Leon O. Chua

University of California, Berkeley | UCB · Computer Science Division

Resistive memories are outstanding electron devices that have displayed a large potential in a plethora of applications such as nonvolatile data storage, neuromorphic computing, hardware cryptography, etc. Their fabrication control and performance have been notably improved in the last few years to cope with the requirements of massive industrial p...

A nonlinear system, exhibiting a unique asymptotic behaviour, while being continuously subject to a stimulus from a certain class, is said to suffer from fading memory. This interesting phenomenon was first uncovered in a non-volatile tantalum oxide-based memristor from Hewlett Packard Labs back in 2016 out of a deep numerical investigation of a pr...

The Edge of Chaos Principle lies at the origin of emergent phenomena in physical systems. Recurring to powerful concepts from the theory, establishing its rules, it is possible to identify regions of the parameter space of a system, endowing the latter with a high degree of excitability, which can then manifest itself vividly, as complexity emerges...

Memristive devices are the subject of extensive studies nowadays. While the Dynamic Route Map is a powerful tool for analyzing the response of first-order memristors under DC stimuli, the development of an equivalent tool for investigating the response of these devices to AC stimuli is still an open question. Recently, Pershin and Slipko introduced...

Chua Corsage Memristor (CCM) can accurately emulate the neuromorphic behaviors of biological neurons. Recently, we built a working CCM circuit board using only inexpensive and off-the-shelf electronic components. When this poor-man’s memristor is connected to a linear passive L and ${C}$ circuit, the resulting circuit can generate action p...

Memristive technology has been rapidly emerging as a potential alternative to traditional CMOS technology, which is facing fundamental limitations in its development. Since oxide-based resistive switches were demonstrated as memristors in 2008, memristive devices have garnered significant attention due to their biomimetic memory properties, which p...

Resistive memories are outstanding electron devices that have displayed a large potential in a plethora of applications such as nonvolatile data storage, neuromorphic computing, hardware cryptography, etc. Their fabrication control and performance have been notably improved in the last few years to cope with the requirements of massive industrial p...

The Chua's circuit has been considered as a paradigm for the investigation of chaos, but it still presents many unexplored dynamics. Chaotic hysteresis is an effect observed when the hysteresis phenomenon and chaotic dynamics phenomenon act simultaneously. It is an interesting phenomenon since it is observed in a variety of disciplines, and it has...

As established by the second law of thermodynamics, an isolated system is unable to exhibit complex behaviours. Conversely, a physical system, which interacts with the surrounding environment, may support emergent phenomena, provided some of its constitutive components are capable to amplify infinitesimal fluctuations in energy under suitable polar...

After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaot...

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-...

One of the complex phenomena, which most attracted the attention of the scientific community over the past few decades, is the emergence of diffusion-driven instabilities in homogeneous cellular media. Explaining this symmetry-breaking process, which the Russian luminary Ilya Prigogine referred to as the Instability of the Homogeneous, is only poss...

Diffusion-driven instabilities with pattern formation may occur in a network of identical, regularly-spaced, and resistively-coupled cells if and only if the uncoupled cell is poised on a locally-active and stable operating point in the Edge of Chaos domain. This manuscript presents the simplest ever-reported two-cell neural network, combining toge...

A general phenomenological model of the kinetics of thermally induced structural phase transitions in multi-phase alloys is introduced for arbitrary numbers of lattice phases and transitions. The model is based on a system of ODEs yielding the temporal evolution of lattice phase fractions caused by temperature variation described by a heat balance...

The emergence of deep neural networks has allowed the development of fully automated and efficient diagnostic systems for plant disease and pest phenotyping. Although previous approaches have proven to be promising, they are limited, especially in real-life scenarios, to properly diagnose and characterize the problem. In this work, we propose a fra...

Random telegraph noise (RTN) owns its very name to its assumed stochastic nature. In this paper, we follow up previous works that questioned this stochastic nature, and we investigate this assumption using experimentally measured noise coming from properly biased Ni/HfO2 unipolar Resistive RAM memristor nanodevices. We have used established, well–k...

Memristor crossbar architecture is one of the most popular circuit configurations due to its wide range of practical applications. The crossbar architecture can emulate the weighted summation operation, called multiply and accumulate operation (MAC). The errors to MAC computing get introduced due to a range of crossbar variability. We broadly group...

Memristors were proposed in the early 1970s by Leon Chua as a new electrical element linking charge to flux. Since that first introduction, these devices have positioned themselves to be considered as possible fundamental ones for the generations of electronic devices to come. In this paper, we propose a new way to investigate the effects of the el...

As the limits of transistor technology are approached, feature size in integrated circuit transistors has been reduced very near to the minimum physically-realizable channel length, and it has become increasingly difficult to meet expectations outlined by Moore’s law. As one of the most promising devices to replace transistors, memristors have many...

Memristor crossbar architecture is one of the most popular circuit configurations due to its wide range of practical applications. The crossbar architecture can emulate the weighted summation operation, called multiply and accumulate operation (MAC). The errors to MAC computing get introduced due to a range of crossbar variability. We broadly group...

Memristors were proposed in the early ’70s of the XXth century by Leon Chua as a new electrical element linking the charge and the flux. Since that first introduction, these devices have positioned themselves to be considered as possibly fundamental for the new generations of electronic devices. It has to be mentioned that actual memristors have on...

This paper exposes Hodgkin-Huxley's “time-varying conductance” as an ill-conceived conceptual blunder and identifies a fundamental new physical concept dubbed "Edge of Chaos Kernel" as nature's optimal mechanism for creating an "action potential", aka "all-or none" response. As a bonus, it also offers a precise definition of the heretofore unresolv...

Phase Change Memory (PCM) is an emerging technology exploiting the rapid and reversible phase transition of certain chalcogenides to realize nanoscale memory elements. PCM devices are being explored as non-volatile storage-class memory and as computing elements for in-memory and neuromorphic computing. It is well-known that PCM exhibits several cha...

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 kn...

Random telegraph noise (RTN) owns its very name to its assumed stochastic nature. In this paper, we follow up previous works that questioned this stochastic nature, and we investigate this assumption using experimentally measured noise coming from properly biased Ni/HfO 2 unipolar Resistive RAM memristor nanodevices. We have used established, well–...

Memristors were first proposed in 1971 by Leon Chua. These devices are usually regarded as being one of the newest fundamental breakthrough for electronics. Their role in designing new electronic systems is expected to be an important, key-factor. As an example, they already come in many forms: PCA, ReRAM, etc., to mention a few. In any case, since...

We present a compact, continuous, and numerically stable version of a tantalum oxide (TaOx) memristor model which can be employed for robust and reliable simulations of large scale memristor based circuits. The original model contains a piecewise differentiable function in the memductance expression and discontinuous step functions in the state equ...

The ever-increasing amount of data from ubiquitous smart devices fosters data-centric and cognitive algorithms. Traditional digital computer systems have separate logic and memory units, resulting in a huge delay and energy cost for implementing these algorithms. Memristors are programmable resistors with a memory, providing a paradigm-shifting app...

This paper presents a circuit-theoretic analysis of a NbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -Mott memristor fabricated at Hewlett-Packard Labs. It investigates mechanisms behind the origin of complexity based on local activity, which characterizes the behavior of this outstanding...

In 1971, Dr. Leon Chua, known as the father of nonlinear circuits and cellular neural networks, postulated the existence of memristor, a portmanteau of memory resistor, in his seminal paper: “Memristor—The missing circuit element” published in IEEE Transactions on Circuit Theory, the predecessor of IEEE Transactions on Circuits and Systems—I: Regul...

We present and experimentally validate two minimal compact memristive models for spiking neuronal signal generation using commercially available low-cost components. The first neuron model is called the Memristive Integrate-and-Fire (MIF) model, for neuronal signaling with two voltage levels: the spike-peak, and the rest-potential. The second model...

In 1971, Dr. Leon Chua, known as the father of nonlinear circuits and cellular neural networks, postulated the existence of memristor, a portmanteau of memory resistor, in his seminal paper: Memristor-the missing circuit element published in IEEE Transactions on Circuit Theory, the predecessor of IEEE Transactions on Circuits and Systems. Thirty-se...

Neuromorphic computing can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. A locally-active memristor, which possesses the capability to amplify infinitesimal fluctuations in energy and can be used to generate neuromorphic behaviors, is a natural candidate for constructing an electronic equiv...

The dynamical electric behavior of a NiTi smart alloy thin filament when driven by time varying current pulses is studied by a structure-based phenomenological model that includes rate-based effects. The simulation model relates the alloy's electrical resistivity to the relative proportions of the three main structural phases namely Martensite, Aus...

The dynamical electric behavior of a NiTi smart alloy thin filament when driven by time varying current pulses is studied by a structure-based phenomenological model that includes rate-based effects. The simulation model relates the alloy's electrical resistivity to the relative proportions of the three main structural phases namely Martensite, Aus...

Memristor crossbar arrays are used in a wide range of in-memory and neuromorphic computing applications. However, memristor devices suffer from non-idealities that result in the variability of conductive states, making programming them to a desired analog conductance value extremely difficult as the device ages. In theory, memristors can be a nonli...

The introduction of nano-memristors in electronics may allow to boost the performance of integrated circuits beyond the Moore era, especially in view of their extraordinary capability to process and store data in the very same physical volume. However, recurring to nonlinear system theory is absolutely necessary for the development of a systematic...

Resistive Random Access Memories (RRAMs) are based on resistive switching (RS) operation and exhibit a set of technological features that make them ideal candidates for applications related to non-volatile memories, neuromorphic computing and hardware cryptography. For the full industrial development of these devices different simulation tools and...

Memristor crossbar arrays are used in a wide range of in-memory and neuromorphic computing applications. However, memristor devices suffer from non-idealities that result in the variability of conductive states, making programming them to a desired analog conductance value extremely difficult as the device ages. In theory, memristors can be a nonli...

Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state vo...

A pyramidical multi-scale encoder-decoder network, namely PMED-Net, is proposed for medical image segmentation. Different variants of encoder-decoder networks are in practice for segmenting the medical images and U-Net is the most widely used one. However, the existing architectures for segmenting medical images have millions of parameters that req...

The original version of this book was inadvertently published without updating author corrections in Abstract for the following Chapters 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Now, the corrections have been incorporated in all the chapter abstracts in Online.

In article number 2005582, Fei Zhuge and co‐workers develop an all‐optically controlled (AOC) analog memristor based on the relatively mature material InGaZnO. The memconductance is reversibly tunable over a continuous range by varying only the wavelength of the controlling light. The light‐induced multiple memconductance states are nonvolatile. Th...

In this paper, we propose a complex neuro-memristive synapse that exhibits the physiological acts of synaptic potentiation and depression of the human-brain. Specifically, the proposed neuromorphic synapse efficiently imitates the synaptic plasticity, especially long-term potentiation (LTP) and depression (LTD), and short-term facilitation (STF) an...

Memristor devices embedded in pioneering future computing platforms are believed to represent one of the most promising key-enabling technologies for the treatment of massive amount of data. The ideal memristor, a two-terminal circuit element described by a nonlinear relationship between the time integrals of current and voltage (i.e., the current...

Chapter 5 has developed the flux-charge analysis method (FCAM) for the analysis of a class \(\mathcal {L}\mathcal {M}\) of memristor circuits containing memristors, linear resistors, inductors, capacitors, and independent voltage and current sources. The formulation of circuit equations (DAEs and SEs) has been provided in the (φ, q)-domain and in t...

A great deal of efforts have been traditionally devoted in circuit theory to analyze nonstationary steady-state behaviors in networks obtained by locally coupled arrays of simple dynamic circuits (also named cells, oscillators, units, etc.). These arrays can be thought of as a bio-inspired circuit model of complex nonlinear phenomena observable in...

Let us consider a circuit N made of an arbitrary interconnection of (two-terminal) circuit elements. In general, analysis and design of a circuit require to solve a network problem where numerous mathematical (circuit) variables are established and then a set of equations is generated describing the behavior of the composite network. Fundamental pr...

This chapter is devoted to discuss some basic properties of memristors, memcapacitors, and meminductors, a.k.a. mem-elements, that are both of theoretic and practical interest. In the first part (Sects. 2.1 and 2.2), the main focus is on features of a memristor as a (−1, −1)-element of the periodic table (cf. Chap. 1), hereinafter also named ideal...

In this brief chapter we discuss some fundamental dynamic phenomena that can be observed in nonlinear circuits containing time-invariant resistors, inductors, capacitors, and dc sources (autonomous RLC circuits). In Chap. 6 we will study analogous dynamic phenomena for nonlinear circuits containing also memristors. While in first-order autonomous c...

This chapter discusses a device-independent black-box approach to model a broad variety of physical devices. For the purpose of network theory, a circuit element can be considered as a black-box, whose electrical behavior is defined in terms of a mathematical model (i.e., a set of algebraic and/or differential and/or integral equations), relating c...

Neuromorphic computing (NC) is a new generation of artificial intelligence. Memristors are promising candidates for NC owing to the feasibility of their ultrahigh‐density 3D integration and their ultralow energy consumption. Compared to traditional electrical memristors, the emerging optoelectronic memristors are more attractive owing to their abil...

In recent years, the use of memristors as nonlinear dynamical elements for real-time analog signal processing has been a topic of ever increasing interest. Memristors are widely employed in neuromorphic architectures and cellular neural networks, where they behave as nonlinear dynamic devices within neurons (Chap. 10.1007/978-3-030-55651-8_9) or th...

Let us consider a relevant class of nonlinear networks, denoted by ℒℳ, containing at least one memristor in addition to ideal (linear) resistors, inductors, capacitors, and independent voltage or currents sources. Thus, ℒℳ describes nonlinear dynamic networks including ideal memristors.

The main contributions in this chapter are as follows: we identify a wide class of memristor circuits, of any order and with any number of flux- or charge-controlled memristors, and introduce a systematic method for writing in an explicit way the SEs, both in the (φ, q) and in the (v, i)-domain. The conditions for the existence of the SEs for such...

A memristor is a nonlinear device obeying Ohm’s law but, unlike a resistor, the memristor resistance, also called memristance, depends upon the history of the voltage applied or the current flowing through it. A memristor is then both a nonlinear and a memory element in the (v, i)-domain. Another unique property is nonvolatility, namely, when curre...

The paper considers a relevant class of networks containing memristors and (possibly) nonlinear capacitors and inductors. The goal is to unfold the nonlinear dynamics of these networks by highlighting some main features that are potentially useful for real-time signal processing and in-memory computing. In particular, an analytic treatment is provi...

Reliable programming crossbar memristors to the required resistive states is the challenge that hinders VLSI deployment of the memristive neural network circuits, as current memristive devices face the variability issues of resistive switching. There is also a need for on-chip control circuitry that detects malfunctioning memristive nodes in the cr...

Abstract Stochastic resonance, found in many natural and engineered bistable systems, refers to a physical phenomenon wherein the response of nonlinear dynamical systems to weak input signal is enhanced by the presence of noise, tuned to the optimal level. However, the observation of this phenomenon for weak subthreshold periodic magnetic field sig...

In this paper, we analyze the reset transition in bipolar TiN/Ti/HfO2 (10 nm)/Al2O3(2 nm)/W ReRAM devices using a tool that allows studying the temporal behaviour of these devices. This tool, the Dynamic Route Map (DRM), provides information about the temporal evolution of the state variable that governs the behaviour of the device, thus allowing a...

[Full text: https://rdcu.be/b4ovR] Neuromorphic architectures merge learning and memory functions within a single unit cell and in a neuron-like fashion. Research in the field has been mainly focused on the plasticity of artificial synapses. However, the intrinsic plasticity of the neuronal membrane is also important in the implementation of neurom...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Memristors have emerged as key candidates for beyond-von-Neumann neuromorphic or in-memory computing owing to the feasibility of their ultrahigh-density three-dimensional integration and their ultralow energy consumption. A memristor is generally a two-terminal electronic element with conductance that varies nonlinearly with external electric stimu...