Threshold flux-controlled memristor model and its equivalent circuit implementation

Modeling a memristor is an effective way to explore the memristor properties due to the fact that the memristor devices are still not commercially available for common researchers. In this paper, a physical memristive device is assumed to exist whose ionic drift direction is perpendicular to the direction of the applied voltage, upon which, corresponding to the HP charge-controlled memristor model, a novel threshold flux-controlled memristor model with a window function is proposed. The fingerprints of the proposed model are analyzed. Especially, a practical equivalent circuit of the proposed model is realized, from which the corresponding experimental fingerprints are captured. The equivalent circuit of the threshold memristor model is appropriate for various memristors based breadboard experiments.

Exponential flux-controlled memristor model and its floating emulator

As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the mernristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance （memristance） will keep monotonically increasing or decreasing unless the voltage＇s polarity reverses （if not approach the boundaries）, is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor （especially the demand for a larger current）. The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator.

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other.The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity.In this paper,a memristor is used to simulate a synapse,a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored.We explore the influence of system parameters on the dynamical behaviors of the discrete small-world network,and the system shows a variety of firing patterns such as spiking firing and triangular burst firing when the neuronal parameterαis changed.The results of a numerical simulation based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network,and the higher the reconnection probability and number of the nearest neurons,the more significant the synchronization state of the neurons.In addition,by increasing the coupling strength of memristor synapses,synchronization performance is promoted.The results of this paper can boost research into complex neuronal networks coupled with memristor synapses and further promote the development of neuroscience.

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Research on discrete memristor-based neural networks has received much attention.However,current research mainly focuses on memristor–based discrete homogeneous neuron networks,while memristor-coupled discrete heterogeneous neuron networks are rarely reported.In this study,a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V–I diagram.Based on two-dimensional(2D)discrete Izhikevich neuron and 2D discrete Chialvo neuron,a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons.Considering the coupling strength as the control parameter,chaotic firing,periodic firing,and hyperchaotic firing patterns are revealed.In particular,multiple coexisting firing patterns are observed,which are induced by different initial values of the memristor.Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength.Furthermore,the effect of Gaussian white noise on synchronization behaviors is also explored.We demonstrate that the presence of noise not only leads to the transition of firing patterns,but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

Neuromorphic circuits based on memristors: endowing robots with a human-like brain

Robots are widely used,providing significant convenience in daily life and production.With the rapid development of artificial intelligence and neuromorphic computing in recent years,the realization of more intelligent robots through a pro-found intersection of neuroscience and robotics has received much attention.Neuromorphic circuits based on memristors used to construct hardware neural networks have proved to be a promising solution of shattering traditional control limita-tions in the field of robot control,showcasing characteristics that enhance robot intelligence,speed,and energy efficiency.Start-ing with introducing the working mechanism of memristors and peripheral circuit design,this review gives a comprehensive analysis on the biomimetic information processing and biomimetic driving operations achieved through the utilization of neuro-morphic circuits in brain-like control.Four hardware neural network approaches,including digital-analog hybrid circuit design,novel device structure design,multi-regulation mechanism,and crossbar array,are summarized,which can well simulate the motor decision-making mechanism,multi-information integration and parallel control of brain at the hardware level.It will be definitely conductive to promote the application of memristor-based neuromorphic circuits in areas such as intelligent robotics,artificial intelligence,and neural computing.Finally,a conclusion and future prospects are discussed.

Application of artificial synapse based on all-inorganic perovskite memristor in neuromorphic computing

Artificial synapse inspired by the biological brain has great potential in the field of neuromorphic computing and artificial intelligence.The memristor is an ideal artificial synaptic device with fast operation and good tolerance.Here,we have prepared a memristor device with Au/CsPbBr_(3)/ITO structure.The memristor device exhibits resistance switching behavior,the high and low resistance states no obvious decline after 400 switching times.The memristor device is stimulated by voltage pulses to simulate biological synaptic plasticity,such as long-term potentiation,long-term depression,pair-pulse facilitation,short-term depression,and short-term potentiation.The transformation from short-term memory to long-term memory is achieved by changing the stimulation frequency.In addition,a convolutional neural network was constructed to train/recognize MNIST handwritten data sets;a distinguished recognition accuracy of~96.7%on the digital image was obtained in 100 epochs,which is more accurate than other memristor-based neural networks.These results show that the memristor device based on CsPbBr3 has immense potential in the neuromorphic computing system.

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Synaptic crosstalk is a prevalent phenomenon among neuronal synapses,playing a crucial role in the transmission of neural signals.Therefore,considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks are highly necessary.In this paper,we propose a heterogeneous discrete neural network(HDNN)consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron.These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered.The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents.It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths.Furthermore,the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated,revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

Recent Advances in In-Memory Computing:Exploring Memristor and Memtransistor Arrays with 2D Materials

The conventional computing architecture faces substantial chal-lenges,including high latency and energy consumption between memory and processing units.In response,in-memory computing has emerged as a promising alternative architecture,enabling computing operations within memory arrays to overcome these limitations.Memristive devices have gained significant attention as key components for in-memory computing due to their high-density arrays,rapid response times,and ability to emulate biological synapses.Among these devices,two-dimensional(2D)material-based memristor and memtransistor arrays have emerged as particularly promising candidates for next-generation in-memory computing,thanks to their exceptional performance driven by the unique properties of 2D materials,such as layered structures,mechanical flexibility,and the capability to form heterojunctions.This review delves into the state-of-the-art research on 2D material-based memristive arrays,encompassing critical aspects such as material selection,device perfor-mance metrics,array structures,and potential applications.Furthermore,it provides a comprehensive overview of the current challenges and limitations associated with these arrays,along with potential solutions.The primary objective of this review is to serve as a significant milestone in realizing next-generation in-memory computing utilizing 2D materials and bridge the gap from single-device characterization to array-level and system-level implementations of neuromorphic computing,leveraging the potential of 2D material-based memristive devices.

Advances in memristor based artificial neuron fabrication-materials,models,and applications

Spiking neural network(SNN),widely known as the third-generation neural network,has been frequently investigated due to its excellent spatiotemporal information processing capability,high biological plausibility,and low energy consumption characteristics.Analogous to the working mechanism of human brain,the SNN system transmits information through the spiking action of neurons.Therefore,artificial neurons are critical building blocks for constructing SNN in hardware.Memristors are drawing growing attention due to low consumption,high speed,and nonlinearity characteristics,which are recently introduced to mimic the functions of biological neurons.Researchers have proposed multifarious memristive materials including organic materials,inorganic materials,or even two-dimensional materials.Taking advantage of the unique electrical behavior of these materials,several neuron models are successfully implemented,such as Hodgkin–Huxley model,leaky integrate-and-fire model and integrate-and-fire model.In this review,the recent reports of artificial neurons based on memristive devices are discussed.In addition,we highlight the models and applications through combining artificial neuronal devices with sensors or other electronic devices.Finally,the future challenges and outlooks of memristor-based artificial neurons are discussed,and the development of hardware implementation of brain-like intelligence system based on SNN is also prospected.

One memristor–one electrolyte-gated transistor-based high energy-efficient dropout neuronal units

Artificial neural networks(ANN) have been extensively researched due to their significant energy-saving benefits.Hardware implementations of ANN with dropout function would be able to avoid the overfitting problem. This letter reports a dropout neuronal unit(1R1T-DNU) based on one memristor–one electrolyte-gated transistor with an ultralow energy consumption of 25 p J/spike. A dropout neural network is constructed based on such a device and has been verified by MNIST dataset, demonstrating high recognition accuracies(> 90%) within a large range of dropout probabilities up to40%. The running time can be reduced by increasing dropout probability without a significant loss in accuracy. Our results indicate the great potential of introducing such 1R1T-DNUs in full-hardware neural networks to enhance energy efficiency and to solve the overfitting problem.

Electrochemical anodic oxidation assisted fabrication of memristors

Owing to the advantages of simple structure,low power consumption and high-density integration,memristors or memristive devices are attracting increasing attention in the fields such as next generation non-volatile memories,neuromorphic computation and data encryption.However,the deposition of memristive films often requires expensive equipment,strict vacuum conditions,high energy consumption,and extended processing times.In contrast,electrochemical anodizing can produce metal oxide films quickly(e.g.10 s) under ambient conditions.By means of the anodizing technique,oxide films,oxide nanotubes,nanowires and nanodots can be fabricated to prepare memristors.Oxide film thickness,nanostructures,defect concentrations,etc,can be varied to regulate device performances by adjusting oxidation parameters such as voltage,current and time.Thus memristors fabricated by the anodic oxidation technique can achieve high device consistency,low variation,and ultrahigh yield rate.This article provides a comprehensive review of the research progress in the field of anodic oxidation assisted fabrication of memristors.Firstly,the principle of anodic oxidation is introduced;then,different types of memristors produced by anodic oxidation and their applications are presented;finally,features and challenges of anodic oxidation for memristor production are elaborated.

Tailoring Classical Conditioning Behavior in TiO_(2) Nanowires:ZnO QDs-Based Optoelectronic Memristors for Neuromorphic Hardware

Neuromorphic hardware equipped with associative learn-ing capabilities presents fascinating applications in the next generation of artificial intelligence.However,research into synaptic devices exhibiting complex associative learning behaviors is still nascent.Here,an optoelec-tronic memristor based on Ag/TiO_(2) Nanowires:ZnO Quantum dots/FTO was proposed and constructed to emulate the biological associative learning behaviors.Effective implementation of synaptic behaviors,including long and short-term plasticity,and learning-forgetting-relearning behaviors,were achieved in the device through the application of light and electrical stimuli.Leveraging the optoelectronic co-modulated characteristics,a simulation of neuromorphic computing was conducted,resulting in a handwriting digit recognition accuracy of 88.9%.Furthermore,a 3×7 memristor array was constructed,confirming its application in artificial visual memory.Most importantly,complex biological associative learning behaviors were emulated by mapping the light and electrical stimuli into conditioned and unconditioned stimuli,respectively.After training through associative pairs,reflexes could be triggered solely using light stimuli.Comprehen-sively,under specific optoelectronic signal applications,the four features of classical conditioning,namely acquisition,extinction,recovery,and generalization,were elegantly emulated.This work provides an optoelectronic memristor with associative behavior capabilities,offering a pathway for advancing brain-machine interfaces,autonomous robots,and machine self-learning in the future.

The voltage-current relationship and equivalent circuit implementation of parallel flux-controlled memristive circuits

A flux-controlled memristor characterized by smooth cubic nonlinearity is taken as an example, upon which the voltage-current relationships （VCRs） between two parallel memristive circuits - a parallel memristor and capacitor circuit （the parallel MC circuit）, and a parallel memristor and inductor circuit （the parallel ML circuit） - are investigated. The results indicate that the VCR between these two parallel memristive circuits is closely related to the circuit parameters, and the frequency and amplitude of the sinusoidal voltage stimulus. An equivalent circuit model of the memristor is built, upon which the circuit simulations and exper/mental measurements of both the parallel MC circuit and the parallel ML circuit are performed, and the results verify the theoretical analysis results.

Volatile threshold switching memristor:An emerging enabler in the AIoT era

With rapid advancement and deep integration of artificial intelligence and the internet-of-things,artificial intelligence of things has emerged as a promising technology changing people’s daily life.Massive growth of data generated from the devices challenges the AIoT systems from information collection,storage,processing and communication.In the review,we introduce volatile threshold switching memristors,which can be roughly classified into three types:metallic conductive filament-based TS devices,amorphous chalcogenide-based ovonic threshold switching devices,and metal-insulator transition based TS devices.They play important roles in high-density storage,energy efficient computing and hardware security for AIoT systems.Firstly,a brief introduction is exhibited to describe the categories(materials and characteristics)of volatile TS devices.And then,switching mechanisms of the three types of TS devices are discussed and systematically summarized.After that,attention is focused on the applications in 3D cross-point memory technology with high storage-density,efficient neuromorphic computing,hardware security(true random number generators and physical unclonable functions),and others(steep subthreshold slope transistor,logic devices,etc.).Finally,the major challenges and future outlook of volatile threshold switching memristors are presented.

Design of multilayer cellular neural network based on memristor crossbar and its application to edge detection

Memristor with memory properties can be applied to connection points(synapses)between cells in a cellular neural network(CNN).This paper highlights memristor crossbar-based multilayer CNN(MCM-CNN)and its application to edge detection.An MCM-CNN is designed by adopting a memristor crossbar composed of a pair of memristors.MCM-CNN based on the memristor crossbar with changeable weight is suitable for edge detection of a binary image and a color image considering its characteristics of programmablization and compactation.Figure of merit(FOM)is introduced to evaluate the proposed structure and several traditional edge detection operators for edge detection results.Experiment results show that the FOM of MCM-CNN is three times more than that of the traditional edge detection operators.

High-performance artificial neurons based on Ag/MXene/GST/Pt threshold switching memristors

Threshold switching(TS) memristors can be used as artificial neurons in neuromorphic systems due to their continuous conductance modulation, scalable and energy-efficient properties. In this paper, we propose a low power artificial neuron based on the Ag/MXene/GST/Pt device with excellent TS characteristics, including a low set voltage(0.38 V)and current(200 nA), an extremely steep slope(< 0.1 m V/dec), and a relatively large off/on ratio(> 10^(3)). Besides, the characteristics of integrate and fire neurons that are indispensable for spiking neural networks have been experimentally demonstrated. Finally, its memristive mechanism is interpreted through the first-principles calculation depending on the electrochemical metallization effect.

Firing activities in a fractional-order Hindmarsh–Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh–Rose(HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval(ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic(A-periodic)bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.

Memristor’s characteristics: From non-ideal to ideal

Memristor has been widely studied in the field of neuromorphic computing and is considered to be a strong candidate to break the von Neumann bottleneck. However, the non-ideal characteristics of memristor seriously limit its practical application. There are two sides to everything, and memristors are no exception. The non-ideal characteristics of memristors may become ideal in some applications. Genetic algorithm(GA) is a method to search for the optimal solution by simulating the process of biological evolution. It is widely used in the fields of machine learning, combinatorial optimization,and signal processing. In this paper, we simulate the biological evolutionary behavior in GA by using the non-ideal characteristics of memristors, based on which we design peripheral circuits and path planning algorithms based on memristor networks. The experimental results show that the non-ideal characteristics of memristor can well simulate the biological evolution behavior in GA.

Exploration and mitigation of protrusion behavior in Ga-ion doped h-BN memristors

Using hexagonal boron nitride(h-BN)to prepare resistive switching devices is a promising strategy.Various doping methods have aroused great interest in the semiconductor field in recent years,but many researchers have overlooked the various repetitive anomalies that occur during the testing process.In this study,the basic electrical properties and additive protrusion behavior of Ga-ion-doped h-BN memristors at micro–nanoscale during the voltage scanning process are investigated via atomic force microscopy(AFM)and energy dispersive spectroscopy.The additive protrusion behavior is subjected to exploratory research,and it is concluded that it is caused by anodic oxidation.An approach is proposed that involves filling the AFM chamber with nitrogen gas to improve the stability of memristor testing,and this method provides a solution for enhanced testing stability of memristors.

Threshold-type memristor-based crossbar array design and its application in handwritten digit recognition

Neuromorphic computing simulates the operation of biological brain function for information processing and can potentially solve the bottleneck of the Von Neumann architecture.Inspired by the real characteristics of physical memristive devices,we propose a threshold-type nonlinear voltage-controlled memristor mathematical model which is used to design a novel memristor-based crossbar array.The presented crossbar array can simulate the synaptic weight in real number field rather than only positive number field.Theoretical analysis and simulation results of a 2×2 image inversion operation validate the feasibility of the proposed crossbar array and the necessary training and inference functions.Finally,the presented crossbar array is used to construct the neural network and then applied in the handwritten digit recognition.The Mixed National Institute of Standards and Technology(MNIST)database is adopted to train this neural network and it achieves a satisfactory accuracy.