Memristor-based System Research Articles

Fractional-order memristor-based chaotic system with a stable equilibrium point, its fractional-order PI-based sliding mode control and switching synchronisation

In this paper, we discuss a new fractional-order memristor-based three-dimensional chaotic system with a stable equilibrium point. The proposed system belongs to the category of hidden attractors dynamical system. The system is new in the sense that it is a fractional-order memristor-based chaotic system and exhibits hidden attractors. The chaotic behaviour of the system is accessed by various numerical techniques such as Lyapunov exponents, bifurcation diagrams, instantaneous phase plot, attractor analyses and frequency spectrum plots. A fractional-order proportional integral (PI)-based sliding mode control is designed for chaos suppression of the proposed system. Further, the switching synchronisation of the new system in the form of the master and the slave systems is presented.

A memristor-based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption

A memristor-based system with hyperchaos and hidden attractors is introduced in this research work. The proposed four-dimensional memristor-based system exhibits both line equilibrium and no-equilibrium for different choice of parameters. An experimental emulation of the memristor-based system is carried out by an electronic circuit. An adaptive integral sliding mode controller is designed for globally synchronising a pair of memristor-based hyperchaotic systems with unknown parameters. As another application, the memristive system with hyperchaos is applied for voice encryption, which has potential applications in cryptosystems, computing and secure communication.

An Optimized Memristor-Based Hyperchaotic System With Controlled Hidden Attractors

A new memristor-based hyperchaotic system is described in this paper. After studying on its basic dynamic characteristics, it is found that the hidden attractors can be obtained by adding a nonzero parameter (which named optimized factor in this paper) to the system. Moreover, when the optimized factor is varying, the corresponding hidden attractors of the system is symmetrical and can convert between double scrolls and a single scroll. Further, the optimized memristor-based hyperchaotic system is implemented by analog circuits. Corresponding experimental results are completely consistent with the theoretical analysis.

Dynamic analysis of symmetric behavior in flux-controlled memristor circuit based on field programmable gate array

<sec> The lack of the relationship between flux and charge has been made up for by the memristor which is suitable to constructing chaotic circuits as a nonlinear element. Commonly, the memristor-based chaotic systems are constructed by introducing the model of memristor into various classical nonlinear circuits, and more special and abundant dynamic behaviors are existent in these memristive systems. With the deepening of research, several novel nonlinear phenomena of memristor circuits have been found, such as hidden attractors, self-excited attractors and anti-monotonic characteristic. Meanwhile, multistability of a memristor-based circuit explained by the coexistence of multiple attractors with different topological structures is a typical phenomenon in a nonlinear system, and it is also one of the hotspots in this field. In addition, the chaotic sequences generated by the memristive circuits are used as additional signals for information transmission or image encryption. Therefore, the study of modeling memristor systems and analyzing various nonlinear behaviors is of certain valuable.</sec><sec> In this paper, a four-dimensional flux-controlled memeristive circuit is constructed by introducing an active memristor with absolute value into an improved Chua’s circuit, and the special dynamic behaviors are observed. Through the bifurcation diagrams and Lyapunov exponent spectra, the symmetric bifurcations are shown, and the symmetric system states in parameter mappings are found. Besides, the distribution maps of memristive circuit are used to analyze the multistability in a symmetrical attraction domain, and the corresponding phase diagrams are depicted to confirm the existence of multistability. Furthermore, the circuit experiments of the flux-controlled memeristive circuit are implemented by the field programmable gate array simulation, and the experimental results are obtained on a digital oscilloscope, which proves the physical implementability of the memristor-based system.</sec>

A memristor-based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption

A memristor-based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption

Stabilization of the memristor-based hyperchaotic complex Lu system in a finite time

In this paper, we deal with the finite-time stabilization problem of a memristor-based hyperchaotic complex L\"u system. Based on the finite-time stability theory, two control strategies are presented to achieve stabilization of the memristor-based hyperchaotic complex L\"u system in a finite time. Two numerical simulations have been conducted, the simulation results demonstrate the validity and feasibility of the theoretical analysis.

Dimensionality Reduction Analysis for Detecting Initial Effects on Synchronization of Memristor-Coupled System

This paper presents a 9-D memristor-coupled system with three ideal memristors and investigates its initial effects on synchronization using dimensionality reduction analysis method. The 9-D memristor-coupled system is yielded from two identical 4-D ideal memristor-based hyper-jerk systems via coupling an ideal memristor, from which the initials-dependent synchronization with parallel offset for larger coupling strength is numerically exhibited. To explore the initial effects on synchronization, an equivalent 6-D dimensionality reduction model is built using state variable mapping (SVM) method, from which the implicit initials of the 9-D memristor-coupled system are transformed into the explicitly initials-related system parameters of such a 6-D dimensionality reduction model. Thus, the inherent initial mismatches between the two coupled identical 4-D subsystems are explicitly expressed as the initials-related parameter mismatches between the two coupled non-identical 3-D dimensionality reduction subsystems. The initials-related boundedness of the error system between the two non-identical 3-D dimensionality reduction subsystems is derived by Lyapunov analysis method, upon which the initial effects on synchronization with parallel offset are expounded quantitatively. Furthermore, the initials-dependent synchronization is well confirmed by the numerical simulations, which demonstrates that the initials do have great influence on synchronization dynamics of the coupled memristive system.

Digital Emulation of a Versatile Memristor With Speech Encryption Application

Memristor characteristics such as nonlinear dynamics, state retention and accumulation are useful for many applications. FPGA implementation of memristor-based systems and algorithms provides fast development and verification platform. In this work, we first propose a versatile digital memristor emulator that exhibits either continuous or discrete behaviors, similar to valence change memories (VCM) and the electrochemical metallization memories. Secondly, the proposed memristor emulator is used to design a chaotic generator circuit utilizing the memristor's nonlinearity. Finally, the chaotic system is used to design a speech encryption engine to demonstrate its capabilities. The memristor emulator, chaotic generator, and the encryption system were implemented on Nexys 4 Artix-7 FPGA XC7A100T. The implementation results show an efficiency in throughput and hardware resources utilization compared to the previous works. In addition, the encryption system results show good performance against several perceptual, statistical attacks in addition to resistance to security attacks tests including differential attacks, NIST tests, key space analysis, mean square error (MSE), correlation, histogram and spectrogram.

Initial conditions-related dynamical behaviors in PI-type memristor emulator-based canonical Chua’s circuit

PurposeThe purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors.Design/methodology/approachThis paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit.FindingsThe system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit.Originality/valueThese memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

Multiple coexisting attractors of the serial–parallel memristor-based chaotic system and its adaptive generalized synchronization

The nonlinear circuit with serial–parallel memristors shows special internal characteristics and external performance, which indicates that the serial–parallel memristors can greatly change the dynamic characteristics of the nonlinear system. Mathematical model of the system is established to analyze the influence of the serial–parallel memristors on the dynamical behaviors with the change of system parameters, and then the basin of attraction is used to exhibit the coexisting multiple attractors with different initial conditions and the serial–parallel memristors, which can reveal that the serial–parallel flux-controlled or charge-controlled memristors have different effects on the generation of chaos and multistability phenomenon. Moreover, the hardware description of memristor-based system through FPGA is realized by Verilog language and the experimental results are observed from digital oscilloscope. Finally, based on the Lyapunov stability theory and adaptive control law, a nonlinear controller is designed to achieve the adaptive generalized synchronization between five memristor-based chaotic systems, and numerical results of the adaptive generalized synchronization are presented to prove the correctness and effectiveness of the proposed method.

Device solutions to scientific computing

A memristor-based system can solve partial differential equations with better energy efficiency than methods based on conventional computers.

Stabilization and destabilization of nonlinear systems via intermittent stochastic noise with application to memristor-based system

This paper considers the stabilization and destabilization of a given nonlinear system by an intermittent Brownian noise perturbation. We give some distinct conditions and conclusions on almost sure exponential stability and instability, which are related to the control period T and the noise width δ. These results are then exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system. Two numerical examples are presented to illustrate the theoretical results.

Optogenetics-Inspired Tunable Synaptic Functions in Memristors.

Two-terminal memristors with internal Ca2+-like dynamics can be used to faithfully emulate biological synaptic functions and have been intensively studied for neural network implementations. Inspired by the optogenetic technique that utilizes light to tune the Ca2+ dynamics and subsequently the synaptic plasticity, we develop a CH3NH3PbI3 (MAPbI3)-based memristor that exhibits light-tunable synaptic behaviors. Specifically, we show that by increasing the formation energy of iodine vacancy (VI·/VI×), light illumination can be used to control the VI·/VI× generation and annihilation dynamics, resembling light-controlled Ca2+ influx in biological synapses. We demonstrate that the memory formation and memory loss behaviors in the memristors can be modified by controlling the intensity and the wavelength of the illuminated light. Coincidence detection of electrical and light stimulations is also implemented in the memristive device with real-time (≤20 ms) response to light illumination. These results open options to modify the synaptic plasticity effects in memristor-based neuromorphic systems and can lead to the development of electronic systems that can faithfully emulate diverse biological processes.

Sandwich synchronization of memristor-based hyperchaos systems with time delays

In this paper, a memristor-based hyperchaotic system is introduced. Considering time delays between the drive system and the response system in the process of synchronization, this paper designs one kind of flexible sandwich controller, which includes a rest in the sandwich structure, to realize the synchronization between two memristor-based hyperchaotic systems. Based on Lyapunov stability theory, matrix inequality, sandwich control and considering time delays, the exponential synchronization conditions for the memristor-based hyperchaotic systems with time delays via sandwich control are given. Finally, simulation results are displayed to verify the effectiveness and feasibility of this method.

Parasitic Effect Analysis in Memristor-Array-Based Neuromorphic Systems

Neuromorphic systems using memristors as artificial synapses have attracted broad interest for energy-efficient computing applications. However, networks based on these purely passive devices can be affected by parasitic effects such as series resistance and sneak path problems. Here, we analyze the effects of parasitic factors on the performance of memristor-based neuromorphic systems. During vector-array multiplication, the line resistance can cause significant distortion of the output current and the activity of the corresponding neurons. An approach to compensate the line resistance effects based on an approximate model consisting of only few known parameters is proposed and shows excellent ability to capture the complex network behavior. During training and feature detection, the series resistance can cause significant degradation of the learned dictionary, with only a few dominant neurons being trained. Using a scaling factor based on the proposed simple model, these effects can be successfully mitigated, and the correct network operations can be restored. These results provide insight and practical measures on the parasitic effects for implementation of the neuromorphic system using memristor arrays.

Memristor-based multi-scroll chaotic system and its pulse synchronization control

The memristor is a nonlinear element and intrinsically possesses memory function. When it works as nonlinear part of a chaotic system, the complexity and the randomness of signal will be enhanced. In this paper memristor is introduced into a three-dimensional chaotic system based on the augmented L system. The interesting and promising behaviors of complex single, double and four-scroll chaotic attractors generated only by varying a parameter have not been reported in memristive chaotic system and thus they deserve to be further investigated. It is also obvious that such a simple change of one parameter could be used to generate a variety of quite complex attractors. Therefore, as a nonlinear device the memristor plays an important role in this system. Firstly, some basic dynamical properties of the memristive chaotic system, including symmetry and in-variance, the existence of attractor, equilibrium, and stability are investigated in detail. By numerically simulating the power spectrum, Lyapunov exponent, Poincare map and bifurcation diagram, in this paper we verify that the proposed system has abundant dynamical behaviors. The sensitivities of system parameters to the chaotic behaviors are further explored by calculating, in detail, its Lyapunov exponent spectrum and bifurcation diagrams. The results of simulation and experiment are in good agreement, thereby proving the veracity of analysis. The memristive chaotic circuit is designed using the memristor, operational amplifier, analog multiplier and other conventional components. The circuit implementation of the memristive system is simulated using SPICE (simulation program with integrated circuit emphasis). The SPICE simulation results and the theoretical analysis are found to be in good agreement, and thus verifying that the system can produce chaos. Pulse synchronization has the following characteristics: low energy consumption, fast synchronization and easy-to-implement single-channel transmission. Therefore, it is more practical in chaotic secure communication. Subsequently the pulse chaos synchronization is realized from the perspective of the maximum Lyapunov exponent, and numerical simulations show the existence of new memristive chaotic system and the feasibility of pulse synchronization control, and also provide an experimental basis for further studying the applications of the memristive chaotic system in voice secure communication and information processing.

The future of electronics based on memristive systems

A memristor is a resistive device with an inherent memory. The theoretical concept of a memristor was connected to physically measured devices in 2008 and since then there has been rapid progress in the development of such devices, leading to a series of recent demonstrations of memristor-based neuromorphic hardware systems. Here, we evaluate the state of the art in memristor-based electronics and explore where the future of the field lies. We highlight three areas of potential technological impact: on-chip memory and storage, biologically inspired computing and general-purpose in-memory computing. We analyse the challenges, and possible solutions, associated with scaling the systems up for practical applications, and consider the benefits of scaling the devices down in terms of geometry and also in terms of obtaining fundamental control of the atomic-level dynamics. Finally, we discuss the ways we believe biology will continue to provide guiding principles for device innovation and system optimization in the field. This Perspective evaluates the state of the art in memristor-based electronics and explores the future development of such devices in on-chip memory, biologically inspired computing and general-purpose in-memory computing.

Formula omitted]th moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô’s differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy–Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results.

Chaos and Hopf bifurcation control in a fractional-order memristor-based chaotic system with time delay

In this paper, a time-delayed feedback controller is proposed in order to control chaos and Hopf bifurcation in a fractional-order memristor-based chaotic system with time delay. The associated characteristic equation is established by regarding the time delay as a bifurcation parameter. A set of conditions which ensure the existence of the Hopf bifurcation are gained by analyzing the corresponding characteristic equation. Then, we discuss the influence of feedback gain on the critical value of fractional order and time delay in the controlled system. Theoretical analysis shows that the controller is effective in delaying the Hopf bifurcation critical value via decreasing the feedback gain. Finally, some numerical simulations are presented to prove the validity of our theoretical analysis and confirm that the time-delayed feedback controller is valid in controlling chaos and Hopf bifurcation in the fractional-order memristor-based system.

Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria

Memristor-based nonlinear dynamical system easily presents the initial condition-dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors, which has been received much attention in recent years. By introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting memristor-based chaotic system with hypogenetic jerk equation and circuit forms is proposed. The most striking feature is that this system has four line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. Stability of these line equilibria are analyzed, and coexisting infinitely many attractors’ behaviors with the variations of the initial conditions are investigated by bifurcation diagrams, Lyapunov exponent spectra, attraction basins, and phased portraits, upon which the forming mechanism of extreme multistablity in the memristor-based hypogenetic jerk system is explored. Specially, unusual transition behavior of long term transient period with steady chaos, completely different from the phenomenon of transient chaos, can be also found for some initial conditions. Moreover, a hardware circuit is design and fabricated and its experimental results effectively verify the truth of extreme multistablity.