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.

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.

Dynamics and synchronization of neural models with memristive membranes under energy coupling

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms.The electrophysiological environment inside and outside of the nerve cell is different.Due to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical features.In this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance.It is found that the memristive neural circuit can present abundant firing patterns without stimulus.The Hamilton energy function is deduced using the Helmholtz theorem.Further,a neuronal network consisting of memristive neurons is proposed by introducing energy coupling.The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

We analyze the energy aspects of single and coupled Hindmarsh–Rose(HR) neuron models with a quadratic flux controlled memristor. The energy function for HR neuron with memristor has been derived and the dynamics have been analyzed in the presence of various external stimuli. We found that the bursting mode of the system changes with external forcing. The negative feedback in Hamilton energy function effectively stabilizes the chaotic trajectories and controls the phase space. The Lyapunov exponents have been plotted to verify the stabilization of trajectories. The energy aspects during the synchronous dynamics of electrically coupled neurons have been analyzed. As the coupling strength increases, the average energy fluctuates and stabilizes at the point of synchronization. When the neurons are coupled via chemical synapse,the average energy variations show three important regimes: a fluctuating regime corresponding to the desynchronized, a stable region indicating synchronized and a linearly increasing regime corresponding to the amplitude death states have been observed. The synchronization transitions are verified by plotting the transverse Lyapunov exponents. The proposed method has a large number of applications in controlling coupled chaotic systems and in analyzing the energy change during various metabolic processes.

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.

An improved memristor model for brain-inspired computing

Memristors, as memristive devices, have received a great deal of interest since being fabricated by HP labs. The forgetting effect that has significant influences on memristors＇ performance has to be taken into account when they are employed. It is significant to build a good model that can express the forgetting effect well for application researches due to its promising prospects in brain-inspired computing. Some models are proposed to represent the forgetting effect but do not work well. In this paper, we present a novel window function, which has good performance in a drift model. We analyze the deficiencies of the previous drift diffusion models for the forgetting effect and propose an improved model. Moreover,the improved model is exploited as a synapse model in spiking neural networks to recognize digit images. Simulation results show that the improved model overcomes the defects of the previous models and can be used as a synapse model in brain-inspired computing due to its synaptic characteristics. The results also indicate that the improved model can express the forgetting effect better when it is employed in spiking neural networks, which means that more appropriate evaluations can be obtained in applications.

Switching mechanism for TiO_2 memristor and quantitative analysis of exponential model parameters

The memristor, as the fourth basic circuit element, has drawn worldwide attention since its physical implementation was released by HP Labs in 2008. However, at the nano-scale, there are many difficulties for memristor physical realization. So a better understanding and analysis of a good model will help us to study the characteristics of a memristor. In this paper, we analyze a possible mechanism for the switching behavior of a memristor with a Pt/TiO2/Pt structure, and explain the changes of electronic barrier at the interface of Pt/TiO2. Then, a quantitative analysis about each parameter in the exponential model of memristor is conducted based on the calculation results. The analysis results are validated by simulation results. The efforts made in this paper will provide researchers with theoretical guidance on choosing appropriate values for(α, β, χ, γ) in this exponential model.

SPICE modeling of memristors with multilevel resistance states

With CMOS technologies approaching the scaling ceiling, novel memory technologies have thrived in recent years, among which the memristor is a rather promising candidate for future resistive memory （RRAM）. Memristor＇s potential to store multiple bits of information as different resistance levels allows its application in multilevel cell （MCL） tech- nology, which can significantly increase the memory capacity. However, most existing memristor models are built for binary or continuous memristance switching. In this paper, we propose the simulation program with integrated circuits emphasis （SPICE） modeling of charge-controlled and flux-controlled memristors with multilevel resistance states based on the memristance versus state map. In our model, the memristance switches abruptly between neighboring resistance states. The proposed model allows users to easily set the number of the resistance levels as parameters, and provides the predictability of resistance switching time if the input current/voltage waveform is given. The functionality of our models has been validated in HSPICE. The models can be used in multilevel RRAM modeling as well as in artificial neural network simulations.

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field,external forcing current,time delay,etc.In this paper,a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed.A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons.Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns,such as spiking firings,bursting firings,and chaotic firings,and enable neurons to generate larger firing amplitudes.The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing.Based on the existing medical treatment background of mental illness,the effects of time lag in the coupling process against neuron firing are studied.The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay,and keep periodic firing under a wide range of external forcing current.

A phenomenological memristor model for synaptic memory and learning behaviors

Properties that are similar to the memory and learning functions in biological systems have been observed and reported in the experimental studies of memristors fabricated by different materials. These properties include the forgetting effect, the transition from short-term memory（STM） to long-term memory（LTM）, learning-experience behavior, etc. The mathematical model of this kind of memristor would be very important for its theoretical analysis and application design.In our analysis of the existing memristor model with these properties, we find that some behaviors of the model are inconsistent with the reported experimental observations. A phenomenological memristor model is proposed for this kind of memristor. The model design is based on the forgetting effect and STM-to-LTM transition since these behaviors are two typical properties of these memristors. Further analyses of this model show that this model can also be used directly or modified to describe other experimentally observed behaviors. Simulations show that the proposed model can give a better description of the reported memory and learning behaviors of this kind of memristor than the existing model.

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.

Continuous non-autonomous memristive Rulkov model with extreme multistability

Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.

A generalized model of TiOx-based memristive devices and its application for image processing

Memristive technology has been widely explored, due to its distinctive properties, such as nonvolatility, high density,versatility, and CMOS compatibility. For memristive devices, a general compact model is highly favorable for the realization of its circuits and applications. In this paper, we propose a novel memristive model of TiOx-based devices, which considers the negative differential resistance（NDR） behavior. This model is physics-oriented and passes Linn＇s criteria. It not only exhibits sufficient accuracy（IV characteristics within 1.5% RMS）, lower latency（below half the VTEAM model）,and preferable generality compared to previous models, but also yields more precise predictions of long-term potentiation/depression（LTP/LTD）. Finally, novel methods based on memristive models are proposed for gray sketching and edge detection applications. These methods avoid complex nonlinear functions required by their original counterparts. When the proposed model is utilized in these methods, they achieve increased contrast ratio and accuracy（for gray sketching and edge detection, respectively） compared to the Simmons model. Our results suggest a memristor-based network is a promising candidate to tackle the existing inefficiencies in traditional image processing methods.

On the Production Testing of Memristor Ratioed Logic (MRL) Gates

This paper focuses on the production testing of Memristor Ratioed Logic (MRL) gates. MRL is a family that uses memristors along with CMOS inverters to design logic gates. Two-input NAND and NOR gates are investigated using the stuck at fault model for the memristors and the five-fault model for the transistors. Test escapes may take place while testing faults in the memristors. Therefore, two solutions are proposed to obtain full coverage for the MRL NAND and NOR gates. The first is to apply scaled input voltages and the second is to change the switching threshold of the CMOS inverter. In addition, it is shown that test speed and order should be taken into consideration. It is proven that three ordered test vectors are needed for full coverage in MRL NAND and NOR gates, which is different from the order required to obtain 100% coverage in the conventional NAND and NOR CMOS designs.

Behavioral Model of Molecular Gap-Type Atomic Switches and Its SPICE Integration

Atomic switches can be used in future nanodevices and to realize conceptually novel electronics in new types of computer architecture because of their simple structure, ease of operation, stability, and reliability. The atomic switch is a single solid-state switch with inherent learning abilities that exhibits various nonlinear behaviors with network devices. However, previous studies focused on experiments and nonvolatile memory applications, and studies on the application of the physical properties of the atomic switch in computing were nonexistent. Therefore, we present a simple behavioral model of a molecular gap-type atomic switch that can be included in a simulator. The model was described by three simple equations that reproduced the bistability using a double-well potential and was able to easily be transferred to a simulator using arbitrary numerical values and be integrated into HSPICE. Simulations using the experimental parameters of the proposed atomic switch agreed with the experimental results. This model will allow circuit designers to explore new architectures, contributing to the development of new computing methods.

分数阶忆阻器模型特性

由于忆阻器具有对电变量的记忆特性,所以在工业领域有着广泛的应用前景。但是,它的机理和特性较为复杂,现今还没有得到广泛认同的数学模型,因而急需为其建立精确的数学模型,从而实现工业应用和商业化。基于忆阻器的数学定义,结合分数阶理论知识,为其建立精确的分数阶数学模型。通过对建立模型的时域和频域的分析,得到忆阻器模型的工作性能和特点:在时域内,电压和电流的旁瓣面积随着数学模型的阶次变化而变化;在频域内,模型的幅值随频率的升高而下降,相位变化相对较小。研究为进一步研究忆阻器的特点夯实了基础。

基于双曲函数的通用型荷控忆阻器电路等效模型分析

目前,忆阻器模拟器的研究主要集中在磁控忆阻器,对荷控忆阻器模拟器的研究不多,双曲函数型的荷控忆阻器模拟器也很少涉及。因此,该文提出一种基于双曲函数的通用型荷控忆阻器模拟器。模拟器通过电压-电流的相互转换电路,实现电路中电压和电流信号之间的相互转换,再通过电路中对应的电路模块对产生的信号进行计算,最终得到通用型双曲荷控忆阻器模型。模拟器能够实现双曲正弦、双曲余弦以及双曲正切函数对应的荷控忆阻器模型。通用型双曲函数荷控忆阻器模拟器对应的等效电路,主要由运算放大器、电阻、电容、三极管等基本元件组成。分析模拟器在不同幅值以及不同频率的输入信号下的伏安特性曲线,得出荷控忆阻器模拟器符合记忆元件的基本特性。该文提出的通用型双曲函数荷控忆阻器模型,对忆阻器模型的发展具有一定的参考意义。

Knowm忆阻混沌电路:建模、分析与实验验证

以往忆阻器及其混沌应用的研究主要集中于模拟忆阻器而展开,对以真实忆阻器构建混沌电路的研究不多.为了给Knowm忆阻器的混沌应用提供依据,在选定Knowm忆阻器模型参数的基础上,基于Knowm忆阻器设计了一类混沌电路,建立该混沌电路的数学模型,分析此电路的平衡点特性,并对系统进行数值仿真和电路实验.结果表明,理论分析结果与电路实验结果一致.研究结果验证了选定的Knowm忆阻器参数的正确性、模型的有效性以及以Knowm忆阻器等构建混沌电路的可行性.

Experimental demonstration of SnO_(2) nanofiber-based memristors and their data-driven modeling for nanoelectronic applications

This paper demonstrated the fabrication,characterization,datadriven modeling,and practical application of a 1D SnO_(2)nanofiber-based memristor,in which a 1D SnO_(2)active layer wassandwiched between silver(Ag)and aluminum(Al)electrodes.Thisdevice yielded a very high ROFF:RON of~104(ION:IOFF of~105)with an excellent activation slope of 10 mV/dec,low set voltage ofVSET~1.14 V and good repeatability.This paper physically explained the conduction mechanism in the layered SnO_(2)nanofiber-basedmemristor.The conductive network was composed of nanofibersthat play a vital role in the memristive action,since more conductive paths could facilitate the hopping of electron carriers.Energyband structures experimentally extracted with the adoption of ultraviolet photoelectron spectroscopy strongly support the claimsreported in this paper.An machine learning(ML)–assisted,datadriven model of the fabricated memristor was also developedemploying different popular algorithms such as polynomialregression,support vector regression,k nearest neighbors,andartificial neural network(ANN)to model the data of the fabricateddevice.We have proposed two types of ANN models(type I andtype II)algorithms,illustrated with a detailed flowchart,to modelthe fabricated memristor.Benchmarking with standard ML techniques shows that the type II ANN algorithm provides the bestmean absolute percentage error of 0.0175 with a 98%R^(2)score.The proposed data-driven model was further validated with the characterization results of similar new memristors fabricated adoptingthe same fabrication recipe,which gave satisfactory predictions.Lastly,the ANN type II model was applied to design and implementsimple AND&OR logic functionalities adopting the fabricatedmemristors with expected,near-ideal characteristics.

新型二阶磁控忆阻器简化模型的设计与验证

忆阻理论的提出极大地推进了混沌系统的发展,丰富了混沌电路的动力学行为。运算放大器因其强大的信号处理能力,成为忆阻器电路模型的重要组成部分。本文基于低功耗差分对构建了一种极简化的运算放大器,该运算放大器将所需晶体管数目减少至2个;以此运算放大器为基础,设计了新型二阶磁控忆阻器的模拟等效电路模型和硬件实验电路。结果表明:激励信号频率增加,斜“8”字形紧磁滞回线的旁瓣面积减小;激励信号幅度增加,斜“8”字形紧磁滞回线的旁瓣面积增加。电路仿真结果与硬件电路实验结果验证了新型磁控忆阻器模型的有效性与设计方法的正确性。