Memristive Diode Research Articles

Dynamical Analysis of a Memristive Chua’s Oscillator Circuit

In this work, a novel memristive Chua’s oscillator circuit is presented. In the proposed circuit, a linear negative resistor, which is parallel coupled with a first-order memristive diode bridge, is used instead of the well-known Chua’s diode. Following this, an extensive theoretical and dynamical analysis of the circuit is conducted. This involves numerical computations of the system’s phase portraits, bifurcation diagrams, Lyapunov exponents, and continuation diagrams. A comprehensive comparison is made between the numerical simulations and the circuit’s simulations performed in Multisim. The analysis reveals a range of intriguing phenomena, including the route to chaos through a period-doubling sequence, antimonotonicity, and coexisting attractors, all of which are corroborated by the circuit’s simulation in Multisim.

On the dynamics of a new memristive diode emulator-based Chua’s circuit

The study of nonlinear systems has been the subject of numerous publications. When controlling the symmetry of chaotic oscillators, it has been observed that the symmetrical structure of the diode-bridge memristive emulators is continuously modified to break the symmetry of its current–voltage characteristic. This allows the nature of the symmetry of the oscillator in which they are incorporated to be influenced. In this paper, we present a simple memristive emulator based on simple electronic elements. This new emulator enables a simplified symmetry control method. By varying a control resistor, we modify the symmetry of the current–voltage characteristic of the memristor emulator and thus the symmetry of Chua oscillator in which it is incorporated as nonlinear component. Using dynamical systems analysis tools such as bifurcation diagrams and Lyapunov spectra, we describe how by simply varying a control parameter the symmetry is gradually broken. We highlight striking dynamic properties such as the coexistence of multiple symmetric and asymmetric oscillations and antimonotone bifurcations as well. Laboratory experimental studies are carried out to support the theoretically obtained results.

Diverse Bursting Oscillations in an Asymmetric Memristive Sallen-Key Filter

The asymmetric memristive diode bridge-based the Sallen-Key Filter (AMSKF) achieved by introducing an asymmetry diode bridge connected with a capacitor and an inductor to the Sallen-Key Filter, is studied in this paper. Through the analysis of equilibrium point, the stability of the circuit is discussed. Combined with the bifurcation diagram, it can be seen that the negative feedback gain of the Sallen-Key Filter greatly affects the dynamics of the circuit. Diverse dynamic behaviors are discovered by means of phase portraits and Lyapunov exponents, which include six types of typical oscillating behaviors: Period, Quasi-period, Quasi-periodic bursting, Period-2 bursting, Chaotic bursting and Period-1 bursting. Especially, bifurcation mechanisms of various bursting oscillating behaviors are researched by separating the formal equations into two parts, consisting of the fast spiking subsystem and the slow spiking subsystem, based on the fast-slow analysis method. Finally, Multisim experiments are carried out to validate the results of numerical simulations. Compared with the Sallen-Key Filter cascaded with the symmetric memristive diode bridge, bursting oscillating behaviors with larger amplitude and wider periodic range are obtained.

Dynamical behaviors of a chaotic jerk circuit based on a novel memristive diode emulator with a smooth symmetry control

This paper presents a new chaotic memristive circuit, which is derived from the autonomous jerk circuit by replacing the first-order generalized memristive diode bridge with a simple second-order memristive emulator, which consists of six elementary electronic elements. This second-order memristive emulator model addresses the problem of changing the configuration of the diode-bridge memristor model when used for symmetry control of chaotic systems. It also allows to reduce the gap between the experimental and the numerical simulations in that during the experimental, the symmetry breaking is done by a discrete modification of the number of diodes on the branches of the diode bridge, whereas during the numerical simulations, the variation of the symmetry control parameter corresponding to the number of diodes is continuous. Thus, a new memristor emulator consisting of two diodes, two resistors and two capacitors is developed and proposes a method of control by continuous variations of a potentiometer to perform symmetry breaking. Using tools for characterizing dynamic systems such as bifurcation diagrams, Lyapunov spectrum and phase portraits, to name just a few, it is shown how the new memristive emulator model can be used to check symmetry. The first major contribution of this work is the control of the symmetry of a jerk oscillator when the resistors of the memristive emulator take different values without modifying its structure. The second major contribution of this work is the ability to change the nature of an attractor as a function of its position in phase space without changing the nature of its associated symmetric attractor, which is demonstrated using phase portraits and initial condition diagrams. An electronic circuit is presented showing how symmetry control is achieved by varying a potentiometer. And an experimental study is performed to validate the results.

Dynamic analysis of a memristive diode bridge-based higher order autonomous Van der Pol-Duffing oscillator

Dynamic analysis of a memristive diode bridge-based higher order autonomous Van der Pol-Duffing oscillator

A memristive chaotic system with rich dynamical behavior and circuit implementation

In this paper, a novel four-dimensional autonomous chaotic system based on memristive diode bridge is presented, and it consists of a simple linear oscillation and a memristor. According to the mathematical model of the system, the equilibrium point is analyzed, and the phase portraits, time-domain sequences, bifurcation diagrams and Lyapunov exponent spectrums are numerically simulated. The rich dynamical behavior of proposed system is investigated. It includes multistability, offset boosting and chaotic bursting. In addition, the circuit simulation and Field-Programmable Gate Array (FPGA) hardware experiment are carried out to verify the feasibility of the system. Then the application of proposed system in chaotic image encryption is presented. By carrying out some security performance analyses, we show that the proposed system has good security performance.

Complex Dynamics in a Memristive Diode Bridge-Based MLC Circuit: Coexisting Attractors and Double-Transient Chaos

This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of multiple attractors and double-transient chaos. Also, period-doubling, chaos, crisis scenarios are observed in the system when varying the amplitude of the external excitation. Numerical simulation tools like phase portrait, cross-section basin of attraction, Lyapunov spectrum, bifurcation diagrams and time series are used to highlight the complex dynamical behaviors in the memristive system. Further, practical realizations of the circuit both in PSpice and real-laboratory measurements match well with the observed numerical simulations.

On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study

• This work addresses the dynamics of a generalized memristive diode bridge-based jerk circuit whose I − V characteristic symmetry can be varied. The main motivation of this work lies in the following three keys points: • To evaluate the effects of symmetry-breaking imperfections on the dynamics of the class of memristive circuits considered in this work; • To verify the predictions of the theoretical investigations by performing out laboratory experimental studies of the physical circuit; • To enrich the literature by highlighting new behaviors engendered in symmetric systems in general and the model considered in particular, in the presence of symmetry-breaking. It is widely accepted that for any physical system, symmetries are rarely exact. Therefore, some symmetry imperfections must be always assumed to be present. The dynamics of memristor-based chaotic circuits with symmetric hysteresis loop is well documented. However, only a few works are devoted to the dynamics of these types of circuits when the current-voltage characteristic of the considered memristor is no longer symmetrical. Accordingly, we consider in this work (as a case study) the dynamics of a generalized memristive diode-bridge-based jerk circuit whose symmetry can be varied. We denote by k the dissymmetry coefficient. The tools used for the analysis are the Routh-Hurwitz criterion, bifurcation diagrams, phase portraits, and basins of attraction. It is shown that in the symmetric configuration (i.e. when k = 1.0 ) there are three symmetric equilibria whereas in the asymmetric configuration (i.e. when k ≠ 1.0 ) we always have two equilibrium with fixed position in state space and a third one whose location varies according to the value of the dissymmetry coefficient. The intrinsic nonlinearity of the memristor is responsible for the plethora of nonlinear and complex behaviours observed in both configurations. These include the coexistence of symmetric and asymmetric attractors, coexisting symmetric and asymmetric bubbles of bifurcation, and symmetric and asymmetric double-scroll chaotic attractors, just to name a few. In addition, the experimental investigations agree well with the results of theoretical and numerical studies.

Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit

In this paper, a non-autonomous memristive FitzHugh-Nagumo (FHN) circuit is constructed using a second-order memristive diode bridge with LC network. For convenience of circuit implementation, an AC voltage source is adopted to substitute the original AC current stimulus. Stimulated by the slowly varying AC voltage source, the number, locations and stabilities of the equilibrium points slowly evolve with the time, which are thus indicated as the AC equilibrium points. Different sequences of fold and/or Hopf bifurcations are encountered in a full period of time series evolutions, leading to various kinds of chaotic or periodic bursting activities. To figure out the related bifurcation mechanisms, the fold and Hopf bifurcation sets are mathematically formulated to locate the critical bifurcation points. On this basis, the transitions between the resting and repetitive spiking states are clearly illustrated by the time series of the AC equilibrium points and state variables, from which Hopf/subHopf, Hopf/Hopf, and Hopf/fold bursting oscillations are identified in the specified parameter regions. Finally, based on a fabricated hardware circuit, the experimental measurements are executed. The results verify that the presented memristive FHN circuit indeed exhibits complex bursting activities, which enriches the family of memristor-based FHN circuits with bursting dynamics.

Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect

Abstract The design and analysis of simple autonomous memristive circuits are of great significance in theoretical research and practical application of complex dynamics. This paper designs a simple autonomous three-element-based memristive circuit with fast-slow effect, which is constructed by parallel connecting an active second-order memristive diode bridge with a parallel LC filter. The corresponding mathematical model is established, upon which stability analysis of the equilibrium point is performed by Routh–Hurwitz criterion. Theoretical derivation results indicate that the presented memristive circuit is always unstable, and then complex dynamical behaviors of period, chaos, quasi-period, and periodic bursting oscillation are numerically revealed through phase plane orbit, time-domain sequence, Lyapunov exponent spectrum and bifurcation diagram. In addition, bifurcation mechanisms of the periodic bursting behavior are further explored by fast-slow dynamics analysis, from which it can be found that the periodic bursting oscillation of the presented memristive circuit is a type of symmetric fold/Hopf cycle-cycle bursting oscillation. Especially, two types of dynamical behaviors of quasi-periodic oscillation and periodic bursting oscillation with a symmetric fold/Hopf cycle-cycle burster simultaneously appear in such a simple autonomous memristive circuit is amusing, which has never been reported in the previous literatures.

A new chaotic oscillator containing generalised memristor, single op-amp and RLC with chaos suppression and an application for the random number generation

In this paper, a new chaotic oscillator consists of a single op-amp, two capacitors, one resistor, one inductor, and memristive diode bridge cascaded with an inductor is proposed. The proposed chaotic oscillator has a line of equilibria. In the new oscillator circuit, negative feedback, i.e. inverting terminal of the op-amp is used, and the non-inverting terminal is grounded. The new oscillator has chaotic, periodic, quasi-periodic behaviours, as seen from the Lyapunov spectrum plots. Some more theoretical and numerical tools are used to present the dynamical behaviours of the new oscillator like bifurcation diagram, phase plot. Further, a non-singular terminal sliding mode control (N-TSMC) is designed for the suppression of the chaotic states of the new oscillator. An application of the new oscillator is shown by designing a chaos-based random number generator. Raspberry Pi 3 is used for the realisation of the random number generator.

Extremely slow passages in low-pass filter-based memristive oscillator

Slow passage effect in a nonlinear dynamical system commonly generates a delay in the bifurcation point, which can cause an uncertainty in the prediction of dynamics around the bifurcation point. This paper presents a simple memristive oscillator achieved by linking a second-order memristive diode bridge to the in-phase input of a Sallen-Key low-pass filter (LPF). The dynamics of the simple memristive oscillator highly depends on the negative feedback gain of the LPF. Abundant dynamical behaviors are revealed, which mainly include two types of oscillating behaviors: general periodic and quasi-periodic oscillations as well as special periodic, quasi-periodic, chaotic and chaotic 2-torus bursting oscillations. Particularly, an interesting phenomenon of extremely slow passage is found in these bursting oscillations. Through constructing Hopf bifurcation set of the fast spiking subsystem, bifurcation mechanisms of various bursting oscillating behaviors with such extremely slow passages are explored. In addition, Multisim simulations and circuit experiments are performed to validate the numerical simulations.

Bursting oscillations and coexisting attractors in a simple memristor-capacitor-based chaotic circuit

The design and analysis of a simple autonomous memristive chaotic circuit are important in theoretical, numerical, and experimental demonstrations of complex dynamics. In this paper, a simple autonomous memristive circuit is implemented, which only consists of an active second-order memristive diode bridge and a capacitor. Based on the available circuit, the mathematical model is established and its symmetry, dissipativity, and equilibrium stability are analyzed. Numerical simulations show that the proposed circuit exhibits complex behaviors of unipolar periodic and chaotic bursting oscillations along with coexisting attractors. It is worth noting that the circuit exhibits such a special bursting behavior previously unobserved in third-order autonomous memristive circuits. Moreover, spectral entropy complexities are calculated to provide an intuitive and effectual method for the circuit parameter configurations. The circuit simulations and hardware experiments verify the theoretical analyses and numerical simulations.

Addressing the sneak-path problem in crossbar RRAM devices using memristor-based one Schottky diode-one resistor array

Abstract Resistive random access memories (RRAMs) are favorable contenders in the race towards future technologies. Moreover, the desirable properties of memristor-based RRAM devices make them very good competitors in this field. The sneak paths problem poses one of the main difficulties in the construction of crossbar memory devices. This problem can be effectively suppressed by applying the 1diode-1resistor (1D1R) design structure. The Schottky diode has many advantages compared to the PN junction diode. The low-power (∼1 µW) ZnO active-layered thin-film (60 nm thick) one Schottky diode-one memristor device fabricated in this study included a top Ag electrode and a bottom Al electrode. The material makeup of the device was confirmed via energy dispersive X-ray spectroscopy (EDAX). The memristive and Schottky diode characteristics of the Ag/ZnO/Al device were resolved by measuring the time-dependent voltage/current. The characteristic pinched hysteresis memristive loops were observed at the first quadrant of the current-voltage plane, whereas the diode curves were seen at the third quadrant. Using the current-voltage curves, the height of the Schottky barrier, ideality factor and threshold voltage of the Schottky diode were found to be 0.68 eV, 3.75 and 0.49 V, respectively. After physical implementation and characterization of the one diode-one memristor device, its anti-crosstalk characteristics were investigated. Taking into account the 10% read margin, the maximum crossbar size was found to be 87.

Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit

In this paper, a new memristive diode bridge-based RC hyperjerk circuit is proposed. This new memristive hyperjerk oscillator (MHO) is obtained from the autonomous 4-D hyperjerk circuit (Leutcho et al. in Chaos Solitons Fractals 107:67–87, 2018) by replacing the nonlinear component (formed by two antiparallel diodes) with a first order memristive diode bridge. The circuit is described by a fifth-order continuous time autonomous (‘elegant’) hyperjerk system with smooth nonlinearities. The dynamics of the system is investigated in terms of equilibrium points and stability, phase portraits, bifurcation diagrams and two-parameter Lyapunov exponents diagrams. The numerical analysis of the model reveals interesting behaviors such as period-doubling, chaos, offset boosting, symmetry recovering crisis, antimonotonicity (i.e. concurrent creation and destruction of periodic orbits) and several coexisting bifurcations as well. One of the most attractive features of the new MHO considered in this work is the presence of several coexisting attractors (e.g. coexistence of two, three, four, five, six, seven, or nine attractors) for some suitable sets of system parameters, depending on the choice of initial conditions. Accordingly, the distribution of initial conditions related to each coexisting attractor is computed to highlight different basins of attraction. Laboratory experimental measurements are carried out to verify the theoretical analysis.

Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.

Crisis‐induced coexisting multiple attractors in a second‐order nonautonomous memristive diode bridge‐based circuit

SummaryThis paper reports a second‐order nonautonomous memristive diode bridge‐based circuit, upon which a system model is established. The AC and DC equilibrium points and their stability evolutions are theoretically analyzed, and the mechanisms of complex dynamical behaviors are explored in detail. Furthermore, the stimulus‐dependent dynamical behaviors are numerically performed by the single‐parameter bifurcation diagrams, Lyapunov exponents, and phase portraits. Of particular concern, it should be highly emphasized that multiple kinds of crisis scenarios associated with the initial conditions are found in a specified parameter region, resulting in that coexisting multiple attractors under different initial conditions are discovered for the fixed system parameters. Additionally, hardware experiments and PSpice circuit simulations are used to confirm the numerically simulated results.

Coexistence of multiple bifurcation modes in memristive diode-bridge-based canonical Chua’s circuit

ABSTRACTBased on a memristive diode bridge cascaded with series resistor and inductor filter, a modified memristive canonical Chua’s circuit is presented in this paper. With the modelling of the memristive circuit, a normalised system model is built. Stability analyses of the equilibrium points are performed and bifurcation behaviours are investigated by numerical simulations and hardware experiments. Most extraordinary in the memristive circuit is that within a parameter region, coexisting phenomenon of multiple bifurcation modes is emerged under six sets of different initial values, resulting in the coexistence of four sets of topologically different and disconnected attractors. These coexisting attractors are easily captured by repeatedly switching on and off the circuit power supplies, which well verify the numerical simulations.

Uncertain destination dynamics of a novel memristive 4D autonomous system

This paper studies the dynamics of a novel memristive 4D autonomous system obtained by replacing the memristive diode bridge in the original circuit of [Chaos, Solitons and Fractals 91 180–197 (2016)] with a flux control memristor. The new memristor oscillator is described by a continuous time four-dimensional autonomous system with a line of equilibria. The analysis is carried out in terms of its parameters by using bifurcation diagrams, phase space trajectory plots, Poincaré sections, bifurcation like sequences, and graphs of Lyapunov exponents. The system is shown to experience the unusual phenomenon of extreme multistability characterized by the possibility of an infinite number of attractors for the same parameters setting. Period doubling and symmetry restoring crisis scenarios are reported. To the best of the authors’ knowledge, the results of this work represent the first report on the phenomenon of extreme multistability in a jerk system and thus deserve dissemination.

Complementary memristive diode cells for the memory matrix of a neuromorphic processor

This research covers the sphere of neuromorphic electronics, with a new memory cell developed. Its circuit design and topology is based on a complementary memristor, which is switched through a Zener diode. The above-mentioned cells can be implemented on-chip in the form of a parallel matrix or on-bit access type to a storage device in a neuromorphic processor. The suggested topology of a memristor-diode cell enables a high degree of integration in the case these cells get combined in a very large matrix. In this regard, all the square matrices are filled with memristor cells of a nanometric size. The rest of large elements are moved to the matrix periphery to vacate the specific square area of memristor technological placement. The cell under discussion implicates the parallel connection of electrical loads in the matrix related to simple memristor circuit crossbars since the total resistance of each cell always remains high, and the current resistance through complementary memristors is always minimal.