically stable equilibrium points separated by a saddle. Under periodic excitation, the system exhibits coexisting limit cycles, period-doubling cascades, boundary crises, and transitions to chaos. Lyapunov exponent analysis reveals repeated crossings of the edge-of-chaos regime, where the largest nonzero exponent approaches zero, marking a balance between stability and sensitivity to perturbations. The effects of additive Gaussian white noise are analyzed by reformulating the dynamics in terms of an effective potential landscape, where noise induces random transitions between coexisting attractors. Transition rates are accurately described in the weak-noise regime by the Eyring–Kramers formula. When periodic forcing and noise act jointly, the system exhibits stochastic resonance, with optimal synchronization occurring when the forcing period matches the mean noise-induced transition time. These results demonstrate that memristor-based nonlinear circuits naturally operate near critical dynamical regimes and provide a compact hardware platform for studying noise-assisted computation and edge-of-chaos dynamics in neuromorphic systems.

The electrical engineering community, interested to develop bio-inspired circuits, approaching the efficiency of the neural networks, is searching passionately for accurate yet simple electronic neurons, or neuristors for short. In recent years, the advent of volatile memristor devices, typically referred to as threshold switches, which admit a negative differential resistance under suitable polarization, similarly as the sodium and potassium ion channels across neuronal axon membranes, has opened up new exciting opportunities in neuromorphic circuit design, enabling innovative analogue electronic cells, capable to reproduce closely the intricate dynamical behaviors of biological neurons without requiring a disproportionate use of resources. The study, presented in this manuscript, achieves an important milestone in this area of research, demonstrating, through a circuit design approach based upon concepts and techniques from Dynamical System Theory, how to leverage the rich dynamics of a threshold switch, capable to boost a periodic sine-wave current signal of infinitesimal amplitude, while acting as a source of local energy, when poised on a suitable bias point, lying along the negative differential resistance branch of the respective S-shaped DC current-voltage characteristic, to induce, one after the other, the three fundamental bifurcations, governing the evolution of an electrical voltage spike from birth to extinction via the All-to-None effect across a biological axon membrane under a reverse sweep in the net synaptic current, according to the fourth-order Hodgkin-Huxley neuron model, in a second-order three-element circuit of unprecedented simplicity, as the current, generated by a DC source, appearing in parallel to a linear capacitor as well as to the volatile locally-active memristor, is subject to a monotonic increase.

This manuscript sheds light into the fundamental importance of the Principles of Local Activity and Edge of Chaos for the future design of innovative circuits, which, employing biomimetic memristive devices, are ideally suited for the development of energy-efficient artificially-intelligent technical systems. The focus of the work is the design of a Second-Order Reactance-Less Oscillator, across which oscillations may develop if and only if at least one of its two different volatile thermally-activated memristor physical realizations is biased along a negative differential resistance branch of the respective DC locus, which turns it into a source of local energy. Very importantly, the proposed cell is first found to lock in the oscillatory mode out of a local Hopf Supercritical Bifurcation when its design parameters are chosen from the Edge of Chaos region, providing clear evidence for the high degree of excitability it acquires as a result.

Neuromorphic circuits using emerging memory technologies have recently gained popularity since they facilitate dense integration with reduced design complexity. In this work, we introduce a simplified modeling approach for the analysis of threshold switch (TS) based neuron circuits where, under given constraints, we represent the TS device as a nonlinear resistor in series with a parasitic inductor. As a result, we define the current of the TS as its state variable. In order to demonstrate the feasibility of the proposed approach, we analyze the conventional Leaky Integrate and Fire (LIF) neuron circuit along with two of its modified variants. We validate the accuracy of the provided analysis and key predictions through numerical simulation results. As a significant contribution, we demonstrate the effectiveness of the proposed method in modifying the nullclines of the TS based LIF neuron and qualitatively align them with the nullclines of a 2ndorder biologically plausible neuron model.

We present a two-cell Tantalum oxide-based Memristor Cellular Neural Network (M-CellNN) capable of performing multiple logic operations (AND, OR, XOR) by changing only the initial states of its memristors. This flexible design leverages the dynamic state-change properties of memristors to adjust logic functions. Our results show that this approach significantly broadens the range of achievable logic tasks within a compact architecture, underscoring the potential of memristive elements for versatile and robust circuit designs. Additionally, we examine the impact of non-idealities in coupling weights and initial conditions on the outputs of the network.

Realized memristors exhibit a unique phenomenon called the fading memory effect, where the memristor response to an AC signal is determined by its characteristics (waveform, amplitude, frequency, and DC offset) rather than the memristor initial conditions. Recently, a method for programming Hewlett Packard’s TaOxmemristor to a target state was proposed, involving configuring the DC offset of a high-frequency square-wave AC voltage input. This served as a basic application example that exploits fading memory in non-volatile memristors, but didn’t consider non-ideal effects. Here, we assess the method applicability in a HfOx-based VCM resistive switch from Forschungszentrum Julich incorporating a variability-aware physics-based model.

We have successfully fabricated one of the earliest array-scale prototypes of a Memristive Cellular Nonlinear Network (M-CNN) with interconnected cells. In this live demonstration, we will showcase the operation of this 4x4 M-CNN array performing an edge detection task according to our previous work [1]. A user-defined input will be applied to the network, and the computing results will be visualized alongside the simulated operation of a standard CNN for comparison.

As demand grows for efficient, localized processing in edge and in-sensor computing, novel architectural approaches are essential to meet low-power, high-density requirements. Memristor Cellular Nonlinear Networks (M-CNNs) offer a promising path forward, leveraging the unique properties of memristors for adaptable and scalable computation. This paper presents a study of novel M-CNN cell configurations designed to enhance computational versatility and address operational challenges in M-CNN-based systems. By leveraging memristor technology within CNN cells, we propose three distinct configurations: (1) incorporating parallel and series resistive elements for refined control over cell dynamics, (2) introducing a fixed bias voltage to expand computational capabilities, and (3) integrating the Full-Range CNN (FR-CNN) model into M-CNNs for the first time. The proposed topologies are evaluated through dynamic route maps (DRM) and vector field analysis to systematically assess stability and performance across varying design parameters.

Chua corsage memristor (CCM) is characterized by its local activity and can be used to construct neuron circuits. Edge of chaos is a subset of the locally active domain, which is responsible for the emergence of complexity and neuromorphic behaviors. When two identical resting “dead” CCM neurons poised on the edge of chaos are coupled through a linear passive resistor, these two neurons can be activated and a couple of oscillations appear. This phenomenon is referred to as the Smale paradox, which has not been observed from hardware circuits. The present paper addresses this issue by proposing the stability criterion of the two-port coupled system using the small-signal analysis method and then derives an emergence condition of the Smale paradox based on two coupled “dead” CCM neurons in terms of the parameter value ranges. Simulation results demonstrate the correctness of the theoretical analysis. Interestingly, anti-phase synchronization is observed after two identical neurons are coupled with a linear resistor, which is different from the traditional in-phase synchronization between resistively coupled oscillators. The resistively coupled memristive neurons are implemented by hardware based on the poor man’s circuit. The experimental results confirm the reproduction of the Smale paradox and reveal the effect of the coupling resistance on the dynamics of the system.

Inspired by recent research reported in [1], this paper investigates the bio-inspired bifurcation patterns of a simple memristive neuron on edge of chaos. The adopted memristive neuron, comprising a DC current source, a current-controlled locally active memristor, and a capacitor, successfully reproduces the bifurcation cascade patterns observed in the Hodgkin-Huxley (H-H) neuron model, including fold limit cycle bifurcation (FLCB), subcritical Hopf bifurcation (SUB-HB), and supercritical Hopf bifurcation (SUP-HB). Through attraction basin analysis and pulse-based initial state regulation, we verify the coexistence phenomenon of stable and unstable limit cycles induced by FLCB, as well as the bistable behaviors triggered by SUB-HB. Furthermore, taking resistively coupled memristive neurons as an example, we explore the influence of the dynamics of individual neurons on the bifurcation patterns of coupled networks, where two neurons have identical parameters but different initial states. The results demonstrate that the three bifurcation modes also emerge in memristive coupled networks, and their evolutionary patterns are closely related to the dynamic behaviors of individual neurons. Finally, hardware experiments successfully reproduce the bifurcation cascade phenomenon thereby validating the correctness of theoretical analysis and simulation results.

The Edge of Chaos Principle lies at the origin of emergent phenomena in physical systems. Recurring to powerful concepts from the theory, establishing its rules, it is possible to identify regions of the parameter space of a system, endowing the latter with a high degree of excitability, which can then manifest itself vividly, as complexity emerges across the respective physical medium upon apparently-harmless changes to the environmental conditions. In this manuscript, the first of a two-paper contribution, the Edge of Chaos Principle is invoked to explain the mechanisms, underlying the development of recently-reported yet-unexplained oscillations across a biological cell, consisting of a voltage-driven sodium ion channel, including leakage effects. Our in-depth investigation of the Local Activity and Edge of Chaos of the biological cell, based upon the rigorous mathematical description, first proposed by Hodgkin and Huxley in 1952, identifies the subcritical Hopf, which emerges across its physical medium as it enters one of its two Edge of Chaos domains, giving birth to the aforementioned oscillations, whose unstable nature is thus revealed. The existence of an unstable limit-cycle attractor in the state space of the Hodgkin-Huxley neuron model is crucially important for the All-to-None dynamical phenomenon, which distinctively characterises the evolution of the membrane capacitance voltage under DC synaptic current sweep. Thus the discovery of the capability of the sodium ion channel to generate unstable oscillations on its own, highlights the fundamental role of this biological memristor in the mechanisms behind emergence and extinction of an Action Potential across a neuronal axon. As the cell, studied in this manuscript, is unable to sustain stable oscillations, the second companion paper shall demonstrate how the insertion of a membrane capacitance across the sodium ion channel, reduced to a first-order system by neglecting the dynamics of the fast activation gate variable, is necessary and sufficient to endow the original biological cell with the capability to undergo also a supercritical Hopf bifurcation, besides the subcritical one, which allows the observation of the entire life cycle of a neuronal spike under DC synaptic current sweep, including, especially, the All-to-None phenomenon spawned out of a fold or saddle-node limit cycle bifurcation.

This paper investigates the essential role of local activity theorem in pancreatic$\beta $-cells in the process of insulin secretion. It is shown that the ion channels in$\beta $-cells distributed over the pancreas are in fact generic memristors from the perspective of electrical circuit theory. Through our comprehensive analyses and extensive simulations from the Chay-Keizer Pancreatic$\beta $-model, Phantom Bursting Model (PBM)-I and PBM-II, this paper rigorously provides an ambient proof that the secretion and release of the insulin in the form of bursting or action potential are possible only when it satisfies the condition of local activity theorem. The local activity principle is analyzed by the small signal admittance function, pole zero diagram, and edge of chaos theorem. It is shown that the external stimulus or cell parameters chosen within the subset of the locally domain regime where the negative real part of the admittance function and the positive real part of the zeros (equivalent to the Eigen values) lead to the generation of complicated electrical signals in pancreatic$\beta $-cells. The examples presented in this paper demonstrate the local activity theorem is a novel and efficient tool for testing whether the secretion of insulin by pancreatic$\beta $-cells are possible or not. It follows from our in-depth analysis that the local activity is essential for the synthesis, secretion, and release of insulin by pancreatic$\beta $-cells. This principle serves as a critical condition, highlighting the intrinsic role of cellular dynamics in insulin regulation and emphasizing its significance in understanding pancreatic function and metabolic health.

In this paper, the design of an isolated Memristor Cellular Nonlinear Network (CNN) cell with discrete electronic elements is presented. The proposed versatile circuit allows for adjustable cell dynamical characteristics, controlled by design parameters, while the discrete element approach enables simple on-board implementation without the need for large-scale integration, which is necessary for testing hardware with individual fabricated memristors. A voltage-mode approach, that makes use of the diversity of operational amplifiers, is preferred here over a current-mode one that necessitates a large number of individual transistors. The dynamical properties of the system are initially investigated through the calculation of equilibrium points and further illustrated applying the concept of State Dynamic Routes (SDRs) for the cell assuming that the memristor dynamics are much slower than the capacitor voltage dynamics. Moreover, the effect of design parameters on the cell dynamics is being investigated, showing how the scaling of the operating voltage, as well as a plethora of CNN variants -i.e., the Chua-Yang and Full Range models-, can be implemented within the same design. Finally, the nonlinear conductance properties of real memristor devices are incorporated into the study, demonstrating interesting bifurcation phenomena between the cell monostability and bistability for specific parameter values.

Biological synapses behave as dynamically-rich nonlinear elements, participating in complicated computing tasks through their adaptation due to external stimuli. Such adaptivity constitutes an intrinsic property of non-volatile memristor devices, which are also able to maintain their internal state, under zero input, enabling novel bio-inspired learning operations. In this work, a synaptic element based on a memristive bridge, containing two resistors and two memristors, is studied, aiming to investigate complex memristor-based topologies that may result in rich synaptic dynamics. The proposed memristive bridge allows the realization of both positive and negative synaptic weights, while an asymmetric tuning of a weight, stemming from memristor's features and bridge topology, is demonstrated. In particular, by properly selecting the memristor's position and polarity within the bridge, different tuning behaviors have been observed, showcasing versatile learning properties of the topology. Along with the synaptic weight tuning, the read overall process of the synaptic weight, necessary for inference operations, is also investigated. We explore the dynamics of the bridge via numerical simulations.

This paper presents an analytical investigation of the transient and steady-state response of non-volatile memristors to high frequency periodic inputs, using as a case study a$\textrm {TaO}_{\textrm {x}}$-based nano-scale memristor model derived at HP Labs. For the first time, we provide a mathematical proof for the fading memory phenomenon in memristors stimulated by periodic inputs in the high frequency limit. Specifically, we demonstrate that the steady-state response of a non-volatile memristor, exhibiting asymmetric switching kinetics with respect to the polarity of the input, depends only on the amplitude of the testing signal and not on the device initial conditions. Based on the results of our analyses, we provide an alternative method for tuning the memristor state by using high-frequency AC inputs, and introduce a new system-theoretic visualization tool, namely the input-referred High-Frequency Dynamic Route Map (HF-DRM), that allows the reproduction of the memristor time-response to any high-frequency periodic input from each admissible initial condition. The purely theoretical results introduced in this paper could inspire new approaches for modulating the memory states of practical non-volatile memristors.

This paper proposes the derivation of a physics-based model of an analog memristive device realized as a bi-layer Al2O3/NB2O5stack. Memristive crossbar arrays implementing matrix-vector multiplications are a central building block of novel computing-in-memory architectures for artificial neural network and neuromorphic computing applications. The presented memristor shows analog, multi-level switching at high resistances without electroforming and is suitable for crossbar operations with low energy consumption. By including a graphical analysis method of the I-V curves obtained in a quasi-static approach, the dynamic behavior is analyzed with regard to ohmic and Poole-Frenkel behavior. Finally, a compact model, represented by an algebraic differential equation, is proposed and verified by fitting calculated solutions to experimental data.

Cellular Nonlinear Networks (CNN) as a powerful paradigm is highly suitable for signal processing of multiple tasks, since they can execute cascaded processing operations in a one-layer array via real-time template updating. Their VLSI implementation by using the conventional CMOS-based integration technology, however, remains a big challenge. The memristive CNN (M-CNN) offers several merits over conventional CNN, such as compactness, nonvolatility, versatility. This paper presents a direct comparison of computing performance between the M-CNN and the conventional CNN for the implementation of a LOGAND operation template using circuit simulation. Our findings show that the M-CNN implementation offers rapid attainment of equilibrium state compared to the CNN implementation. In addition, the result is stored in a non-volatile manner in the M-CNN whereas the CNN only offers a volatile storage.

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.

Diffusion-driven instabilities with pattern formation may occur in a network of identical, regularly-spaced, and resistively-coupled cells if and only if the uncoupled cell is poised on a locally-active and stable operating point in the Edge of Chaos domain. This manuscript presents the simplest ever-reported two-cell neural network, combining together only 7 two-terminal components, namely 2 batteries, 3 resistors, and 2 volatile NbOx memristive threshold switches from NaMLab, and subject to diffusion-driven instabilities with the concurrent emergence of Turing patterns. Very remarkably, this is the first time an homogeneous cellular medium, with no other dynamic element than 2 locally-active memristors, hence the attribute all-memristor coined to address it in this paper, is found to support complex phenomena. The destabilization of the homogeneous solution occurs in this second-order two-cell array if and only if the uncoupled cell circuit parameters are chosen from the Edge of Chaos domain. A deep circuit- and system-theoretic investigation, including linearization analysis and phase portrait investigation, provides a comprehensive picture for the local and global dynamics of the bio-inspired network, revealing how a theory-assisted approach may guide circuit design with inherently non-linear memristive devices.

We present a compact, continuous, and numerically stable version of a tantalum oxide (TaOx) memristor model which can be employed for robust and reliable simulations of large scale memristor based circuits. The original model contains a piecewise differentiable function in the memductance expression and discontinuous step functions in the state equation. Additionally, the original model does not set a proper upper bound for the state variable and may admit blowing up solutions due to an exponential power term, preventing the use of it for numerically reliable simulations. Considering these drawbacks, we modify the original model so as to i) simplify the memductance function while removing its piecewise differentiable nonlinearity, ii) include a proper window function for the ON state dynamics, which is missing in the original model, iii) modify and bound the exponential power term to prevent an uncontrollable blow-up of the solutions, and iv) apply a process called unification, allowing us to remove the step functions inherent in the model, which is a novelty in state-limited memristor models. We validate the accuracy of the proposed model via DC and transient simulations, dynamic route map analysis and a Spice implementation of an anti-series configuration, showing the applicability of the model.

This paper presents the analytical investigation of complex pattern formation in a Memristor Cellular Nonlinear Network (M-CNN) by applying the theory of local activity. The proposed M-CNN has the conventional two dimensional (2D) planar structure, where all the memristive cells are identical and resistively coupled to each other. The single cell is composed of a suitable combination of a DC voltage source, a bias resistor, a locally active NbOx memristor, and a capacitor. The locally active memristor has a simplified generic form, enhancing the simulation speed, and a functional AC equivalent circuit, facilitating further inspections. The stability analysis of the single cell is followed by the extraction of the parameters of the local activity, edge-of-chaos, and sharp-edge-of-chaos domains. Simulation results demonstrate that pattern formation can emerge in a dissipatively coupled M-CNN with locally active memristors.

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 paper presents a circuit-theoretic analysis of a NbO2-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.

The main focus of this paper is the presentation of reliable methods for the determination of the optimum coloring of a graph, commonly known in the literature as vertex coloring problem. It has been shown that networks of capacitively coupled oscillators can be used to solve vertex coloring problems. In this paper we address the negative impact of an unbalanced number of couplings for the oscillators on the performance of the network and compensate for this non-uniform coupling structure by an adjustment in the network itself. The negative effect of the memristor device-to-device variability of the NbOxmemristor on the array functionality will be investigated and reduced via an adaptation of the memristor operating point. The main improvement in network performance is achieved by setting up a control procedure allowing the network to bypass the local solutions and converge to the global one. Two strategies inspired by global optimization algorithms will be proposed to allow the network to overcome sub-optimal solutions, and find the solution corresponding to the absolute minimum of a performance measure function of the vertex coloring problem.

The introduction of memcomputing memristors into the design of Cellular Nonlinear Networks (CNNs) allows to reduce the integrated circuit area typically allocated to each processing element in hardware realizations. Furthermore, the highly nonlinear dynamics of memristors enriches the multivariate signal processing capabilities of these cellular memprocessing structures. This is demonstrated in this paper, where the standard and generalized Dynamic Route Map analysis tools are employed to elucidate the mechanisms by which a Memristor CNN with bistable-like and analog dynamic nonvolatile memristors executes fundamental image processing operations, respectively.

In this paper, we propose a new model for practical, nano-scale, NbO2-based Mott memristors, which is based on a thorough analysis performed on a recently presented physics-based model for these devices. Our investigations revealed that the 3D Poole-Frenkel conduction mechanism adopted in the aforementioned model, can be well-approximated by a transport equation in which: a) memristor current is expressed as a linear function of memristor voltage and b) the device memductance is solely dependent on the device temperature which represents the memristor state. The resulting simplified mathematical form of the original differential algebraic equation set is not only more suitable for simulating large-scale, nano-scale NbO2-based memristor circuits, but is also ideal for circuit-theoretic investigations which may allow an in depth understanding of the peculiar nonlinear behaviors of these devices.

In this paper we propose a new mem-computing image processing architecture, called Memristor Cellular Nonlinear Network, which leverages the unique capability of nonvolatile memristors to compute and store data in the same physical nano-scale locations. Adopting a bistable-like memristor in place for the linear resistor in the standard realization of a cell of the nonlinear dynamic array, the resulting network is capable to process information by exploiting the time evolution of the voltages across the memristors as well as to store/retrieve results into/ from the memristances. This attractive feature, absent in a standard Cellular Nonlinear Network, may pave the way towards the future development of a new generation of visual processors with unprecedented spatial resolution.

In this two-part paper we present an innovative bio-inspired approach to control the lift of a limb of a humanoid robot called Myon from the stable rest state to the unstable upright position. The proposed paradigm outperforms the state-of-the art approach in terms of time- and energy-efficiency, while maintaining a good degree of adaptability to changes to the nominal operating conditions. This Part I paper introduces the theory behind the novel three-phase control strategy, while the companion Part II manuscript derives its circuit implementation, and analyses its performance to validate the theoretic findings. The critical steps in the proposed strategy are the determination of an estimate for the time duration of the first phase, the storage of the result of this computation over the time interval between two consecutive applications of the control action, and the adaptation of this calculation to changes to the nominal operating conditions. All these three tasks may be successfully accomplished by leveraging the computing, memory, and learning capabilities of a single non-volatile memristor.

The standard Go-Against-the-Force strategy to lift a limb of a humanoid robot from the stable rest state to the upright position and to maintain it there afterwards is slow and consumes a significant amount of energy due to the iterative cycle of sensing and driving operations its application consists of. In order to enhance the performance of the control action, the Part I paper introduced the theory behind an innovative three-phase strategy, called Kick-Fly-Catch paradigm, which is expected to lead to a faster limb motion under a lower energy cost as compared to the original approach. The combined ability of a non-volatile memristor to process data according to Ohm's law, store computation results at power off, and adapt its dynamic behaviour on the basis of its state equation is at the origin for the performance benefits of the proposed strategy over the standard approach. This Part II paper designs a circuit implementation for the overall dynamic system under the new control strategy, and validates the theoretic predictions of the Part I manuscript.

Developing highly accurate and predictive models of redox-based memristive devices is highly important to enable future memory and logic design. As the switching mechanism is not known in all details yet, accurate device modeling is quite challenging. Here, we introduce six evaluation criteria for modeling filamentary switching devices based on the valence change mechanism, which is a subclass of redox-based memristive devices. The criteria include the plausibility of the simulated I-V and I-t characteristics, the nonlinearity of the switching kinetics, the feasibility of predicting complementary resistive switching correctly, the possibility of programming different resistance states, the state-dependence of the resistive switching, and the occurrence of a fading memory behavior. Four different models that have been proposed in literature are analyzed with respect to these criteria. These models are Kvatinsky's VTEAM model, the Stanford RRAM model, Strachan's TaOx memristor model and a nonlinear physics-based model proposed by our group.

This paper proposes a novel BiFeO3memristor-based electronic circuit for the encryption of sensitive medical data. The hardware cryptographic system is tested through the use of neural signals from a patient experiencing a number of focal epileptic seizures. The Cellular Nonlinear Network theoretical framework provides a basis for sophisticated neural signal processing techniques capable to anticipate the emergence of an epileptic seizure in many cases. The application of these techniques to original data successfully reveals changes before the onset of each epileptic seizure. This information may not be extracted from the encoded data, validating the proper functioning of the memristor-based encryption.

Recently a circuit-theoretical work showed that a purely mathematical memristor model may exhibit two distinct stable DC characteristics, as well as two distinct stable pinched hysteresis loops emerging under the same AC periodic excitation by simply changing the memristor initial state. This work presents the first ever real memristor which exhibits such a peculiar bistable behaviour, thus giving a strong practical evidence for the latest theoretical developments in memristor circuit theory.

A class of memristor circuits is obtained by cascading a static nonlinear two-port with a dynamical one-port. The terminals of the input port of the static nonlinearity represent the access nodes for each memristor in the class. The class may be splitted into two sub-classes, namely the current- and voltagecontrolled memristors. Two further sets of memristors may be identied within each of such sub-classes, particularly the current- and voltage state memristors. The simplest memristor circuits from the proposed class employ solely passive two-terminal elements from circuit theory. This represents an absolute novelty in the panorama of memristor emulators. The passive elements from the class are volatile memories. However, non-volatile memory behaviour may arise in case the dynamical one-port contains active elements. The versatile nature of the circuit topologies of the proposed memristors allows the emergence of a wide variety of complex dynamical behaviours, which may enable the accomplishment of novel signal processing tasks or lead to improvements in the performance of conventional circuits.

In this paper1a stability analysis sheds light into aspects of memristor circuit design, revealing a circuit theoretic technique for the stabilization of the NDR portion of the device DC characteristic. This type of studies supports the work of designers exploring memristor potential in electronics. Concepts from nonlinear dynamics theory allow us to gain a deep understanding of the dynamics of our locally-active memristor. The analysis provides hints on how to design an oscillator where limit-cycle behavior emerges from the locally-active threshold switching of the memristor, as theoretically proved here.

Besides being at the core of novel ultra-high density low-power non-volatile memories and innovative pattern recognition systems based upon oscillatory associative and dynamic memories, the nano-scale memristor also has the potential to reproduce the behavior of a biological synapse more efficiently and accurately than any conventional electronic emulator. As in a living being the weight of a synapse is adapted by the ionic flow through it, so the conductance of a memristor is adjusted by the flux across it. This article is organized according to the regulations of the ISCAS2014 special session on the state-of-the-art in memristor-based nonlinear circuits and architectures. In this work we focus on arrays of oscillatory cells locally coupled through memristors. Our investigations shows how the nonlinear dynamics of the memristor plays a key role in the mechanisms underlying the synchronization properties of the networks. This work provides new insights into the nonlinear behavior of the still largely unexplored memristor element, which promises to revolutionize integrated circuit design in the incoming years.

This paper proposes a simple PSpice implementation of the boundary condition model for memristor nano-structures. The boundary condition model is equivalent to the linear drift model except for the introduction of adaptable boundary conditions, which impose an activation threshold of the state dynamics at the boundaries, i.e. once the state gets clipped at one of the boundaries, it may not be released from it unless the input reverses its sign and gets larger than a certain activation threshold in magnitude. Thanks to the adaptability of the boundary behavior, the boundary condition model is able to describe a variety of physical nano-scale systems, where mem-ristor dynamics arise from distinct physical mechanisms. The proposed PSpice emulator may be used for the investigation of potential applications of memristive systems in integrated circuit design, especially for the development of non-volatile memories and neuromorphic platforms. The accuracy of the PSpice circuit model is validated through comparison with experimental results relative to the Hewlett-Packard memristor.

Biological neural systems use self- reconfigurable and self-learning primitive elements (synapses) to extract relevant information from complex and noisy environments, to detect specific spatio-temporal patterns in the data of interest and to compute and simultaneously store some significant features. All these desirable attributes may be realized by using two-terminal elements, memristors (memory resistors), which most closely resemble biological synapses. This article is organized according to the rule of the ISCAS2013 special session having the same title. We present a short summary of the state-of-the-art of memristor theory and Hodgkin-Huxley neural model. In addition, we briefly introduce a comprehensive nonlinear circuit-theoretic foundation for a novel circuit implementation of the Hodgkin-Huxley neural model with memristors.

Chaotic neural networks are able to reproduce chaotic dynamics observable in the brain of various living beings. As a result, study of the dynamical properties of such networks may pave the way towards a better understanding of the memory rules of the brain. In this paper a simple neural circuit employing a theoretical memristive synapse with symmetric charge-flux nonlinearity is found to behave chaotically. After presentation of a novel boundary-condition based model for real memristor nano-structures, conditions under which a suitable arrangement of such nano-structures is dynamically equivalent to the theoretical memristor are derived and validated.

This work presents a novel, simple, accurate and general model capturing the nonlinear dynamics of memristive nano-scale structures including the thin double-layer oxide film manufactured at Hewlett-Packard Labs in 2008. Advantages over other models include ease of analytical integration, existence of closed-form solutions under any input/initial condition combination and opportunity to tune boundary conditions so as to detect either single-valued or multi-valued state-flux characteristics under sign-varying input.

The design of pattern recognition systems based on memristive oscillatory networks need to include a detailed study of the dynamics of the networks and their basic components. A simple two-cell network of this kind, where each cell is made up of a linear circuitry in parallel with a nonlinear memristive element, was found to experience a rich gamut of nonlinear behaviors. In particular, for a synchronization scenario with almost-sinusoidal oscillations, the memristive elements used in the cells exhibited an unusual current-voltage characteristic. This work focuses on the dynamics of the single cell under this synchronization scenario, and, modeling the linear circuitry with a sinusoidal voltage source, analytically derives a rigorous classification of all possible current-voltage characteristics of the periodically-driven memristive element on the basis of amplitude-angular frequency ratio and time hystory of the input source.

Besides being at the basis of next-generation ultra-dense non-volatile memories, a nanoscale memristor also has the potential to reproduce the behavior of a biological synapse. As in a living creature the weight of a synapse is adapted by the ionic flow through it, so the conductance of a memristor is adjusted by the flux across or the charge through it depending on its controlling source. In this manuscript we consider two Hindmarsh-Rose neurons, coupled via a memristive device mimicking a biological synapse. We investigate how the dynamics of the memristive element may influence the syncronization properties of the network.

Floating-capacitor implementations of differential-output log-domain circuits exhibit externally nonlinear behavior. However, the cause of these dynamics may differ from case to case. In a floating-capacitor class AB log-domain parallel resonator it was the finite forward-current gain of a pair of cross-coupled transistors that played a crucial role in the emergence of the nonlinearities. On the other hand, it was recently proved that in floating-capacitor log-domain LC-ladders the BJT parasitic capacitances considerably affect the dynamics and must be taken into account for modeling purposes, no matter how small they are with respect to the floating capacitors. This work proves that, as was the case for the parallel resonator, the base currents of a number of transistors are responsible for the nonlinear dynamics of a class AB log-domain exponential state-space filter. This is achieved by presenting and validating the simplest mathematical model able to capture the nonlinear behavior of the circuit in both the autonomous and non-autonomous cases