Memristor Model Research Articles

Various pseudo random number generators based on memristive chaos map model

Various pseudo random number generators based on memristive chaos map model

Exploring the dynamics of a multistable general model of discrete memristor-based map featuring an exponentially varying memristance

Chua’s groundbreaking discovery in 1971 introduced the memristor as the fourth essential electrical component, joining resistance, capacitance, and inductance. Over the past few years, numerous discrete memristor models have been developed following its formal proposal, expanding our understanding of this subject. However, there is limited discussion about multistable discrete memristor models. This research combines a comprehensive methodology for generating memristive maps using the modulo function and an exponential memristance, resulting in the development of a multistable discrete memristor model. Nonlinear techniques, such as bifurcation diagrams, Lyapunov spectrum diagrams, and phase portraits were utilized to analyze the dynamic characteristics of the system. The findings uncovered a range of captivating phenomena associated with chaos theory, including regular orbits, chaotic orbits, the mechanism of period doubling leading to chaos, crisis phenomena, and the presence of multistability.

Behavioral Modeling of Memristors under Harmonic Excitation.

Memristors are devices built on the basis of fourth passive electrical elements in nanosystems. Because of the multitude of technologies used for memristor implementation, it is not always possible to obtain analytical models of memristors. This difficulty can be overcome using behavioral modeling, which is when mathematical models are constructed according to the input-output relationships on the input and output signals. For memristor modeling, piecewise neural and polynomial models with split signals are proposed. At harmonic input signals of memristors, this study suggests that split signals should be formed using a delay line. This method produces the minimum number of split signals and, as a result, simplifies behavioral models. Simplicity helps reduce the dimension of the nonlinear approximation problem solved in behavioral modeling. Based on the proposed method, the piecewise neural and polynomial models with harmonic input signals were constructed to approximate the transfer characteristic of the memristor, in which the current dynamics are described using the Bernoulli differential equation. It is shown that the piecewise neural model based on the feedforward network ensures higher modeling accuracy at almost the same complexity as the piecewise polynomial model.

Design of a memristor-based neuron for spiking neural networks

The primary objective of neuromorphic system design is to surpass limitations in energy efficiency and scaling of classical von Neumann computing systems, through the emulation of animals’ nervous systems. This is achieved by conducting calculations in memory and encoding information in impulse signals, ultimately leading to enhanced adaptability. Adhering to these principles allows for improved energy efficiency and computational speed when solving machine learning problems, encompassing biomedical applications, embedded systems, and cyber-physical systems. Functional blocks modeling the main elements of the central nervous system, namely neurons and synapses, offer an advantage in implementing learning on a chip. The use of memristive electronic components, capable of altering their resistance based on the charge flowing through them, opens new doors for hardware implementation of neuromorphic systems. These devices offer advantages over conventional transistor electronics with respect to power consumption, component density, and performance. To achieve optimal results, the architecture of neuromorphic systems should be optimized at the device level. Memristive components are utilized to create neurons and synapses. This thesis is specifically focused on producing memristive neuron-like spike signal generators. Previously, memristive neurons were crafted using a locally active element comprised of vanadium dioxide VO2, which incorporated a negative differential resistance section of the IV-curve. One of the recent advancements in this field is a spiking neuron with frequency adaptation [1]. Its drawbacks, however, involve separating the memristive and locally active elements physically, resulting in higher energy consumption and decreased integration quality. In [2], models of memristive neurons with minimal complexity are introduced, which incorporate the Leaky Integrate-and-Fire principle. However, the circuits presented require the application of negative voltage pulses to a DC battery to reset the memristor to its initial high-resistance state. This limitation restricts its sphere of application in neuromorphic systems. This paper proposes a model of a neuron that overcomes these limitations by using the negative differential resistance of the memristor to generate spikes, along with integrating supplementary circuit components to sustain the resistive switching cycles of the memristor. The neuron model under consideration is implemented using the NI Multisim 14.2 SPICE environment and has been verified in the NI LabVIEW 2022 tool environment. The equations of the modified model of the generalized mean metastable switch of the memristor with self-directed channel [3] represent the current in the memristor branch of the neuron equivalent circuit. The simplicity of the equivalent circuitry of the neuron is attained by merging all the nonlinear features necessary for spike generation into one memristor model. The experimental phase of the study employed obtainable memristors from Knowm Corporation and the laboratory prototyping platform NI ELVIS III. The investigation of the proposed neuron model was accomplished through the application of sinusoidal and rectangular input signals. The refractory time of the neuron model was calculated. The chosen stack of computer simulation and semi-natural modeling technologies is applied within the research-driven design concept of electronic devices. This approach considers the importance of refining the properties and identification of the design object or its components during the development cycle.

Dynamics of two neuron-like generators with memristive connection

At present one of the most urgent tasks of interdisciplinary science is the design and research of neuromorphic devices. Such devices are most often used to create systems for processing various kinds of information with algorithms similar to the data processing algorithms of the human brain or the brain of animals. The development of such neuromorphic electronics will allow computing devices and information processing systems to be built based on new principles and with a high level of parallelism [1]. Neuromorphic devices require the development of electronic components: neurons and synapses. The paper [2] proposed a phase-locked loop system with a bandpass filter in the control circuit. A more detailed study of the mathematical model of such a system has shown missing equilibrium states corresponding to the synchronization mode of the phase-locked loop system, but there are self-oscillating modes of varying complexity. Self-oscillations observed in such system are similar to spike and burst oscillation of the neuron’s membrane potential. Hardware implementation [3] of the considered neuron like generator in the form of an electronic device demonstrated the possibility of reproducing the same dynamic modes as in the mathematical model [2]. A fundamental disadvantage of the proposed model [2] and its experimental implementation [3] – the absence of an excitable mode (by excitable we mean a dynamic system with a stable equilibrium state and a periodic pseudoorbit of large amplitude, passing in the vicinity of the equilibrium state), when pulse generation would only respond to external disturbance. At the same time, the vast majority of brain neurons are in the excitable subthreshold mode, and their generation is primarily caused by presence of multiple connection. One of the tasks of this work was to modification the existing model of the neuron-like generator in order to preserve the known dynamics and add a mode of excited oscillator. While solving this problem, a modification of the neuron like generator based on the phase-locked loop system with a band-pass filter in the control circuit was proposed and implemented as an electronic circuit. The modification eliminates the basic drawback of the initial model – inability to work in the excitable mode. The new dynamic mode with the absence of self-oscillations was obtained by adding an electronically controlled switch between the low- and high-pass filters in the control loop. Existence of the excitable mode and the existence of previously known self-oscillating modes of varying complexity was demonstrated experimentally: spike, burst, and chaotic modes was confirmed [4]. Another task in this work was to explore the dynamics of two neuron-like generators with memristive coupling. A second-order memristor model based on Chua's memristor was used as a model of synaptic connection. When solving this problem, nonlinear frequency dependences of the conductivity of the memristive element were found. This dependence has the same character for self-oscillating modes of varying complexity: spike and burst. In addition, it was demonstrated synchronization of two neuron-like generators connected through a memristive element. Synchronization of two coupled neuron-like generators is interim in nature and strongly depends on the current state of the memristive element [5].

Fabrication and characterization of TiOx based single-cell memristive devices

Nowadays, remarkable progress has been observed in research into neuromorphic computing systems inspired by the human brain. A memristive device can behaviorally imitate the biological neuronal synapse therefore memristor-based neuromorphic computing systems have been proposed in recent studies. In this study, the memristive behaviors of titanium dioxide sandwiched between two platinum electrodes were investigated. For this purpose, three SiO2/Pt/TiOx/Pt thin films with 7.2 nm, 40 nm, and 80 nm TiOx metal-oxide layers were fabricated using a pulsed laser deposition technique. The fabrication process, structural properties, photoluminescence properties and electrical transport characterization of each thin film have been investigated. All thin films were analyzed in terms of the film stoichiometry and degree of oxidation using high-resolution x-ray photoelectron spectroscopy. By measuring the layer thickness, density, and surface roughness with the x-ray reflectivity technique, by analyzing the structural defects with photoluminescence spectroscopy and by characterizing the quasi-static electrical properties with the conventional two probes technique, we have shown that the fabricated memristive devices have bipolar digital switching properties with high ROFF/RON ratio. This type of switching behavior is applicable in random access memories. Experimental current–voltage behavior in the form of pinched hysteresis loop of the films have been modelled with generalized memristor model.

A new fractional-order 5D memristive chaotic system with special extreme multistability and its application to image encryption

Introducing memristor into the chaotic system can enrich the dynamic behaviors of the chaotic system. We propose a symbolic function memristor model and introduce it into a chaotic system to construct a fractional-order 5D memristor chaotic system. Through dynamic analysis of equilibrium point, Lyapunov exponents, phase diagram and bifurcation diagram, it is found that the system has abundant dynamic behaviors, for example, the change of equilibrium point type with parameters, transient chaos, offset-boosting and a special kind of extreme multistability. And with the change of parameters, the attractor state and shape will appear rich changes. Then the correctness of the system is verified by circuit simulation. The chaotic system is introduced into the process of image encryption, and an encryption system is constructed, which is composed of Zigzag scrambling, Hilbert curve scrambling, DNA encryption and GF257 diffusion algorithm. Finally, through a variety of security verification, the results show that the encryption system has good security and can resist many kinds of attacks effectively.

A 3D memristor-based chaotic system with transition behaviors of coexisting attractors between equilibrium points

A 3D symmetric memristor-based chaotic system (SMCS) is constructed by introducing a smooth quadratic flux control memristor model into the jerk chaotic system (JCS). The dynamics of SMCS are investigated by means of Lyapunov exponents, bifurcation diagrams, multistability, transient behavior, and spectral entropy complexity. It is found that SMCS is sensitive to parameter b included in the normalized equation. Transition behaviors of coexisting attractors between the equilibrium points will be observed when parameter b changes in a specific interval. Its complexity is demonstrated by the types of three multi-stable behaviors and four types of transient behaviors and distinctly enhanced by the spectral entropy complexity as two parameters variations. Additionally, the physical realizability of SMCS is verified by the implementation of the analog circuit and digital hardware. Finally, the pseudo-random sequence based on JCS and SCMS is compared by NIST testing.

DC operating points of Mott neuristor circuits

In 1960 Hewitt Crane conceptualized neuristors as electronic logic networks that could mimic action potential generation by biological neurons. In 2012 Mott memristors were presented as nano-scale electronic devices for physically constructing neuristor networks. Both the original Mott memristor model and the simplified model presented in 2020 are stiff nonlinear first-order ordinary differential equations (ODEs) that describe the voltage controlled threshold switching and current controlled negative differential resistance, attributed to a Mott insulator-to-metal phase transition. By design, a Mott neuristor contains two identical Mott memristors plus linear resistors and capacitors (no inductors), which enables alternating threshold switching by the memristors to generate periodic (AC) output voltage spikes in response to a DC current or voltage input. This paper presents a steady-state analysis of dynamic neuristor models, including four-, five-, and six-state variables (each of which is a system of first-order ODEs involving the states) based on the original phenomenological model of the Mott memristor. Specifically, it reveals the unique stable operating points that occur for applied currents or voltages below the amounts needed to induce resistive switching. These DC operating points represent the physically meaningful “OFF” states for the circuit when the neuristor does not output voltage spikes. Jacques Hadamard's mathematical criteria for a well-posed physical model (existence, uniqueness, continuity, stability) motivated the search for these DC operating points (OFF states), which are needed for efficiently initializing neuristor models before conducting dynamic neuristor simulations. The key result of our analysis is the neuristor steady-state eq. (29) which is useful for understanding neuristor OFF states as well as the role of negative-differential resistance (NDR) in the operation of the Mott memristor model and neuristor circuits. In addition to the steady-state analysis, three numerical examples of dynamic neuristor circuit operation are also given and MATLAB code for the dynamic four-state model is available for interested readers.

Memristive Autapse-Coupled Neuron Model With External Electromagnetic Radiation Effects

Thanks to their distinct synaptic plasticity and memory effects, memristors not only can mimic biological neuronal synapses but also can describe the influence of external electromagnetic radiation. This paper proposes a novel memristive autapse-coupled neuron model (MACNM) using a locally active memristor as an autapse and simultaneously introducing a flux-controlled piecewise-nonlinear memristor to describe the external electromagnetic radiation. Theoretical analysis and numerical simulation results show that the MACNM is able to generate multiple numbers of grid multi-scroll hidden attractors. Moreover, it can exhibit rich and complex hidden firing dynamics, including periodic spiking/bursting firing, chaotic spiking/bursting firing as well as firing patterns transition. In particular, hidden firing multistability of five coexisting homogeneous chaotic bursting firing patterns with different offsets along the boosting route is discovered, giving raise to the interesting phenomenon of hidden homogeneous multistability. Finally, a circuit is designed to verify the physical feasibility of the abundant electrical activities in the proposed MACNM.

Phenomenological modeling of memristor fabricated by screen printing based on the structure of Ag/polymer/Cu

Phenomenological modeling of memristor fabricated by screen printing based on the structure of Ag/polymer/Cu

Dynamics analysis and cryptographic implementation of a fractional-order memristive cellular neural network model

Due to the fact that a memristor with memory properties is an ideal electronic component for implementation of the artificial neural synaptic function, a brand-new tristable locally active memristor model is first proposed in this paper. Here, a novel four-dimensional fractional-order memristive cellular neural network (FO-MCNN) model with hidden attractors is constructed to enhance the engineering feasibility of the original CNN model and its performance. Then, its hardware circuit implementation and complicated dynamic properties are investigated on multi-simulation platforms. Subsequently, it is used toward secure communication application scenarios. Taking it as the pseudo-random number generator (PRNG), a new privacy image security scheme is designed based on the adaptive sampling rate compressive sensing (ASR-CS) model. Eventually, the simulation analysis and comparative experiments manifest that the proposed data encryption scheme possesses strong immunity against various security attack models and satisfactory compression performance.

FPGA implementation of memristive Hindmarsh–Rose neuron model: Low cost and high-performing through hybrid approximation

Recent memristive neuron models have improved the ability of researchers to describe the operation of biological neurons. We employ FPGA implementation for a memristive neuron model, FPGA implementation provides an improved hardware system for mimicking brain behavior, and provides a better understanding of neurological phenomena. In this manuscript, a memristive Hindmarsh–Rose neuron model taking into account the influence of electromagnetic radiation and two multiplierless approximations of this model are presented. These approximations are piecewise linear (PWL) model and hybrid model, which mimic the behaviors of the original model. In the hybrid model, power 2-based approximation and a novel approximation are used simultaneously. The proposed models were subjected to error analysis, revealing that the PWL model exhibited mean NRMSEs of 3.56% and 2.3% for bursting and spiking modes, respectively. On the other hand, the hybrid model displayed mean NRMSEs of 1.92% and 1.34% for bursting and spiking modes. According to the FPGA implementation results, the PWL model yields the overall resources saving of 75.82% and 47.8% speed-up. But in the hybrid model, by optimizing the approximation functions, in addition to obtaining higher accuracy, better results are provided with a 67.3% improvement in the maximum frequency and the 78.64% saving in hardware resources.

A New Compact Model for Third-Order Memristive Neuron With Box-Shaped Hysteresis and Dynamics Analysis

This paper proposes a new compact model and presents circuit-theoretical analysis for a third-order memristive neuromorphic element fabricated by S. Kumar et al. The proposed model mainly consists of a box-shaped resistor model and a simplified piecewise-linear memristor model. Since the dynamic behavior of the box-shaped hysteresis in the quasi-static current-voltage curve is mostly unexplored, we firstly extract the box-shaped resistor model and construct its oscillators. The coordinate system shifting method and dynamic route analysis method are used to reveal the operating mechanism of box-shaped resistor-based oscillators. Both the theoretical analysis and simulation verification indicate that the box-shaped hysteresis characteristic facilitates the generation of neuromorphic action potentials. The proposed new compact model not only captures quasi-static characteristics, but also includes dynamic behaviors, such as action potential, periodic spiking, and periodic bursting. The influences of the model parameters are further investigated to reveal the mechanism of the neuromorphic behaviors in the box-shaped hysteresis and positive differential resistance regions. Simulation results manifest the feasibility of the proposed model and the correctness of the presented analysis methods, which pave the way to the optimized design of memristive devices and the research of neuromorphic dynamics.

Coexisting firing patterns and circuit design of locally active memristive autapse morris-lecar neuron

A novel bistable locally active memristor is proposed in this paper. A locally active memristive autapse Morris-Lecar neuron model is constructed by using memristor to simulate the autapse of neuron. The equilibrium point and stability of the system are analyzed, and the firing mode and bifurcation characteristics of the neuronal system are revealed by using dynamic analysis methods such as slow-fast dynamics, interspike interval bifurcation diagrams, Lyapunov exponents, phase diagrams and time series diagram. By changing the memristive autapse gain and the initial state of the system, the existence of coexisting firing patterns in the constructed neuron model is confirmed. Finally, to further verify the effectiveness of the numerical simulation, the analog equivalent circuit of the locally active memristive neuron system is designed, which proves that the system is physically realizable.

VLSI Implementation of Hybrid Memristor Based Logic Gates

Practical memristors have gained attention from researchers and scientists due to their potential use in a variety of electronic circuits and devices. In our paper, a hybrid Memristor-CMOS (MeMOS) logic circuit was designed and its transient response was analyzed. This circuit, which uses a N-type metal oxide semiconductor (NMOS), and P-type metal oxide semiconductor (PMOS) transistors, Operational amplifiers (OPAMPs), resistors, capacitors and multipliers replicate memristor characteristics. To facilitate the development of real memristor circuit applications, a memristor emulator is utilized for breadboard experiments. This emulator can be connected in a variety of configurations, including serial, parallel, or a combination of both, with identical or opposite polarities. By simply changing the connection, the emulator can be switched between decremental and incremental configurations. In our paper, we implemented AND logic using MeMOS. PSpice simulation of the proposed emulator have been demonstrated for TiO2 memristor model.

A memristive chaotic system and its application in weak signal detection

In this paper, a novel four-dimensional memristive chaotic system is constructed by incorporating a memristor model into a three-dimensional chaotic system. Through the analysis of the Lyapunov exponent, bifurcation diagram, and Poincaré cross-section of the system, it has been observed that the system is capable of exhibiting a stable chaotic state, as well as complex dynamic behaviors, such as attractor coexistence, transient chaos, and offset boosting. To validate the actual existence of the system, a real circuit has been built based on Multisim simulation, and the numerical simulation results, along with the actual simulation results, are in agreement, thereby confirming the practical feasibility of the circuit. To achieve weak signal detection, a backstepping synchronization controller has been designed, which can detect the frequency and amplitude of unknown signals. It is obvious that this method does not require the determination of the critical threshold. Instead of, it relies on the system being in a chaotic state. The proposed detection method provides a new perspective for weak signal detection.

Characterization of second-order chaotic circuits with heterogeneous memristors

Abstract Amnesia-resistive chaotic circuits have various application prospects due to their unique circuit characteristics. In this paper, by studying the relationship between memristors and chaotic circuits, two models of magneto-controlled memristors with smooth quadratic monotonic rise nonlinear characteristics are constructed based on Tsai’s circuit, and an active memristor circuit composed of negative conductance is combined to replace Tsai’s diode in Tsai’s circuit system, and then a magneto-controlled memristor is inserted between the LC resonant part of the circuit, thus establishing a heterogeneous memristor second-order chaotic circuit. Multisim is used for device modeling, circuit construction, and system composition and simulation. The simulation tests show that when t ∈ [0,900] ∪ [1800,2500], the system exhibits a chaotic state. When t ∈ (900,1800), the system exhibits a periodic state. As the initial value parameter d varies between [2,4.64], the state of the system shifts between chaotic and hyperchaotic states, while the complexity of the system changes back and forth. This study demonstrates that the heterogeneous magneto-controlled memristor chaotic circuit has a rich, chaotic behavior, providing an effective reference for applying chaotic memristor circuits.

A novel grid multi-structure chaotic attractor and its application in medical image encryption

Grid multi-scroll/wing chaotic systems are complex non-linear dynamic systems, which are widely used in secure communication. The grid multi-scroll/wing chaotic systems are usually realized by using the function control method, which has a complex realization method, many control parameters, and a simple unit attractor structure. In this paper, based on the Hopfield neural network, a memristive Hopfield neural network model is proposed by using the memristor synapse control method. The model can generate novel grid multi-structure chaotic attractors, which have the characteristics of a simple implementation method, few control parameters, and complex unit attractor structure. Firstly, the generation mechanism of the grid multi-structure chaotic attractors is analyzed by the equilibrium points and stability. Secondly, its basic dynamical characteristics including the Lyapunov exponent spectrum, fractal dimension, time series, power spectrum, bifurcation diagram, and Poincaré section are analyzed. Thirdly, an analog circuit of the neural network model is designed and realized by Multisim. Finally, combined with the chaos encryption principle, an image encryption scheme is designed based on the generated grid multi-structure attractors. Experimental results show that compared with the existing schemes, the proposed scheme has larger information entropy, higher key sensitivity, and a good application prospect.

Finite-Time Synchronization of Memristive Neural Networks Modeling in Terms of Voltage-Flux-Time

In this paper, the finite-time synchronization problem of delayed memristive neural networks (MNNs) is addressed by adopting a flux-controlled memristor model. First, based on the presented memristor model, the MNNs behave as a class of continuous systems with 22n2+n variables. Then, the finite-time controllers are proposed to synchronize the voltage and flux states between the drive and response MNNs, respectively. Based on the inequality techniques and the Lyapunov method, new synchronization criteria for delayed MNNs are derived. Finally, the results are verified by numerical simulations.