Generic Memristor Research Articles

Modeling Excitable Cells with Memristors

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.

Analytical Solutions for Charge and Flux in HP Ideal Generic Memristor Model With Joglekar and Prodromakis Window Functions

Analytical Solutions for Charge and Flux in HP Ideal Generic Memristor Model With Joglekar and Prodromakis Window Functions

Symmetry, Multistability and Antimonotonicity of a Shinriki Oscillator with Dual Memristors

In this paper, a type of modified dual memristive Shinriki oscillator is constructed with a flux-controlled absolute-type memristor and a voltage-controlled generic memristor, and the proposed oscillator with abundant dynamical behaviors, including the multistability and antimonotonicity, is comprehensively studied through dynamical distribution graphs, bifurcation diagrams, Lyapunov exponents and phase portraits. It is found that the passive/active state of memristor, which means different characteristics in the [Formula: see text]–[Formula: see text] domain with positive and negative parameters of the elements, can affect the state of the oscillator. For example, if the memristor is active, the oscillator will change more frequently in the multistable region. Also, it is noted that, for inherent initial-related symmetry and circuit structures with duality, both phenomena have strong symmetric characteristics and opposite evolution trends modulated by values of corresponding components. Especially, the bubbles, which are symmetric about parameters with duality and own complex evolution laws, have rarely been explored in previous works. In addition, the memristive oscillator is modularized based on field programmable gate array (FPGA) technology, and the multiple coexisting attractors are captured, which verifies the accuracy of the numerical results.

Simple cyclic memristive neural networks with coexisting attractors and large-scale amplitude control.

The memristor's unique memory function and non-volatile nature make it an ideal electronic bionic device for artificial neural synapses. This paper aims to construct a class of memristive neural networks (MNNs) with a simple circular connection relationship and complex dynamics by introducing a generic memristor as synapse. For placing the memristive synapse in different coupling positions, three MNNs with the same coupling cyclic connection are yielded. One remarkable feature of the proposed MNNs is that they can yield complex dynamics, in particular, abundant coexisting attractors and large-scale parameter-relied amplitude control, by comparing with some existing MNNs. Taking one of the MNNs as an example, the complex dynamics (including chaos, period-doubling bifurcation, symmetric coexisting attractors, large-scale amplitude control) and circuit implementation are studied . The number of equilibria and their stabilities are discussed. The parameter-relied dynamic evolution and the coexisting attractors are numerically shown by using bifurcations and phase portraits. A microcontroller-based hardware circuit is given to realize the network, which verifies the correctness of the numerical results and experimental results.

Shortcuts to Edge-of-Chaos Domains of Memristive Circuits and Historic Measurement of Contiguous Triple-Branch V – I Curve of Chua Corsage Memristor

Locally-active memristors blessed with an edge-of-chaos domain, which can be destabilized for generating action potentials, are natural candidates for emulating biological neurons. Pinpointing the edge-of-chaos domain, where neuromorphic behaviors may occur, is important for studying neuromorphic dynamics of memristors. This paper proposes a short-cut method for locating the edge-of-chaos domains in two kinds of generic memristors, and in several typical memristive 1-port circuits using only the Jacobian matrix in terms of their equations. Taking the Chua Corsage Memristor (CCM) and several CCM-based memristive 1-port circuits as examples, we verify the proposed new methods, and calculates their edge-of-chaos domains. Also, we carry out a complete classification of all the parameter regions of the CCM and several CCM-based memristive 1-port circuits, namely the locally-passive, locally-active but unstable, and edge-of-chaos domains, under both voltage and frequency control. Near the calculated edge-of-chaos domain, we uncover some new neuromorphic behaviors. To confirm the physical interpretations and predictions of the edge-of-chaos theorem, this paper presents an inexpensive electronic circuit realization of the complete set of equations defining the CCM using only off-the-shelf circuit components. When this poor-man’s memristor is connected to various linear passive R, L, C circuits, and a battery, the resulting circuit can be tuned to generate action potentials, and a garden variety of neuromorphic phenomena, including chaos. But the highlight of this paper is reserved for the CCM itself where the world’s first oscilloscope picture of a contiguous self-intersecting triple-branch DC V–I curve of the CCM is displayed in real time.

Edge of Chaos Kernel and neuromorphic dynamics of a locally-active memristor

Edge of Chaos Kernel (EOCK), the crown jewel of edge of chaos, is a nature’s optimal mechanism for creating action potentials, which can be exploited to uncover the neuromorphic dynamics of memristors. A memristor blessed with an EOCK, which can emulate the neuromorphic behaviors of biological neurons, is a natural candidate to be applied in neuromorphic computing. This paper proves that a first-order memristor blessed with an EOCK has a pole in the open left half plane (LHP), and presents a simple method for testing if a generic voltage-controlled first-order memristor has an EOCK using only its first-order Taylor series expansion coefficients. This paper presents, for the first time, that locally active voltage-controlled generic memristors contain an EOCK. Also, this paper designs a theoretical memristor model blessed with an EOCK, and constructs a memristive circuit for observing the relationship between the EOCK and neuromorphic behaviors. The memristor blessed with an EOCK generates some well-known neuromorphic behaviors, further verify the innate ability of Edge of Chaos Kernel to exhibit the complex phenomena. This paper pave the way towards further expounding the generating mechanism of the action potential from the perspective of circuit.

A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane

Memristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the [Formula: see text]-axis and the plane [Formula: see text], which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane [Formula: see text]. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane [Formula: see text], are bounded and cannot escape to infinity.

Convergence of a Class of Delayed Neural Networks with Real Memristor Devices

Neural networks with memristors are promising candidates to overcome the limitations of traditional von Neumann machines via the implementation of novel analog and parallel computation schemes based on the in-memory computing principle. Of special importance are neural networks with generic or extended memristor models that are suited to accurately describe real memristor devices. The manuscript considers a general class of delayed neural networks where the memristors obey the relevant and widely used generic memristor model, the voltage threshold adaptive memristor (VTEAM) model. Due to physical limitations, the memristor state variables evolve in a closed compact subset of the space; therefore, the network can be mathematically described by a special class of differential inclusions named differential variational inequalities (DVIs). By using the theory of DVI, and the Lyapunov approach, the paper proves some fundamental results on convergence of solutions toward equilibrium points, a dynamic property that is extremely useful in neural network applications to content addressable memories and signal-processing in real time. The conditions for convergence, which hold in the general nonsymmetric case and for any constant delay, are given in the form of a linear matrix inequality (LMI) and can be readily checked numerically. To the authors knowledge, the obtained results are the only ones available in the literature on the convergence of neural networks with real generic memristors.

A Novel Multiscroll Memristive Hopfield Neural Network

Memristors are usually introduced into neuron models as neural synapses to investigate firing activities. In this paper, a novel generic memristor with smooth cosine memductance is proposed, and its dynamic characteristic concerning multistability, which is completely different from any known memristors, is analyzed and validated by numerical and PSIM simulations. The PSIM simulations intuitively reflect the memory properties of the constructed memristor emulator. To investigate the application of the proposed memristor, a multiscroll memristive Hopfield neural network is modeled by introducing the memristor into a tri-neuron Hopfield neural network as a synapse weight. Homogeneous single-scroll and double-scroll multistability phenomena are revealed by utilizing some analytical tools, such as bifurcation diagrams, local attraction basins, phase plane portraits, and so on. It is found that there is a multi-double-scroll attractor with growing scrolls for appropriate parameters. Furthermore, the average Hamiltonian energy, dependent on the homogeneous dynamics, is analyzed based on Helmholtz’s theorem. It is discovered that the homogeneous dynamics is closely related to the energy transition, which may provide a new explanation for the occurrence of multistability in the human brain. Finally, several circuit experiments are carried out to confirm the dynamical behaviors, and it is found that the circuit can show similar dynamics as the numerical simulations.

FPGA Implementation of a Novel Two-internal-State Memristor and its Two Component Chaotic Circuit

Objectives: To propose a second-order locally- active memristor, a twocomponent chaotic circuit resulting from this current-controlled generic memristor and an application in steganography. Methods/statistical analysis: Using a one-state-variable first-order memristor, a model is proposed which is obtained by modifying a locally-active memristor based on a current-controlled generic memristor. The model has two internal state variables: a voltage stored up in a capacitor and a current stored up in an inductor. With an external inductor, 3D-two-component chaotic circuit is developed. Numerical studies are made using MATLAB and confirmed by a field programmable gate array (FPGA) based hardware implementation. Findings: A two-state-variable based second-order memristor model is presented. The novel memristor configuration leads to the design of a simple two-component chaotic circuit. By investigating the characteristics of the memristor, it is shown that the memristor can be switched from a predominantly passive region to an active region with a wide locally-active region. An application in steganography helps to hide a secrete message inside an image. Application/improvements: The results obtained in this investigation will enrich the literature of memristive circuits, enhance the simplification of chaotic circuits and can be used to improve the memristive circuit based applications in many research domains such as secure information in telecommunications, Random Number Generation (RNG) and image encryption. Keywords: Memristor; Two component circuit; Chaos; Local activity; FPGA; Steganography

Cyclic voltammetry of volatile memristors in the Venus flytrap: short-term memory.

Plants have sensory, short-term and long-term memory. Possible candidates for memory in plants are memristors; resistors with memory. Memristors have been found in seeds, plants, flowers and fruits. The electrostimulation of plants by bipolar periodic waves can induce electrical responses with fingerprints of volatile or non-volatile memristors. Here, we show that the electrostimulation of the Venus flytrap (Dionaea muscipula Ellis) by unipolar sinusoidal or triangular periodic electrical trains induces electrical responses in plants with fingerprints of volatile memristors. The discovery of volatile generic memristors in plants opens new directions in the modelling and understanding of electrical phenomena in the plant kingdom.

Memristive biophysical neuron models forming an excitatory–inhibitory neural network for modeling PING rhythm generation

SPICE models are constructed for memristive devices to form associated biophysical neuron circuit models such as the Hodgkin–Huxley (HH) type II excitability neuron circuit model, the HH type III excitability neuron circuit model, the simplified HH neuron circuit model, the Morris–Lecar neuron circuit model, and the memristive based direct-current (DC) circuit model. Rigorous nonlinear circuit-theoretic principles are also applied to analyze the different behaviors of the generic memristor Na $$^{+}$$ -ion, K $$^{+}$$ -ion, and Ca $$^{++}$$ -ion channels forming these biophysical neuron circuit models. Detailed explanations and clarifications are presented on the memristive HH type II and HH type III axonal excitabilities based on mathematical analysis as well as the circuit models. This is done from the perspective of the spike patterns generated by both of these biophysical neuron circuit models. Moreover, various experimental studies have revealed a synchronous brain state known as gamma rhythms that are responsible for sensory, memory, and motor processes. This suggests that understanding how the gamma oscillation (30–100 Hz) is generated in the brain will be extremely important to unravel the link between the activity of an individual neuron and the cognitive processing achieved by a population of networked neurons. We thus also study the dynamics of an interconnected excitatory–inhibitory (E–I) network population, which is ubiquitous in the brain. Utilizing biophysical models of the E–I network, we investigate the generation of pyramidal-interneuronal network gamma (PING) rhythms caused by the external input to the network and the connectivity heterogeneities. The results reveal that synchronous strong PING and sparsely firing weak PING rhythms are generated based on the network connectivities and external input heterogeneities in simulations of 100 memristive HH type II excitability neurons forming an E–I network.

Nonlinear Dynamics, Switching Kinetics and Physical Realization of the Family of Chua Corsage Memristors

This article reviews the nonlinear dynamical attributes, switching kinetics, bifurcation analysis, and physical realization of a family of generic memristors, namely, Chua corsage memristors (CCM). CCM family contains three 1-st order generic memristor dubbed as 2-lobe, 4-lobe, and 6-lobe Chua corsage memristors and can be distinguished in accordance with their asymptotic stable states. The 2-lobe CCM has two asymptotically stable equilibrium states and regarded as a binary memory device. In contrast, the versatile 4-lobe CCM and 6-lobe CCM are regarded as a multi-bit-per-cell memory device as they exhibit three and four asymptotic stable states, respectively, on their complex and diversified dynamic routes. Due to the diversified dynamic routes, the CC memristors exhibit a highly nonlinear DC V-I curve. Unlike most published highly-nonlinear DC V-I curves with several disconnected branches, the DC V-I curves of CCMs are contiguous along with a locally active negative slope region. Moreover, the DC V-I curves and parametric representations of the CCMs are explicitly analytical. Switching kinetics of the CCM family can be demonstrated with universal formulas of exponential state trajectories xn(t), time period tfn, and applied minimum pulse amplitude VA and width Δw. These formulas are regarded universal as they can be applied to any piecewise linear dynamic routes for any DC or pulse input and with any number of segments. When local activity, and bifurcation and chaos theorems are employed, CMMs exhibit unique stable limit cycles spawn from a supercritical Hopf bifurcation along with static attractors. In addition, the nonlinear circuit and system theoretic approach is applied to explain the asymptotic stability behavior of CCMs and to design real memristor emulators using off-the-shelf circuit components.

Computation of Pinched Hysteresis Loop Area From Memristance-vs-State Map

The voltage-current characteristic of memristor driven by sinusoidal signal has the shape of hysteresis loop pinched at the origin. The lobe area of the hysteresis loop has been computed so far either from the voltage-current plane for all types of memristors or from the constitutive relation in the flux-charge plane of ideal memristor. In this brief, we provide an alternative approach in computing the lobe area from the memristance-versus-state map of ideal and ideal generic memristors driven by sinusoidal or periodic continuous piecewise linear signal with zero dc component. The applicability of the proposed approach is demonstrated through a number of examples.

Truly Concomitant and Independently Expressed Short- and Long-Term Plasticity in a Bi2 O2 Se-Based Three-Terminal Memristor.

Concomitance of diverse synaptic plasticity across different timescales produces complex cognitive processes. To achieve comparable cognitive complexity in memristive neuromorphic systems, devices that are capable of emulating short-term (STP) and long-term plasticity (LTP) concomitantly are essential. In existing memristors, however, STP and LTP can only be induced selectively because of the inability to be decoupled using different loci and mechanisms. In this work, the first demonstration of truly concomitant STP and LTP is reported in a three-terminal memristor that uses independent physical phenomena to represent each form of plasticity. The emerging layered material Bi2 O2 Se is used for memristors for the first time, opening up the prospects for ultrathin, high-speed, and low-power neuromorphic devices. The concerted action of STP and LTP allows full-range modulation of the transient synaptic efficacy, from depression to facilitation, by stimulus frequency or intensity, providing a versatile device platform for neuromorphic function implementation. A heuristic recurrent neural circuitry model is developed to simulate the intricate "sleep-wake cycle autoregulation" process, in which the concomitance of STP and LTP is posited as a key factor in enabling this neural homeostasis. This work sheds new light on the development of generic memristor platforms for highly dynamic neuromorphic computing.

Exact Analysis and Physical Realization of the 6-Lobe Chua Corsage Memristor

A novel generic memristor, dubbed the 6-lobe Chua corsage memristor, is proposed with its nonlinear dynamical analysis and physical realization. The proposed corsage memristor contains four asymptotically stable equilibrium points on its complex and diversified dynamic routes which reveals a 4-state nonlinear memory device. The higher degree of versatility of its dynamic routes reveal that the proposed memristor has a variety of dynamic paths in response to different initial conditions and exhibits a highly nonlinear contiguous DC V-I curve. The DC V-I curve of the proposed memristor is endowed with an explicit analytical parametric representation. Moreover, the derived three formulas, exponential trajectories of state xnt, time period tfn, and minimum pulse amplitude VA, are required to analyze the movement of the state trajectories on the piecewise linear (PWL) dynamic route map (DRM) of the corsage memristor. These formulas are universal, that is, applicable to any PWL DRM curves for any DC or pulse input and with any number of segments. Nonlinear dynamics and circuit and system theoretic approach are employed to explain the asymptotic quad-stable behavior of the proposed corsage memristor and to design a novel real memristor emulator using off-the-shelf circuit components.

The non-linear electrical properties of human skin make it a generic memristor

An electrical measurement is non-linear when the applied stimulus itself affects the electrical properties of the underlying tissue. Corresponding voltage-current plots may exhibit pinched hysteresis loops which is the fingerprint of a memristor (memory resistor). Even though non-linear electrical properties have been demonstrated for different biological tissues like apples, plants and human skin, non-linear measurements as such have not been defined, yet. We are studying the non-linear properties of human skin systematically and initiate non-linear measurements on biological tissues as a field of research in general by introducing applicable recording techniques and parameterization. We found under which voltage stimulus conditions a measurement on human skin is non-linear and show that very low voltage amplitudes are already sufficient. The non-linear properties of human skin originate from the sweat ducts, as well as, from the surrounding tissue, the stratum corneum and we were able to classify the overall skin memristor as a generic memristor. Pinched hysteresis loops vary largely among subjects; an indication for the potential use in biomedical sensor applications.

A Locally Active Memristor and Its Application in a Chaotic Circuit

In this brief, we propose a novel locally active memristor based on a voltage-controlled generic memristor model and use the analysis methods of standard nonlinear theory to analyze its characteristics and illustrate the concept of local activity via the dc v-i loci of memristor and non-volatile memory via the power-off plot of memristor. A chaotic attractor is observed with a simple nonlinear circuit that only includes three circuit elements in parallel: 1) a nonlinear locally active memristor; 2) a linear passive inductor; and 3) a linear passive capacitor. Then, we analyze the dynamical characteristics of the above circuit and show complex bifurcation behaviors.

About Fingerprints of Chua's Memristors

In this paper, we present an analysis of some selected fingerprints of Chua's memristors. First, the memristor is presented not as a concrete nanodevice but, more generally, as a manifestation of permanent natural principle. Next, an overview of the current classification of memristors is given in the light of various mechanisms of the memristance adjustment by internal state and by terminal variables. It is shown that only the ideal and ideal generic memristors have their stamps in Chua's table of fundamental elements and in the equivalent storeyed structure, both of them being based on the idea of predictive modeling. A brief overview on the memristor fingerprints is presented. The homothety fingerprint is discussed in detail, and all existing elements complying with this fingerprint are identified. Finally, it is argued that the most natural fingerprint of the original memristors introduced by L. Chua in 1971 should be sought in the charge-flux coordinates of their constitutive relations.

Oscillation with 4-Lobe Chua Corsage Memristor

In this paper we propose a new first-order generic memristor, namely, a 4-lobe Chua corsage memristor, as an extension of the 2-lobe Chua corsage memristor. The newly designed corsage memristor exhibits more complex dynamical routes with three stable equilibrium points for which it reveals a higher degree of versatility that the dynamic route changes in response to a change in initial conditions. One of the most important feature of our new memristor is its contiguous DC V-I curve. In contrast, most published highly-nonlinear DC V-I curves have several disconnected branches. Moreover, in this paper, we exploit the properties of the 4-lobe Chua corsage memristor to design an oscillator by connecting the memristor in series with an inductor and a battery. The resulting circuit oscillates about a locallyactive operating point located on the negative slope region of the memristor?s DC V-I curve. We investigate the local activity, edge of chaos, and Hopf bifurcation phenomena and carry out an in-depth analysis of the nonlinear dynamics of the oscillation in our oscillator circuit.