Memristance controlling approach based on modification of linear M–q curve

The memristor has broad application prospects in many fields, while in many cases, those fields require accurate impedance control. The nonlinear model is of great importance for realizing memristance control accurately, but the im- plementing complexity caused by iteration has limited the actual application of this model. Considering the approximate linear characteristics at the middle region of the memristance-charge （M-q） curve of the nonlinear model, this paper pro- poses a memristance controlling approach, which is achieved by linearizing the middle region of the M-q curve of the nonlinear memristor, and establishes the linear relationship between memristances M and input excitations so that it can realize impedance control precisely by only adjusting input signals briefly. First, it analyzes the feasibility for linearizing the middle part of the M-q curve of the memristor with a nonlinear model from the qualitative perspective. Then, the lin- earization equations of the middle region of the M-q curve is constructed by using the shift method, and under a sinusoidal excitation case, the analytical relation between the memristance M and the charge time t is derived through the Taylor series expansions. At last, the performance of the proposed approach is demonstrated, including the linearizing capability for the middle part of the M-q curve of the nonlinear model memristor, the controlling ability for memristance M, and the influence of input excitation on linearization errors.

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.

Memristive feature and mechanism induced by laser-doping in defect-free 2D semiconductor materials

Memristors as non-volatile memory devices have gained numerous attentions owing to their advantages in storage,in-memory computing, synaptic applications, etc. In recent years, two-dimensional(2D) materials with moderate defects have been discovered to exist memristive feature. However, it is very difficult to obtain moderate defect degree in 2D materials, and studied on modulation means and mechanism becomes urgent and essential. In this work, we realized memristive feature with a bipolar switching and a configurable on/off ratio in a two-terminal MoS_(2) device(on/off ratio ~100), for the first time, from absent to present using laser-modulation to few-layer defect-free MoS_(2)(about 10 layers), and its retention time in both high resistance state and low resistance state can reach 2×10^(4) s. The mechanism of the laser-induced memristive feature has been cleared by dynamic Monte Carlo simulations and first-principles calculations. Furthermore, we verified the universality of the laser-modulation by investigating other 2D materials of TMDs. Our work will open a route to modulate and optimize the performance of 2D semiconductor memristive devices.

Optimal and Memristor-Based Control of A Nonlinear Fractional Tumor-Immune Model

In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.

Memristive network-based genetic algorithm and its application to image edge detection

This paper proposes a mem-computing model of memristive network-based genetic algorithm(MNGA)by building up the relationship between the memristive network(MN)and the genetic algorithm(GA),and a new edge detection algorithm where image pixels are defined as individuals of population.First,the computing model of MNGA is designed to perform mem-computing,which brings new possibility of the hardware implementation of GA.Secondly,MNGA-based edge detection integrating image filter and GA operator deployed by MN is proposed.Finally,simulation results demonstrate that the figure of merit(FoM)of our model is better than the latest memristor-based swarm intelligence.In summary,a new way is found to build proper matching of memristor to GA and aid image edge detection.

A novel color image encryption algorithm based on genetic recombination and the four-dimensional memristive hyperchaotic system

Recently, many image encryption algorithms based on chaos have been proposed. Most of the previous algorithms encrypt components R, G, and B of color images independently and neglect the high correlation between them. In the paper, a novel color image encryption algorithm is introduced. The 24 bit planes of components R, G, and B of the color plain image are obtained and recombined into 4 compound bit planes, and this can make the three components affect each other. A four-dimensional(4D) memristive hyperchaotic system generates the pseudorandom key streams and its initial values come from the SHA 256 hash value of the color plain image. The compound bit planes and key streams are confused according to the principles of genetic recombination, then confusion and diffusion as a union are applied to the bit planes,and the color cipher image is obtained. Experimental results and security analyses demonstrate that the proposed algorithm is secure and effective so that it may be adopted for secure communication.

A spintronic memristive circuit on the optimized RBF-MLP neural network

A radial basis function network(RBF)has excellent generalization ability and approximation accuracy when its parameters are set appropriately.However,when relying only on traditional methods,it is difficult to obtain optimal network parameters and construct a stable model as well.In view of this,a novel radial basis neural network(RBF-MLP)is proposed in this article.By connecting two networks to work cooperatively,the RBF’s parameters can be adjusted adaptively by the structure of the multi-layer perceptron(MLP)to realize the effect of the backpropagation updating error.Furthermore,a genetic algorithm is used to optimize the network’s hidden layer to confirm the optimal neurons(basis function)number automatically.In addition,a memristive circuit model is proposed to realize the neural network’s operation based on the characteristics of spin memristors.It is verified that the network can adaptively construct a network model with outstanding robustness and can stably achieve 98.33%accuracy in the processing of the Modified National Institute of Standards and Technology(MNIST)dataset classification task.The experimental results show that the method has considerable application value.

Memristor-based vector neural network architecture

Vector neural network(VNN)is one of the most important methods to process interval data.However,the VNN,which contains a great number of multiply-accumulate(MAC)operations,often adopts pure numerical calculation method,and thus is difficult to be miniaturized for the embedded applications.In this paper,we propose a memristor based vector-type backpropagation(MVTBP)architecture which utilizes memristive arrays to accelerate the MAC operations of interval data.Owing to the unique brain-like synaptic characteristics of memristive devices,e.g.,small size,low power consumption,and high integration density,the proposed architecture can be implemented with low area and power consumption cost and easily applied to embedded systems.The simulation results indicate that the proposed architecture has better identification performance and noise tolerance.When the device precision is 6 bits and the error deviation level(EDL)is 20%,the proposed architecture can achieve an identification rate,which is about 92%higher than that for interval-value testing sample and 81%higher than that for scalar-value testing sample.

Low-power emerging memristive designs towards secure hardware systems for applications in internet of things

Emerging memristive devices offer enormous advantages for applications such as non-volatile memories and inmemory computing(IMC),but there is a rising interest in using memristive technologies for security applications in the era of internet of things(IoT).In this review article,for achieving secure hardware systems in IoT,lowpower design techniques based on emerging memristive technology for hardware security primitives/systems are presented.By reviewing the state-of-the-art in three highlighted memristive application areas,i.e.memristive non-volatile memory,memristive reconfigurable logic computing and memristive artificial intelligent computing,their application-level impacts on the novel implementations of secret key generation,crypto functions and machine learning attacks are explored,respectively.For the low-power security applications in IoT,it is essential to understand how to best realize cryptographic circuitry using memristive circuitries,and to assess the implications of memristive crypto implementations on security and to develop novel computing paradigms that will enhance their security.This review article aims to help researchers to explore security solutions,to analyze new possible threats and to develop corresponding protections for the secure hardware systems based on low-cost memristive circuit designs.

Heterogeneous dual memristive circuit:Multistability,symmetry,and FPGA implementation

An improved heterogeneous dual memristive circuit(DMC)is proposed based on Chua's circuit,which shows good symmetry and multistablility.For the difficulty in controlling the initial conditions,which restricts the engineering applications,the 3 rd-order model(3 OM)in flux-charge domain is derived from the 5 th-order model(5 OM)in volt-ampere domain by using the flux-charge analysis method(FCAM).The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram,Lyapunov exponents,and especially attraction basins.The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit.To avoid the noise in the analog circuit,a field-programmable gate array(FPGA)is utilized to realize the reduction model,which is rarely reported and valuable for relevant research and application.

Memory Analysis for Memristors and Memristive Recurrent Neural Networks

Traditional recurrent neural networks are composed of capacitors, inductors, resistors, and operational amplifiers.Memristive neural networks are constructed by replacing resistors with memristors. This paper focuses on the memory analysis,i.e. the initial value computation, of memristors. Firstly, we present the memory analysis for a single memristor based on memristors’ mathematical models with linear and nonlinear drift.Secondly, we present the memory analysis for two memristors in series and parallel. Thirdly, we point out the difference between traditional neural networks and those that are memristive. Based on the current and voltage relationship of memristors, we use mathematical analysis and SPICE simulations to demonstrate the validity of our methods.

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional（3D） bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion（BCB3DBM）is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system（LTS）. Furthermore, block confusion based on position sequence group（BCBPSG） is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed.

Memristive Behavior Based on Ba-Doped SrTiO3 Films

The Sr0.95Ba0.05 TiO3 （SBT） nanometer film is prepared on the commercially available Pt/TiO2/SiO2/Si substrate by radio-frequency magnetron sputtering. The x-ray diffraction pattern and the scanning electron microscope image of the cross-sectional profile of the SBT nanometer film are depicted. The memristive mechanism is inferred. The mathematical model M（q） = 12.3656 - 267.4038｜q（t）｜is calculated, where M（q） denotes the memristance depending on the quantity of electric charge, and q（t） denotes the quantity of electric charge depending on the time. The theoretical I-V characteristics of the SBT nanometer film are obtained by the mathematical model. The results show that the theoretical I-V characteristics are consistent with the measured I-V characteristics. Moreover, the mathematical model could guide the research on applications of the memristor.

Hidden Attractors in a Delayed Memristive Differential System with Fractional Order and Chaos Synchronization

As an important research branch,memristor has attracted a range of scholars to study the property of memristive chaotic systems.Additionally,time⁃delayed systems are considered a significant and newly⁃developing field in modern research.By combining memristor and time⁃delay,a delayed memristive differential system with fractional order is proposed in this paper,which can generate hidden attractors.First,we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter,and showed that with the increase of the parameter,the system generated rich chaotic phenomena such as bifurcation,chaos,and hypherchaos.Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization.Lastly,examples were provided to analyze and confirm the influence of parameter a,fractional order q,and time delayτon chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q andτ.

Computation of the locus crossing point location of MC circuit

In this paper, the crossing point property of the i-v hysteresis curve in a memristor-capacitor （MC） circuit is analyzed. First, the ideal passive memristor on the crossing point property of i-v hysteresis curve is studied. Based on the analysis, the analytical derivation with respect to the crossing point location of MC circuit is given. Then the example of MC with linear memristance-versus-charge state map is demonstrated to discuss the drift property of cross-point location, caused by the frequency and capacitance value.

SPICE modeling of flux-controlled unipolar memristive devices

Unipolar memristive devices are an important kind of resistive switching devices. However, few circuit models of them have been proposed. In this paper, we propose the SPICE modeling of flux-controlled unipolar memristive devices based on the memristance versus state map. Using our model, the flux thresholds, ON and OFF resistance, and compliance current can easily be set as model parameters. We simulate the model in HSPICE using model parameters abstracted from real devices, and the simulation results show that the proposed model caters to the real device data very well, thus demonstrating that the model is correct. Using the same modeling methodology, the SPICE model of charge-controlled unipolar memristive devices could also be developed. The proposed model could be used to model resistive memory cells, logical gates as well as synapses in artificial neural networks.

Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions

The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are obtained under the framework of Filippov for such systems.Firstly,the novel feedback controller,which includes the discontinuous functions and time delays,is proposed to investigate such systems.Secondly,the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique.At the same time,the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated.In addition,by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems,the global asymptotic synchronization is achieved as a corollary.Finally,a numerical example is given to indicate the correctness of the obtained conclusions.

Sliding Mode Control of Fractional-Order Memristive System

A sliding mode controller for a fractional-order memristor-based chaotic system is designed to address its problem in stabilization control.Firstly,aphysically realizable fractional-order memristive chaotic system was introduced,which can generate a complex dynamic behavior.Secondly,a sliding mode controller based on sliding mode theory along with Lyapunov stability theory was designed to guarantee the occurrence of the sliding motion.Furthermore,in order to demonstrate the feasibility of the controller,a condition was derived with the designed controller＇s parameters,and the stability analysis of the controlled system was tested.A theoretical analysis shows that,under suitable condition,the fractional-order memristive system with a sliding mode controller comes to a steady state.Finally,numerical simulations are shown to verify the theoretical analysis.It is shown that the proposed sliding mode method exhibits a considerable improvement in its applications in a fractional-order memristive system.

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

Embedding any desired number of coexisting attractors in memristive system

A simple variable-boostable system is selected as the structure for hosting an arbitrarily defined memristor for chaos producing.The derived three-dimensional(3-D)memristive chaotic system shows its distinct property of offset,amplitude and frequency control.Owing its merits any desired number of coexisting attractors are embedded by means of attractor doubling and self-reproducing based on function-oriented offset boosting.In this circumstance two classes of control gates are found:one determines the number of coexisting attractors resorting to the independent offset controller while the other is the initial condition selecting any one of them.Circuit simulation gives a consistent output with theoretically predicted embedded attractors.