Memristor Oscillator Research Articles

Approximate symmetry memristive mega-stable oscillator with attractor growing and its Hamilton energy balance

Approximate symmetry memristive mega-stable oscillator with attractor growing and its Hamilton energy balance

Chaos in a memristive oscillator with six lines of equilibria

Chaos in a memristive oscillator with six lines of equilibria

3–5 GHz FSK-OOK ultra wideband transmitter based on memristive ring oscillator

3–5 GHz FSK-OOK ultra wideband transmitter based on memristive ring oscillator

Edge of Chaos Theory Resolves Smale Paradox

No isolated system may ever support complexity. Emergent phenomena may however appear in an open system, if, as established by the Edge of Chaos theory, some of its constitutive elements feature the capability to amplify infinitesimal fluctuations in energy, provided an external source supplies them with a sufficient amount of DC power, which is known to be a signature for locally-active behaviour. In particular, complex behaviours, including static and dynamic pattern formation, may emerge in arrays of identical diffusively-coupled cells, if and only if the basic unit is poised on a particular sub-domain of the Local Activity regime, referred to as Edge of Chaos, within which a quiet state hides in fact a high degree of excitability. Here we show, for the first time, that these counterintuitive phenomena may emerge in a basic memristor cellular neural network, consisting of two identical diffusively-coupled second-order cells. The proposed bio-inspired array represents the simplest ever-reported open system, which reproduces the shocking phenomenon, reported by Smale in 1974, when, while studying a model from cellular biology, he observed two identical reaction cells, “mathematically dead” on their own, pulsating together upon diffusive coupling. Impressively, the bio-inspired two-cell reaction-diffusion network contains only nine circuit elements, specifically two DC voltage sources, three linear resistors, two linear capacitors, and two functional niobium oxide (NbO) memristors from NaMLab. Applying the theory of Local Activity to an accurate model of the memristor oscillator, a comprehensive picture for its local and global dynamics may be drawn, providing a systematic method to tune the design parameters of the two-cell array to enable diffusion-driven instabilities therein.

Hamiltonian energy computation of a novel memristive mega-stable oscillator (MMO) with dissipative, conservative and repelled dynamics

Mega-stable oscillators with memristor have not been investigated in the literature up to now. In this contribution, a novel memristive mega-stable oscillator (MMO) with a plethora of properties is introduced. The originality of the introduced systems is that the 3D model exhibits mega-stability without external perturbation, which was not the case in most existing mega-stable models considered in the literature. The investigation of the volume contraction rate of the oscillator revealed that its processes dissipative, conservative, and repelled dynamics depending on the values of the bifurcation control parameter. The mega-stable nature of the investigated oscillator is characterized by the coexistence of attractors in a nested structure. In addition, the well-known Helmholtz theorem is used to determine the Hamiltonian energy used during the mechanism of the megastability. Finally, multiple coexisting mega-stable attractors are captured in Pspice simulations by configuring the initial conditions, further supporting the numerical results.

Oscillatory Circuits With a Real Non-Volatile Stanford Memristor Model

Stanford memristor model is a widely used model that accurately characterizes real non-volatile metal-oxide resistive random access memory (RRAM) devices with bipolar switching characteristics. The paper studies for the first time the dynamics and bifurcations in a class of nonlinear oscillators with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real non-volatile memristor devices</i> obeying Stanford model. This is in contrast with papers in the literature considering oscillators with ideal, abstract, or artificial memristor models, that are unable to describe physical memristors implemented in nanotechnology. One main new idea in the paper is to use the memristor as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">programmable nonlinear resistor</i> . Namely, two principal modes of operation are considered. 1) Analogue transient phase: the oscillator is designed so that in the transient oscillations the voltage on the memristor is below threshold, hence the main memristor state variable, i.e., the gap of the insulating material, is almost constant and the memristor behaves as a static nonlinear resistor. 2) Programming phase: the nonlinear characteristic of the memristor, which depends on the gap, can be changed via the application of voltages above threshold. The paper studies nonlinear oscillations in the transient phase for a fixed gap as well as the bifurcations phenomena displayed when the gap is varied. The paper also discusses the differences between the approach in the paper and those to design other memristor oscillators with non-volatile memristors.

Mutual Transformation of Flux-Controlled and Charge-Controlled Memristors

Two-ports for mutual transformation between flux-controlled memristors and charge-controlled memristors are proposed. Attention is paid to memristors with the region of negative differential memristance in the charge-flux constitutive relation, when such a transformation should be made carefully. Connections between this transformation, duality rules, and Chua&#x2019;s table of higher-order elements are described. The proposed transforming cells can be made up of commercially available integrated circuits. Their proper operation is demonstrated via simulations and lab experiments with memristive oscillators.

A new autonomous memristive megastable oscillator and its Hamiltonian-energy-dependent megastability.

Multistability is a special issue in nonlinear dynamics. In this paper, a three-dimensional autonomous memristive chaotic system is presented, with interesting multiple coexisting attractors in a nested structure observed, which indicates the megastability. Furthermore, the extreme event is investigated by local riddled basins. Based on Helmholtz's theorem, the average Hamiltonian energy with respect to initial-dependent dynamics is calculated and the energy transition explains the occurrence mechanisms of the megastability and the extreme event. Finally, by configuring initial conditions, multiple coexisting megastable attractors are captured in PSIM simulations and FPGA circuits, which validate the numerical results.

Nonlinear analysis and minimum L2-norm control in memcapacitor-based hyperchaotic system via online particle swarm optimization

Memristor and memcapacitor are two novel memristive devices. Memristive nonlinear elements behave like synapses in the nervous system. In this study, an original physical model of HP memristor is presented based on the movement of the boundary between the doped and undoped regions by causing the charged dopants to drift. Furthermore, a charge-controlled memcapacitor is used to design a novel hyperchaotic oscillator. It is found that the hyperchaotic oscillator, which is based on memristor and memcapacitor, can realize high-security data encryption. Then, the problem of controlling chaos is addressed in the proposed memcapacitor-based hyperchaotic memristor oscillator using a simple feedback control. Moreover, in this study, a novel approach is used to stabilize chaos using the L2–norm minimization method. The feedback control is applied to minimize the L2–norm of state variables as the cost function. An online particle swarm optimization (PSO) technique is developed to design the feedback control using L2–norm minimization. The sensitivity to initial condition is examined for different initial conditions. The proposed technique can be used for chaos stabilization in a complex dynamic system.

A memristive RLC oscillator dynamics applied to image encryption

One of the major challenges in chaos dynamics is the design of simple and realisable electronic circuits capable of complex dynamic behaviours. Our contribution studies the dynamics and implementation of a simple chaotic memristive RLC oscillator circuit of jerky type as well as its application in designing image cryptosystem. The proposed circuit consists of an operational amplifier and an RLC network, comprising a resistor, an inductor, and two capacitors. Considering the crucial role of symmetry in physical, chemical, biological, and mechanical systems, a voltage control memristor emulator is employed to induce symmetry in the proposed circuit. For the dynamic analysis, fourth-order differential equation with exponential nonlinearities is used. Furthermore, standard analysis tools such as Lyapunov spectrum, bifurcation analysis, and phase space trajectories are employed. The phase space is magnetized using four symmetric attractors coexisting for the same set of parameters and different initial conditions indicate the symmetricity of the proposed system. Meanwhile, asymmetric attractor is capable of merging into one symmetric attractor through an attractor-merging bifurcation. Extensive experimental validations of these properties via PSPICE simulations and by using real electronic components are reported. Finally, the chaotic sequences emanating from the proposed oscillator are exploited to design an encryption algorithm that is subsequently validated via simulations and standard image security analysis with prominent outcomes in terms of very low encryption time (0.0746s for 128 × 128 colour image), mean entropy of 7.999 and mean NPCR of 99.62% just to name a few.

Implementation of Hodgkin-Huxley Neuron Model With the Novel Memristive Oscillator

In this brief, in order to simplify the implementation of the classical Hodgkin-Huxley neuron (HH) model, a novel floating memristor emulator is introduced, which consists of four electronic components and can be considered the simplest implementation in the existing literature. Firstly, the schematic diagrams of the proposed novel HH neuron-based memristive oscillator is presented, and the working mechanism and the bursting phenomenon of which are analyzed. Then, the simulation model of the proposed memristive oscillator emulator is developed in MULTISIM using several off-the-shelf components, which is used to implement a HH neuron model. Moreover, the electrical characteristics of it are examined. In particular, the relationship between the ion channels concentration and the variable voltages of the neuron model is described in detail. Simulation results confirm that the proposed model demonstrates rich bursting oscillation behaviors which is more suitable for simulating the giant squid axon compared to the existing model in the literature, which can be utilized to transmit the neuron information and establish the neural network.

Double memristors oscillator with hidden stacked attractors and its multi-transient and multistability analysis

Abstract In this paper, by replacing the two linear resistors in the RLC oscillator with flux-controlled and charge-controlled memristors, a novel double memristors nonlinear circuit system is proposed. From the oscillator circuit, we established the mathematical model of the system and proved that it is a hidden system without equilibrium. The numerical simulation results of the mathematical model are consistent with the circuit. What is more, we also find that one state variable of the system has the typical slow change behavior, which is reflected in the form of step-like or square-like waves, thus forming a novel stacked attractor. Then, through studying the Poincare map, phase diagram, bifurcation diagram, Lyapunov exponents (LEs), it was proved that the system has multi-transient behaviors such as chaos to another chaos, chaos to period, chaos to quasi-period, quasi-period to period. Besides, the memristive oscillator has quasi-periodic multistability when changing the initial values, which is a rare phenomenon for a chaotic system. These findings indicate that the proposed memristive hidden oscillator has complex nonlinear dynamic characteristics. Finally, the Digital Signal Processing (DSP) hardware platform confirms the physical realizability of the oscillator, offering the possibility of engineering applications.

Blinking Networks of Memristor Oscillatory Circuits in the Flux-Charge Domain.

Multistability phenomena and complex nonlinear dynamics in memristor oscillators pave the way to obtain efficient solutions to optimization problems by means of novel computational architectures based on the interconnection of single–device oscillators. It is well-known that topological properties of interconnections permit to control synchronization and spatio–temporal patterns in oscillatory networks. When the interconnections can change in time with a given probability to connect two oscillators, the whole network acts as a complex network with blinking couplings. The work of has shown that a particular class of blinking complex networks are able to completely synchronize in a faster fashion with respect to other coupling strategies. This work focuses on the specific class of blinking complex networks made of Memristor–based Oscillatory Circuits (MOCs). By exploiting the recent Flux–Charge Analysis Method, we make clear that synchronization phenomena in blinking networks of memristor oscillators having stochastic couplings, i.e., Blinking Memristor Oscillatory Networks (BMONs), correspond to global periodic oscillations on invariant manifolds and the effect of a blinking link is to shift the nonlinear dynamics through the infinite (invariant) manifolds. Numerical simulations performed on MOCs prove that synchronization phenomena can be controlled just by changing the coupling amongst them.

Symmetry and asymmetry induced dynamics in a memristive twin-T circuit

ABSTRACT The dynamics of memristor–based chaotic oscillators with perfect symmetry is very well documented. However, the literature is relatively poor concerning the behaviour of such types of circuits when their symmetry is perturbed. In this paper, we consider the dynamics of a memristive twin-T oscillator . Here, the symmetry is broken by assuming a memristor with an asymmetric pinched hysteresis loop characteristics. A variable disturbance term is introduced into the current-voltage relationship of the memristor in order to obtain an asymmetric characteristic. Phase portraits, bifurcations, basins of attraction, and Lyapunov exponents are used to illustrate various nonlinear patterns experienced by the underlined memristive circuit. It is shown that in the absence of the disturbance term, the characteristic of the memristor is perfectly symmetric which induces typical behaviours such as coexisting symmetric bifurcation and bubbles, spontaneous symmetry-breaking, symmetry recovering, and coexistence of several pairs of mutually symmetric attractors. With the perturbation term, the symmetry of the oscillator is destroyed resulting in more complex nonlinear phenomena such as coexisting asymmetric bubbles of bifurcation, critical transitions, and multiple coexisting (i.e. up to five) asymmetric attractors. Also, PSpice simulation studies confirm well the results of theoretical predictions.

Bifurcation set for a disregarded Bogdanov-Takens unfolding: Application to 3D cubic memristor oscillators

Motivated by the dynamical analysis of certain memristor-based oscillators, in this paper we derive the bifurcation set for a three-parametric Bogdanov-Takens unfolding that has not been previously considered in the literature (the saddle-focus-saddle case). By using several first-order Melnikov functions, we obtain for the first time analytical approximations for the bifurcation curves corresponding to homoclinic and heteroclinic connections, which along with the curves associated to local bifurcations organize the parametric regions with different qualitative phase planes. Our interest is the study of a family of 3D memristor oscillators, whose memristor characteristic function is a cubic polynomial. We show that these systems have a first integral; thus, after reducing the problem in one dimension, we can take advantage of the bifurcation set previously obtained. For a certain parameter region, the existence of closed surfaces completely foliated by periodic orbits in the original three-dimensional setting is shown. Additionally, we clarify some misconceptions that arise from the numerical simulations of these systems, emphasizing the important role played by the invariant manifolds associated to the involved first integral.

Resonance synchronisation between memristive oscillators and network without variable coupling

Continuous energy pumping and exchange along the coupling channel can balance the energy release between nonlinear oscillators for reaching complete synchronisation. When external stimulus is applied, energy is injected and encoded for regulating the dynamics of nonlinear oscillators and circuits. In this paper, the synchronisation between memristive Rossler oscillators is investigated by reactivating one memristive variable, and external stimuli are changed to detect the occurrence of synchronisation without direct variable coupling. In the presence of periodical stimulus, stochastic switch and feedback on the memristive variable can induce synchronisation between two memristive oscillators and chain network composed of memristive oscillators. In the presence of noise, stochastic feedback and disturbance on the memristive variable can keep synchronisation stable between two oscillators, and complete synchronisation is realised. In addition, the synchronisation factor and spatial patterns are calculated to confirm the occurrence of synchronisation between more chaotic oscillators when memristive function is activated even when no coupling channels are switched on.

On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control

Abstract In the present paper, for the first time, we propose a variable-order hyperchaotic system for information security. Firstly, we study the dynamical behaviors of a memristor oscillator through well-known numerical and analytical tools, such as the Lyapunov exponents, stability of equilibria, and bifurcation diagram. Then as an engineering application, a variable-order fractional version of the system is proposed for sound encryption. In comparison with integer and conventional constant fractional-order chaotic memristor oscillator, the proposed variable-order fractional system shows more complex characteristics and more degrees of freedom due to the existence of time-varying fractional derivatives. Thus, the proposed system is an appropriate choice for data transmission and information security. To illustrate the proper performance of the suggested system for encryption purposes, sound encryption is successfully performed, and its excellent results are demonstrated. The predictor-corrector method is utilized for numerical simulation. Then, a new type-2 fuzzy disturbance observer-based robust control is offered for synchronization of the variable-order hyperchaotic system. The stability and convergence of the disturbance estimator and closed-loop system are proven. Lastly, the synchronization results, which confirm the appropriate performance of the proposed method in the presence of the external disturbances, are demonstrated.

Hamiltonian Energy Computation of a Novel Memristive Mega-Stable Oscillator (MMO) with Dissipative, Conservative and Repelled Dynamics

Hamiltonian Energy Computation of a Novel Memristive Mega-Stable Oscillator (MMO) with Dissipative, Conservative and Repelled Dynamics

Reservoir Computing Using Complex Systems

Reservoir Computing is an emerging machine learning framework which is a versatile option for utilising physical systems for computation. In this paper, we demonstrate how a single node reservoir, made of a simple electronic circuit, can be employed for computation and explore the available options to improve the computational capability of the physical reservoirs. We build a reservoir computing system using a memristive chaotic oscillator as the reservoir. We choose two of the available hyperparameters to find the optimal working regime for the reservoir, resulting in two reservoir versions. We compare the performance of both the reservoirs in a set of three non-temporal tasks: approximating two non-chaotic polynomials and a chaotic trajectory of the Lorenz time series. We also demonstrate how the dynamics of the physical system plays a direct role in the reservoir's hyperparameters and hence in the reservoir's prediction ability.

A memristive chaotic oscillator with controllable amplitude and frequency

Abstract Broadband frequency property of chaos stands in the way of application. Internal parameter of a memristor leaves a new opportunity for easy amplitude/frequency control. Based on a variable-boostable chaotic system, such an amplitude-frequency controllable chaotic system is derived, which exhibits relatively robust chaotic oscillation compared with other multistable memristive systems. Furthermore, the controllable chaotic system gives a symmetric pair of oscillations, which finally merges to be a single symmetric one. Circuit experiment based on STM32 agrees well with the systematic analysis and numerical simulation.