Dynamical analysis of a fractional-order memristive bridge-coupled HR and FN neuron model with crosstalk

The dynamical mechanism of noise-induced complete chaotic synchronization of two uncoupled periodically driven FitzHugh-Nagumo (FHN) neuron models is initially researched in this paper. Here we show: based on a nonlinear dynamical analysis and numerical evidence, that under the perturbation of weak noise strange non-chaotic attractor (SNA) can be induced to appear in FHN neuron model, which is formed through transitions among chaotic attractor, periodic attractor and chaotic saddle in two sides of boundary crisis point of system respectively. When SNA appears the maximum Lyapunov exponent of the attractor is non-positive and there is thus no sensitive dependence on initial conditions. The two FHN neuron models are identical but there is slight difference between their initial states. After the attractors of the two FHN neuron models become strange non-chaotic attractors from strange chaotic attractors under the appropriate noise, the responses of the two systems, which are no sensitive dependence on initial conditions, are complete synchronous. The dynamical mechanism of noise-induced complete chaotic synchronization of two non-coupled FHN neuron models is related to the strange non-chaotic attractor induced to appear by noise.

Nowadays, noise was considered to play a key role in the neural system, which improved the weak signal detection and enhanced the information transmission, as deeply research on stochastic resonance (SR). Traditionally, stochastic resonance was thought to be the result of the interaction between subthreshold signals with noise in nonlinear system. Particularly, the existence of noise was thought to be harmful to the response of system with suprathreshold signal input commonly. Observing the response of FitzHugh-Nagumo (FHN) neuron model to the suprathreshold input, it was improved gradually as the amplitude of input rising from subthreshold to suprathreshold. Signal-to-noise ratio and cross correlation coefficient were defined as performance evaluation functions separately, then the response of FHN neuron model to periodic and aperiodic suprathreshold signal input was studied. At the same time, the threshold characteristic was discussed, and some basic parameters for practical application were provided. The simulation result illustrates the information transmission can be enhanced by the noise even if input signal is suprathreshold in FHN neuron model.

A low power analog implementation of FitzHugh-Nagumo (FHN) neuron model is presented in this paper for large scale spiking neural network and neuromorphic algorithm realization. The FHN neuron model is designed using $\log $-domain low pass filters and translinear multipliers to emulate voltage-like variable with cubic non-linearity and a recovery variable. Various spiking behaviors observed in biological neurons are demonstrated in simulation results. The neuron model was designed in 45 nm CMOS process which has 1.6 nW and 40 nW power consumption at rest and for a single spiking event respectively.

In this article, inspired by the state-of-the-art research progress of the fractional-order memristor, a fractional-order memristive prediction model of the trading price of future is attempted to be proposed, which can feasibly predict the variation trend of the following unknown trading price data only depending on a small sampling of the given ones in a previous short time. At first, the analogy analysis of the relationship between an actual system of future trading and a physical memristive system of charge transfer is achieved. Second, the achievement of a corresponding capacitive string scaling fracmemristor (LCSF) is mathematically derived and analyzed in detail. Third, a 5-years data from 2015 to 2019 of the 300 exchange traded fund open-end index securities investment fund of Shanghai Stock Exchange is selected to verify the multiscale prediction ability of trading price of future of the LCSF. The theoretical contribution of this article is the first application of the fractional-order memristive electronic system to feasibly achieve an intelligent prediction model of the financial technology.

In this paper, the fractional calculus is introduced into charge-controlled memristor to establish a fractional-order charge-controlled memristor model. The fractional derivative is a generalization of integer derivatives. Memristor represents the missing relation between the charge and flux among the conventional elements. A unified cubic model is proposed which is more general and comprehensive, and the model is analyzed when the fractional-order a change in the range of 0 to 1.0. Some integer-order memristor model simulation are given to have a better understanding for the fractional-order model. Some interesting phenomena are found when researching the fractional-order model that the V-I characteristic is not the conventional double-loop V-I curves, but an curve can be called triple-loop V-I curves. The area inside the hysteresis loops decreases by the increasing of input frequency and the decreasing of the fractional-order α.

The implementation of biological neuron models plays an important role in understanding the functionality of the brain. Generally, analog and digital methods are preferred during implementation processes. The Raspberry Pi (RPi) microcontroller has the potential to be a new platform that can easily solve complex mathematical operations and does not have memory limitations, which will take advantage while realizing biological neuron models. In this paper, Hodgkin-Huxley (HH), FitzHugh-Nagumo (FHN), Morris-Lecar (ML), Hindmarsh-Rose (HR), and Izhikevich (IZ) neuron models have been implemented on a standard-equipped RPi. For the numerical solution of each neuron model, the one-step method (4th order Runge-Kutta (RK4), the new version of Runge-Kutta (RKN)), the multi-step method (Adams-Bashforth (AB), Adams-Moulton (AM)), and predictor-corrector method (Adams-Bashforth-Moulton (ABM)) are preferred to compare results. The implementation of HH, ML, FHN, HR, and IZ neuron models on RPi and the comparison of numerical models RK4, RKN, AB, AM, and ABM in the implementation of neuron models were made for the first time in this study. Firstly, MATLAB simulations of the various behaviors belonging to the HH, ML, FHN, HR, and IZ neuron models were completed. Then those models were realized on RPi and the outputs of the models are experimentally produced. The errors are also presented in the tables. The results show that RPi can be considered as a new alternative tool for making complex neuron models.

Spintronic-based neuron devices for neural network hardware are gaining increasing attention. However, the majority of these devices are designed to replicate a highly simplified neuronal model known as the leaky integrate-and-fire (LIF) neuron. We present a domain wall motion-based magnetic tunnel junction (DW-MTJ) device that emulates the more bio-plausible FitzHugh–Nagumo neuron model. The neuron characteristics are realized using spin–orbit torque (SOT) driven DW motion in a circular nano-pillar. We obtain sustained magnetization relaxation oscillations in the presence of a DC charge current. The shape, frequency, and phase of the FitzHugh–Nagumo oscillations are controlled by SOT and voltage. A thorough parametric analysis of the proposed neuron device structure is done to assess the device viability with different material systems and environmental conditions. The device consumes energy per spike in the range from 9 to 47.5 fJ, depending upon the parameters. Furthermore, we map the device characteristics to the FitzHugh–Nagumo neuron model by tuning the parameters. The device model is integrated into a fully connected, 3-layer spiking neural network (SNN) framework to classify the MNIST handwritten digit images dataset. We train and test the network under different device conditions. The SNN achieves a classification accuracy of more than 98% in all cases, showcasing its potential for efficient, bio-plausible neuromorphic systems.

A memristor is a nonlinear resistor with time memory. The resistance of a classical memristor at a given time is represented by the integration of all the full states before the time instant, a case of ideal memory without any loss. Recent studies show that there is a memory loss of the HP TiO2 linear model, in which the width of the doped layer of HP TiO2 model cannot be equal to zero or the whole width of the model. Based on this observation, a fractional-order HP TiO2 memristor model with the order between 0 and 1 is proposed, and the fingerprint analysis of the new fractional-order model under periodic external excitation is made, thus the formula for calculating the area of hysteresis loop is obtained. It is found that the shape and the area enclosed by the hysteresis loop depend on the order of the fractional-order derivative. Especially, for exciting frequency being bigger than 1, the memory strength of the memristor takes its maximal value when the order is a fractional number, not an integer. Then, the current-voltage characteristics of the simple series one-port circuit composed of the fractional-order memristor and the capacitor, or composed of the fractional-order memristor and the inductor are studied separately. Results demonstrate that at the periodic excitation, the memristor in the series circuits will have capacitive properties or inductive properties as the fractional order changes.

Stochastic resonance induced by novel random transitions of motion of FitzHugh–Nagumo neuron model

Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model

In this paper, we describe the asymptotic behavior of a network of locally connected oscillators. The main result concerns asymptotic synchronization. The presented study is stated in the framework of neuronal modeling of visual object segmentation using oscillatory correlation. The practical motivations of the synchronization analysis are based on neurophysiological experiments which led to the assumptions that existence of temporal coding schemes in the brain by which neurons, with oscillatory dynamics, coding for the same coherent object synchronize their activities, while neurons coding for different objects oscillate with nonzero phase lags. The oscillator model considered is the FitzHugh–Nagumo neuron model. We restrict our study to the mathematical analysis of a network of such neurons. We firstly show the motivations and suitability of choosing FitzHugh–Nagumo oscillator, mainly for stimulus coding purposes, and then we give sufficient conditions on the coupling parameters which guarantee asymptotic synchronization of oscillators receiving the same external stimulation (input). We have used networks of such oscillators to design a layered architecture for object segmentation in gray-level images. Due to space limitations, description of this architecture and simulation results are briefly referred to by the end of the paper.

Dynamic behaviors of the FitzHugh–Nagumo neuron model with state-dependent impulsive effects

Ghost stochastic resonance induced by a power-law distributed noise in the FitzHugh–Nagumo neuron model

Analysis of two spectral Galerkin approximation schemes for solving the perturbed FitzHugh-Nagumo neuron model

Mode transition and energy dependence of FitzHugh-Nagumo neural model driven by high-low frequency electromagnetic radiation