Memristor-based System Research Articles

A Novel Memristor Chaotic System with a Hidden Attractor and Multistability and Its Implementation in a Circuit

By introducing an ideal and active flux-controlled memristor and tangent function into an existing chaotic system, an interesting memristor-based self-replication chaotic system is proposed. The most striking feature is that this system has infinite line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. In this paper, bifurcation diagrams and Lyapunov exponential spectrum are used to analyze in detail the influence of various parameter changes on the dynamic behavior of the system; it shows that the newly proposed chaotic system has the phenomenon of alternating chaos and limit cycle. Especially, transition behavior of the transient period with steady chaos can be also found for some initial conditions. Moreover, a hardware circuit is designed by PSpice and fabricated, and its experimental results effectively verify the truth of extreme multistability.

Bursting oscillations and bifurcation mechanism in a fully integrated piecewise-smooth chaotic system

This paper aims to show and investigate bursting oscillator and bifurcation phenomena in a piecewise-smooth memristor-based Shimizu–Morioka (SM) system. First, a piecewise-smooth nonlinear system is built. Second, considering the memory characteristic of the memristor and the formation of the bursting oscillations circuit, a memristor and a periodic excitation are introduced into the system which leads to the piecewise-smooth memristor-based systems with a single slow variable. As the slow variable changes periodically in different scopes, we discover intricate bursting oscillation phenomena, namely, asymmetric Fold/Fold bursting, damped oscillation-sliding, asymmetric Fold/Fold-delayed supHopf/supHopf bursting, compressed oscillation phenomenon within the limit cycle, random bursting, double loop oscillations and so on. To make the circuit low power consumption and portable in practice, it is fully integrated. In the course of the study, it is found that the properties of the nominal equilibrium orbits, limit cycles, and the non-smooth boundary contribute to the bursting. Finally, a fully integrated circuit is designed and the accuracy of the study is verified by some circuit simulation results.

Qualitative Analysis and Bifurcation in a Neuron System With Memristor Characteristics and Time Delay.

This article focuses on the hybrid effects of memristor characteristics, time delay, and biochemical parameters on neural networks. First, we propose a novel neuron system with memristor and time delays in which the memristor is characterized by a smooth continuous cubic function. Second, the existence of equilibria of this type of neuron system is examined in the parameter space. Sufficient conditions that ensure the stability of equilibria and occurrence of pitchfork bifurcation are given for the memristor-based neuron system without delay. Third, some novel criteria of the addressed neuron system are constructed for guaranteeing the delay-dependent and delay-independent stability. The specific conditions are provided for Hopf bifurcations, and the properties of Hopf bifurcation are ascertained using the center manifold reduction and the normal form theory. Moreover, there exists a phenomenon of bistability for the delayed memristor-based neuron system having three equilibria. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation

In this paper, a fractional-order memristive model with infinite coexisting attractors is investigated. The numerical solution of the system is derived based on the Adomian decomposition method (ADM), and its dynamic behaviors are analyzed by means of phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum (LEs), dynamic map based on SE complexity and maximum Lyapunov exponent (MLE). Simulation results show that it has rich dynamic characteristics, including asymmetric coexisting attractors with different structures and offset boosting. Finally, the digital signal processor (DSP) implementation verifies the correctness of the solution algorithm and the physical feasibility of the system.

Synchronization, circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller

In this paper, we investigate a circuit implementation of memristor-based chaotic synchronization with a single input controller. Firstly, based on the cubic function model of memristor, a circuit with the grounded flux-control memristor-based hyperchaotic system is designed and implemented. Secondly, a single input controller is proposed to synchronize the two memristor-based hyperchaotic systems, and a sufficient condition of the synchronized system is obtained by the Routh-Hurwitz criterion and minimum phase theory. Then, a circuit of the proposed controller for memristor-based chaotic synchronization system is designed and implemented. Finally, secure communication based on memristor-based chaotic synchronization system is given to show the feasibility of the signal encryption scheme.

Chaos in the discrete memristor-based system with fractional-order difference

The mathematical modeling of memristor in discrete-time domain is an attractive new issue, but there are still some problems to be explored. This paper studies an interesting second-order memristor-based map model, and the model is constructed to three systems based on Caputo fractional-order difference. Their dynamic behaviors are investigated by the volt–ampere curve, bifurcation diagram, maximum Lyapunov exponent, attractor phase diagram, complexity analysis and basin of attraction. Numerical simulation analysis shows that the fractional-order system exhibits quasi periodic, chaos, coexisting attractors and other complex behaviors, which demonstrates more abundant dynamic behaviors of the fractional-order form. It lays a good foundation for the future analysis or engineering application of the discrete memristor.

A novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions.

Based on the pure mathematical model of the memristor, this paper proposes a novel memristor-based chaotic system without equilibrium points. By selecting different parameters and initial conditions, the system shows extremely diverse forms of winglike attractors, such as period-1 to period-12 wings, chaotic single-wing, and chaotic double-wing attractors. It was found that the attractor basins with three different sets of parameters are interwoven in a complex manner within the relatively large (but not the entire) initial phase plane. This means that small perturbations in the initial conditions in the mixing region will lead to the production of hidden extreme multistability. At the same time, these sieve-shaped basins are confirmed by the uncertainty exponent. Additionally, in the case of fixed parameters, when different initial values are chosen, the system exhibits a variety of coexisting transient transition behaviors. These 14 were also where the same state transition from period 18 to period 18 was first discovered. The above dynamical behavior is analyzed in detail through time-domain waveforms, phase diagrams, attraction basin, bifurcation diagrams, and Lyapunov exponent spectrum . Finally, the circuit implementation based on the digital signal processor verifies the numerical simulation and theoretical analysis.

Minimum variance control of chaos in a hyperchaotic memristor based oscillator using online particle swarm optimization

This paper introduces a new hyperchaotic oscillator base on a new boundary-restricted Hewlett-Packard memristor model. Firstly, the complex system is designed based on a memristor-based hyperchaotic real system, and its properties are analyzed by means of Lyapunov exponents, Lyapunov dimension and phase portraits diagrams. Secondly, a simple feedback control based on the minimum variance control technique is designed to stabilize the hyperchaotic oscillator system, which is one of the new developed approaches for controlling the chaos in high-dimensional hyperchaotic systems. In this method, the time series variance is considered for designing and calculating the state feedback control gain. Furthermore, the state feedback control is designed so that to minimize the variance as a cost function, followed by developing an online optimization technique using the particle swarm optimization method in order to calculate the state feedback control based on the minimum variance strategy. Then, the application of this method is examined on a hyperchaotic memristor-based oscillator. Finally, the sensitivity of the proposed method is evaluated in different initial conditions that greatly influence the hyperchaotic dynamics. Considering that the optimization is online, simulation results show highly good effectiveness of the presented technique in controlling the chaos in high-dimensional hyperchaotic oscillators

Memristor-Based Image Enhancement: High Efficiency and Robustness

Due to many outstanding physical characteristics, memristors have attracted much attention from all over the world. As a tendency, memristor-based systems are beginning to be applied in various fields of image processing, such as pattern recognition and edge detection. For the first time, memristors are introduced to image enhancement in this work, which dexterously processes the images twice via memristors’ intrinsic properties. Adopting a coarse transmission map and nonlinear memristive characteristics, the algorithm is highly efficient, which enormously reduces the computational cost, and image quality assessment demonstrates that it maintains comparable performance with classical algorithms. Furthermore, the temperature effect and the memristor instability, namely, the device-to-device variations and the cycle-to-cycle variations, are taken into consideration, and the average of several stacked images is proven effective in relieving the influence of variations. We believe that this work can explore a new application for the memristor.

A bistable memristor-based circuit system and its implementation

A bistable memristor-based circuit system and its implementation

Tri-Valued Memristor-Based Hyper-Chaotic System with Hidden and Coexistent Attractors

Tri-Valued Memristor-Based Hyper-Chaotic System with Hidden and Coexistent Attractors

A bistable memristor-based circuit system and its implementation

A bistable memristor-based circuit system and its implementation

A Multi-Stable Memristor and its Application in a Neural Network

Nowadays, there is a lot of study on memristor-based systems with multistability. However, there is no study on memristor with multistability. This brief constructs a mathematical memristor model with multistability. The origin of the multi-stable dynamics is revealed using standard nonlinear theory as well as circuit and system theory. Moreover, the multi-stable memristor is applied to simulate a synaptic connection in a Hopfield neural network. The memristive neural network successfully generates infinitely many coexisting chaotic attractors unobserved in previous Hopfield-type neural networks. The results are also confirmed in analog circuits based on commercially available electronic elements.

Memristors: Understanding, Utilization and Upgradation for Neuromorphic Computing

The next generation of artificial intelligence systems is generally governed by a new electronic element called memristor. Memristor-based computational system is responsible for confronting memory wall issues in conventional system architecture in the big data era. Complementary Metal Oxide Semiconductor (CMOS) compatibility, nonvolatility and scalability are the important properties of memristor for designing such computing architecture. However, some of the concerns, such as analogue switching and stochasticity, need to be addressed for the use of memristor in novel architecture. Here, we reviewed a number of important scientific works on memristor materials, electrical performance and their integration. In addition, strategies to address the challenges of memristor integration in neuromorphic computing are also being investigated.

Coexisting Infinite Orbits in an Area-Preserving Lozi Map.

Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.

Emerging Memristive Artificial Synapses and Neurons for Energy-Efficient Neuromorphic Computing.

Memristors have recently attracted significant interest due to their applicability as promising building blocks of neuromorphic computing and electronic systems. The dynamic reconfiguration of memristors, which is based on the history of applied electrical stimuli, can mimic both essential analog synaptic and neuronal functionalities. These can be utilized as the node and terminal devices in an artificial neural network. Consequently, the ability to understand, control, and utilize fundamental switching principles and various types of device architectures of the memristor is necessary for achieving memristor-based neuromorphic hardware systems. Herein, a wide range of memristors and memristive-related devices for artificial synapses and neurons is highlighted. The device structures, switching principles, and the applications of essential synaptic and neuronal functionalities are sequentially presented. Moreover, recent advances in memristive artificial neural networks and their hardware implementations are introduced along with an overview of the various learning algorithms. Finally, the main challenges of the memristive synapses and neurons toward high-performance and energy-efficient neuromorphic computing are briefly discussed. This progress report aims to be an insightful guide for the research on memristors and neuromorphic-based computing.

Memristor-based hyper-chaotic circuit for image encryption* *Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB1306600), the National Natural Science Foundation of China (Grant Nos. 62076207 and 62076208), and the Fundamental Science and Advanced Technology Research Foundation of Chongqing, China (Grant Nos. cstc2017jcyjBX0050).

The memristor is a kind of non-linear element with memory function, which can be applied to chaotic systems to increase signal randomness and complexity. In this paper, a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model, which can generate complex chaotic attractors. The basic dynamic theory analysis and numerical simulations of the system, such as the stability of equilibrium points, the Lyapunov exponents and dimension, Poincare maps, the power spectrum, and the waveform graph prove that it has rich dynamic behaviors. Then, the circuit implementation of this system is established. The consistency of simulation program with integrated circuit emphasis (SPICE) simulation and numerical analysis proves the ability to generate chaos. Finally, a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper. The scheme involves a total of two encryptions. By using different security analysis factors, the proposed algorithm is compared with other image encryption schemes, including correlation analysis, information entropy, etc. The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.

Finite-time modified combination synchronization of memristive FitzHugh–Nagumo circuit with unknown disturbances

The memristor-based FitzHugh-Nagumo neuron system shows special dynamical behaviors, which make it have a good application in the fields of image processing and signal transmission. The accurate dimensionality reduction model of the system is established, which facilitates the internal interpretation and physical control of the multistability that depends on the initial values. The dynamical behavior analyses of the dimensionality reduction memristive system with different original initial states are developed through bifurcation diagram and Lyapunov index spectrum. Multistability and antimonotonicity with periodic-chaotic bubbles are investigated. The sliding mode control method with a smooth function is designed to achieve the finite-time synchronization of the multistable memristive neuron systems, which make three different behaviors of systems synchronized. The sliding mode controller can enable the system to quickly and smoothly implement combination synchronization within finite time. Numerical simulations show the effectiveness of the sliding mode controller designed.

Neural signal analysis with memristor arrays towards\xa0high-efficiency brain\u2013machine interfaces

Brain-machine interfaces are promising tools to restore lost motor functions and probe brain functional mechanisms. As the number of recording electrodes has been exponentially rising, the signal processing capability of brain–machine interfaces is falling behind. One of the key bottlenecks is that they adopt conventional von Neumann architecture with digital computation that is fundamentally different from the working principle of human brain. In this work, we present a memristor-based neural signal analysis system, where the bio-plausible characteristics of memristors are utilized to analyze signals in the analog domain with high efficiency. As a proof-of-concept demonstration, memristor arrays are used to implement the filtering and identification of epilepsy-related neural signals, achieving a high accuracy of 93.46%. Remarkably, our memristor-based system shows nearly 400× improvements in the power efficiency compared to state-of-the-art complementary metal-oxide-semiconductor systems. This work demonstrates the feasibility of using memristors for high-performance neural signal analysis in next-generation brain–machine interfaces.