Active Memristor Research Articles

Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit

A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincare maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.

On the Existence of Limit Cycles and Relaxation Oscillations in a 3D van der Pol-like Memristor Oscillator

We study a van der Pol-like memristor oscillator, obtained by substituting a Chua’s diode with an active controlled memristor in a van der Pol oscillator with Chua’s diode. The mathematical model for the studied circuit is given by a three-dimensional piecewise linear system of ordinary differential equations, depending on five parameters. We show that this system has a line of equilibria given by the [Formula: see text]-axis and the phase space [Formula: see text] is foliated by invariant planes transverse to this line, which implies that the dynamics is essentially two-dimensional. We also show that in each of these invariant planes may occur limit cycles and relaxation oscillations (that is, nonsinusoidal repetitive (periodic) solutions), depending on the parameter values. Hence, the oscillator studied here, constructed with a memristor, is also a relaxation oscillator, as the original van der Pol oscillator, although with a main difference: in the case of the memristor oscillator, an infinity of oscillations are produced, one in each invariant plane, depending on the initial condition considered. We also give conditions for the nonexistence of oscillations, depending on the position of the invariant planes in the phase space.

Chua Corsage Memristor: Phase Portraits, Basin of Attraction, and Coexisting Pinched Hysteresis Loops

The Chua Corsage Memristor is the simplest example of a passive but locally active memristor endowed with two asymptotically stable equilibrium points [Formula: see text] and [Formula: see text] when powered by an E-volt battery, where [Formula: see text]. The basin of attraction is defined by [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text], [Formula: see text] for [Formula: see text]. By adding an inductor of appropriate value [Formula: see text] in series with the battery, the resulting circuit undergoes a supercritical Hopf bifurcation and becomes an oscillator for [Formula: see text]. Applying a sinusoidal voltage source [Formula: see text] across the Chua corsage memristor, one finds two distinct coexisting stable periodic responses, depicted by their associated pinched hysteresis loops, of the same frequency [Formula: see text] whose basin of attraction is defined by [Formula: see text], and [Formula: see text], respectively, where [Formula: see text] depends on both amplitude A and frequency f. An in-depth and comprehensive analysis of the above global nonlinear phenomena is presented using tools from nonlinear circuit theory, such as Chua’s dynamic route method, and from nonlinear dynamics, such as phase portrait analysis and bifurcation theory.

Study of bifurcations and chaos in the Muthuswamy–Chua system

The dynamical behavior of an autonomous simplest electronic circuit that consists of three elements connected in series governed by three ordinary differential equations was investigated. The circuit elements are a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. Under variation of two parameters we observed a rich variety of bifurcation phenomena, including periodic, quasi-periodic, intermittent, and chaotic behaviors associated with this very simple nonlinear system. One and two-parameter bifurcation diagrams were studied. Route of period-doubling to chaos through different structures was observed. Our theoretical results are compared with the available experimental results and are found to be in good agreement with these results.

Scanning Probe Characterization of Memristors Based on a Li Intercalation Metal Oxide

Memristor devices are a promising technology to replace CMOS for neuromorphic computing applications. As an alternative to filament-type memristors that require ‘forming’ procedures and which typically exhibit binary ‘on/off’ switching, we are investigating memristors based on a Li ion intercalation oxide LixCoO2. Our devices are composed of simple structures consisting of LixCoO2 films on insulating substrates with top or bottom contacts of Au. The electronic conductivity of the LixCoO2 film strongly depends on the Li-ion concentration and can exhibit synaptic multilevel analog states. However, determining the precise physical mechanisms that give rise to resistive states within a working device remains a challenge. This challenge arises because bulk characterization techniques (i.e. electrochemical impedance spectroscopy (EIS)) can be insensitive to the details of the materials microstructure that are critical to the device behavior. Scanning probe microscopy offers an attractive route to overcome these limitations in order to better understand transport at interfaces and along nanometer length scales. Here, we have carried out in operando Kelvin probe force microscopy (KPFM) on active LixCoO2 memristor devices. Using KPFM, we have directly imaged the potential drops along the device and determined the resistance of the channel versus resistance at the electrode interfaces. By capturing the time evolution of the potential landscape, the ionic and electronic dynamics are separated and their interdependence is revealed. Localized changes in work function suggest regions of Li accumulation and depletion that are associated with particular resistive memory states. The insights we gain from these experiments will guide the fabrication of more complex memristor devices such as row-column addressable arrays.

An accurate locally active memristor model for S-type negative differential resistance in NbOx

A number of important commercial applications would benefit from the introduction of easily manufactured devices that exhibit current-controlled, or “S-type,” negative differential resistance (NDR). A leading example is emerging non-volatile memory based on crossbar array architectures. Due to the inherently linear current vs. voltage characteristics of candidate non-volatile memristor memory elements, individual memory cells in these crossbar arrays can be addressed only if a highly non-linear circuit element, termed a “selector,” is incorporated in the cell. Selectors based on a layer of niobium oxide sandwiched between two electrodes have been investigated by a number of groups because the NDR they exhibit provides a promisingly large non-linearity. We have developed a highly accurate compact dynamical model for their electrical conduction that shows that the NDR in these devices results from a thermal feedback mechanism. A series of electrothermal measurements and numerical simulations corroborate this model. These results reveal that the leakage currents can be minimized by thermally isolating the selector or by incorporating materials with larger activation energies for electron motion.

Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit

Multiple attractors can be found in many nonlinear dynamical system with multistability. Recently, experimental attractors with two stable saddle-foci were reported to find in a non-ideal active voltage-controlled memristor based Chua's circuit. In this paper we focus on the multiple attractors found in the proposed memristive Chua's circuit. Concretely, by numerical simulations of mathematical model, hardware circuit experiments and PSIM circuit simulations, multiple attractors with different initial states are revealed and with the dimensionless system equations, complex dynamics with different initial conditions are further discussed. Theoretical derivation results indicate that the normalized memristive Chua's system has two stable nonzero saddle-foci in globally adjusting normalized parameter region and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

Hopf Bifurcation and Chaos in Simplest Fractional-Order Memristor-based Electrical Circuit

In this article, we investigate the bifurcation and chaos in a simplest fractional-order memristor-based electrical circuit composed of only three circuit elements: a linear passive capacitor, a linear passive inductor and a non-linear active memristor with two-degree polynomial memristance and a second-order exponent internal state. It is shown that this fractional circuit can exhibit a drastically rich non-linear dynamics such as a Hopf bifurcation, coexistence of two, three and four limit cycles, double-scroll chaotic attractor, four-scroll chaotic attractor, coexistence of one (or two) chaotic attractor with one limit cycle and new chaotic attractor which is not observed in the integer case. Finally, the presence of chaos is confirmed by the application of the recently introduced 0–1 test.

Novel chaotic behavior in the Muthuswamy-Chua system using Chebyshev Polynomials

In this paper, three kinds of memristors with memristance functions obtained from the Chebyshev polynomials are used in the Muthuswamy-Chua system, which has only three circuit elements: a linear passive inductor, a linear passive capacitor and a nonlinear active memristor. We use multivariable second-order polynomial functions of current and memristor state for the internal state function of the memristor. This enables our system to generate not only double-scroll but also four-scroll attractors. Systematic studies of chaotic behavior in these systems are performed using phase portraits, bifurcation diagrams and Lyapunov exponents. Simulation results show that all these systems exhibit chaotic behavior over a range of control parameters. Copyright © 2014 John Wiley & Sons, Ltd.

Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial

In this paper, a memristor with a fourth degree polynomial memristance function is used in the simplest chaotic circuit which has only three circuit elements: a linear passive inductor, a linear passive capacitor, and a nonlinear active memristor. We use second order exponent internal state memristor function and fourth degree polynomial memristance function to increase complexity of the chaos. So, the system can generate double-scroll attractor and four-scroll attractor. Systematic studies of chaotic behavior in the integer-order and fractional-order systems are performed using phase portraits, bifurcation diagrams, Lyapunov exponents, and stability analysis. Simulation results show that both integer-order and fractional-order systems exhibit chaotic behavior over a range of control parameters.

Practical guide for validated memristance measurements

Chua [IEEE Trans. Circuit Theory 18, 507-519 (1971)] predicted rather simple charge-flux curves for active and passive memristors (short for memory resistors) and presented active memristor circuit realizations already in the 1970 s. The first passive memristor has been presented in 2008 [D. B. Strukov, G. S. Snider, and D. R. Williams, Nature (London) 453, 80-83 (2008)]. Typically, memristors are traced in complicated hysteretic current-voltage curves. Therefore, the true essence of many new memristive devices has not been discovered so far. Here, we give a practical guide on how to use normalized charge-flux curves for the prediction of hysteretic current-voltage characteristics of memristors. In the case of memristive BiFeO3 thin film capacitor structures, the normalized charge-flux curves superimpose for different numbers of measurement points Ns and a different measurement time per measurement point Ts. Such normalized charge-flux curves can be used for the prediction of current-voltage characteristics for input signals with arbitrarily chosen Ns and Ts.

Equivalent circuit analysis model of charge-controlled memristor and its circuit characteristics

Memristor realized physically is recently a basic two-terminal circuit element with memory property. Based on Taylor series form of φ-q relationship, a charge-controlled memristor equivalent circuit analysis model is built. A charge-controlled memristor model with cubic nonlinearity is taken, as an example, to make a theoretical analysis of circuit characteristics, such as voltage-current relationship, active-passive property, and so on, of the charge-controlled memristor with different parameters. Results indicate that the voltage-current relationship of the charge-controlled memristor has an italic “8” shaped hysteresis loop characteristic, and the charge-controlled memristor shows passivity and activity accompanied with the variations of parameter symbols, resulting in the occurrence of the corresponding variations of circuit characteristics; compared with the passive memristor, the active memristor is more suitable for use as a second harmonic signal generation circuit. An experiment circuit is built based on the equivalent circuit of the charge-controlled memristor characteristic analysis, and the experimental results well verify the theoretical analysis.

AUTOWAVES IN MEMRISTIVE CELLULAR NEURAL NETWORKS

Memristor has received a significant amount of attention after a solid state implementation of it was realized in the Hewlett–Packard laboratories, because of the potential applications of such device in different areas. In this brief paper, we introduce a Cellular Neural/Nonlinear Network based on memristive cells for autowave generation. The basic cell consists of a three-component circuit (the parallel of a capacitor, an inductor and an active memristor) and displays slow–fast dynamics. Such a circuit is then connected through passive resistors to other identical cells to form a reaction–diffusion system. Simulation results show that the system is able to generate autowaves and open the way to the study of other complex phenomena like spiral waves or pattern formation in memristive circuits.

Chaotic memristive circuit: equivalent circuit realization and dynamical analysis

In this paper, a practical equivalent circuit of an active flux-controlled memristor characterized by smooth piecewise-quadratic nonlinearity is designed and an experimental chaotic memristive circuit is implemented. The chaotic memristive circuit has an equilibrium set and its stability is dependent on the initial state of the memristor. The initial state-dependent and the circuit parameter-dependent dynamics of the chaotic memristive circuit are investigated via phase portraits, bifurcation diagrams and Lyapunov exponents. Both experimental and simulation results validate the proposed equivalent circuit realization of the active flux-controlled memristor.

A SIMPLE MEMRISTOR CHAOTIC CIRCUIT WITH COMPLEX DYNAMICS

A simple memristor-based chaotic circuit with an active flux-controlled memristor characterized by a smooth continuous cubic nonlinearity is designed. The proposed chaotic circuit can generate a 2-scroll chaotic attractor on a finite time scale and has an equilibrium set with its stability dependent on the initial state of the memristor. The complex dynamics of the proposed chaotic circuit under different initial state of the memristor are investigated both theoretically and numerically. In particular, some novel transient transition behaviors with different time scales are found in the memristor circuit. Experimental observations based on a universal circuit implementation platform are conducted to partially verify the numerical simulation results.

Analysis and implementation of memristor chaotic circuit

Memristor with memory function is the fourth fundamental two-terminal circuit element, besides resistor, capacitor and inductor. In this paper, a smooth flux-controlled memristor is described by a monotone-increasing nonlinearity curve in the -q plane, and it has an italic type 8 like voltage current relation curve that looks like a pinched hysteresis loop characteristics. By replacing Chua's diode with an active memristor consisting of a smooth flux-controlled memristor and a negative conductance, a memristor based chaotic oscillation is derived from Chua's circuit. Furthermore, the equivalent circuit implementation form for the active memristor is designed by utilizing conventional components such as operational amplifiers and multipliers. The results from theoretical analysis, numerical simulations and circuit simulations are completely identical with each other, and demonstrate that the dynamical behaviors of the memristor chaotic circuit are dependent on the memristor initial state, showing different orbits such as chaotic oscillation, periodic oscillation and stable sink under different initial states.

SIMPLEST CHAOTIC CIRCUIT

A chaotic attractor has been observed with an autonomous circuit that uses only two energy-storage elements: a linear passive inductor and a linear passive capacitor. The other element is a nonlinear active memristor. Hence, the circuit has only three circuit elements in series. We discuss this circuit topology, show several attractors and illustrate local activity via the memristor's DC vM - iM characteristic.