Connecting Spiking Neurons to a Spiking Memristor Network Changes the Memristor Dynamics

Memristors have been suggested as neuromorphic computing elements. Spike-time dependent plasticity and the Hodgkin-Huxley model of the neuron have both been modelled effectively by memristor theory. The d.c. response of the memristor is a current spike. Based on these three facts we suggest that memristors are well-placed to interface directly with neurons. In this paper we show that connecting a spiking memristor network to spiking neuronal cells causes a change in the memristor network dynamics by: removing the memristor spikes, which we show is due to the effects of connection to aqueous medium; causing a change in current decay rate consistent with a change in memristor state; presenting more-linear $I-t$ dynamics; and increasing the memristor spiking rate, as a consequence of interaction with the spiking neurons. This demonstrates that neurons are capable of communicating directly with memristors, without the need for computer translation.Comment: Conference paper, 4 page

Reliable Modeling of Ideal Generic Memristors via State-Space Transformation

The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away

Intelligent Control of Seizure-Like Activity in a Memristive Neuromorphic Circuit based on the Hodgkin-Huxley Model

Memristive neuromorphic systems represent one of the most promising technologies to overcome the current challenges faced by conventional computer systems. They have recently been proposed for a wide variety of applications, such as non-volatile computer memory, neuroprosthetics, and brain-machine interfaces. However, due to their intrinsically nonlinear characteristics, they present a very complex dynamic behavior, including self-sustained oscillations, seizure-like events and chaos, which may compromise their use in closed-loop systems. In this work, a novel intelligent controller is proposed to suppress seizure-like events in a memristive circuit based on the Hodgkin-Huxley equations. For this purpose, an adaptive neural network is adopted within a Lyapunov-based nonlinear control scheme to attenuate bursting dynamics in the circuit, while compensating for modeling uncertainties and external disturbances. The boundedness and convergence properties of the proposed control scheme are rigorously proved by means of a Lyapunov-like stability analysis. The obtained results confirm the effectiveness of the proposed intelligent controller, presenting a much improved performance when compared to a conventional nonlinear control scheme.</p

Everything You Wish to Know About Memristors But Are Afraid to Ask

This paper classifies all memristors into three classes called Ideal, Generic, or Extended memristors. A subclass of Generic memristors is related to Ideal memristors via a one-to-one mathematical transformation, and is hence called Ideal Generic memristors. The concept of non-volatile memories is defined and clarified with illustrations. Several fundamental new concepts, including Continuum-memory memristor, POP (acronym for Power-Off Plot), DC V-I Plot, and Quasi DC V-I Plot, are rigorously defined and clarified with colorful illustrations. Among many colorful pictures the shoelace DC V-I Plot stands out as both stunning and illustrative. Even more impressive is that this bizarre shoelace plot has an exact analytical representation via 2 explicit functions of the state variable, derived by a novel parametric approach invented by the author

Chemical Inductor

A multitude of chemical, biological, and material systems present an inductive behavior that is not electromagnetic in origin. Here, it is termed a chemical inductor. We show that the structure of the chemical inductor consists of a two-dimensional system that couples a fast conduction mode and a slowing down element. Therefore, it is generally defined in dynamical terms rather than by a specific physicochemical mechanism. The chemical inductor produces many familiar features in electrochemical reactions, including catalytic, electrodeposition, and corrosion reactions in batteries and fuel cells, and in solid-state semiconductor devices such as solar cells, organic light-emitting diodes, and memristors. It generates the widespread phenomenon of negative capacitance, it causes negative spikes in voltage transient measurements, and it creates inverted hysteresis effects in current–voltage curves and cyclic voltammetry. Furthermore, it determines stability, bifurcations, and chaotic properties associated to self-sustained oscillations in biological neurons and electrochemical systems. As these properties emerge in different types of measurement techniques such as impedance spectroscopy and time-transient decays, the chemical inductor becomes a useful framework for the interpretation of the electrical, optoelectronic, and electrochemical responses in a wide variety of systems. In the paper, we describe the general dynamical structure of the chemical inductor and we comment on a broad range of examples from different research areas.Funding for open access charge: CRUE-Universitat Jaume

A Frequency Domain Analysis of the Excitability and Bifurcations of the FitzHugh–Nagumo Neuron Model

The dynamics of neurons consist of oscillating patterns of a membrane potential that underpin the operation of biological intelligence. The FitzHugh−Nagumo (FHN) model for neuron excitability generates rich dynamical regimes with a simpler mathematical structure than the Hodgkin−Huxley model. Because neurons can be understood in terms of electrical and electrochemical methods, here we apply the analysis of the impedance response to obtain the characteristic spectra and their evolution as a function of applied voltage. We convert the two nonlinear differential equations of FHN into an equivalent circuit model, classify the different impedance spectra, and calculate the corresponding trajectories in the phase plane of the variables. In analogy to the field of electrochemical oscillators, impedance spectroscopy detects the Hopf bifurcations and the spiking regimes. We show that a neuron element needs three essential internal components: capacitor, inductor, and negative differential resistance. The method supports the fabrication of memristor-based artificial neural networks

Robust Simulation of a TaO Memristor Model

This work presents a continuous and differentiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in software. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable functions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable approximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal candidates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit simulator