Izhikevich Neuron Research Articles

Signal of Death in Izhikevich Neuron Model

Signal of Death in Izhikevich Neuron Model

Multiplierless Implementation of Noisy Izhikevich Neuron With Low-Cost Digital Design.

Fast speed and a high accuracy implementation of biological plausible neural networks are vital key objectives to achieve new solutions to model, simulate and cure the brain diseases. Efficient hardware implementation of spiking neural networks is a significant approach in biological neural networks. This paper presents a multiplierless noisy Izhikevich neuron (MNIN) model, which is used for the digital implementation of biological neural networks in large scale. Simulation results show that the MNIN model reproduces the same operations of the original noisy Izhikevich neuron. The proposed model has a low-cost hardware implementation property compared with the original neuron model. The field-programmable gate array realization results demonstrated that the MNIN model follows the different spiking patterns appropriately.

Beta-Rhythm Oscillations and Synchronization Transition in Network Models of Izhikevich Neurons: Effect of Topology and Synaptic Type

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.

Effect of Lévy noise on the networks of Izhikevich neurons

Levy noise plays a significant role in jump-noise processes found in neurons. We perform numerical simulations of synaptically coupled Izhikevich networks under the effect of general non-Gaussian Levy noise. Firing dynamics of an all-to-all coupled Izhikevich network and two excitatory coupled Izhikevich networks with differing adaptation properties are studied in response to applied Levy noise. Whole parameter space of Levy noise is investigated by changing its characteristic exponent, skewness, scale and mean parameters. The simulation results show that the noise generated from $$\alpha $$ -stable Levy distribution causes significant dynamical changes in the firing pattern of neuronal network. Different firing patterns exhibited by Izhikevich neurons such as tonic spiking, chattering, intrinsic bursting, low threshold spiking and fast spiking are studied in the network level with and without Levy noise. In all cases, neurons are found to be irregularly spiking when Levy noise with characteristic exponent $$\alpha $$ equal to 0.5 is applied. Levy noise with this particular value of $$\alpha $$ as 0.5 causes the Izhikevich network to have a dynamical behaviour independent of topology and heterogeneity of the network. At this value of characteristic exponent, density of the stable Levy distribution in standard parameterisation is maximum. Other parameters of Levy noise do not influence the way in which a particular neuron is firing. The effects of Levy noise on the correlation between individual neurons and on the networks are investigated using statistical measures.

A Forgetting Memristive Spiking Neural Network for Pavlov Experiment

In this paper, we designed a memristive spiking neural network (MSNN) to perform a fully functional Pavlov experiment. A memristor with forgetting effect is adopted to implement synapses while Izhikevich neurons are used for generating tonic spiking and tonic bursting signals. An asymmetric linear spiking time dependent plasticity (STDP) is naturally formed by taking into account the activation time difference between pre-synaptic neurons. Our design realizes associative, correcting, and forgetting processes without learning rule control modules. Moreover, an association will be enhanced if the activation time of two neurons is close enough, otherwise, all conditioned reflex associations will be weakened.

A real-time spike-timing classifier of spatio-temporal patterns

Abstract Considering the problem of recognizing non-verbal cues in Human–Robot Interaction applications, this paper proposes a novel real-time unsupervised spike timing neural network for recognition and early detection of spatio-temporal human gestures. Two spiking network classifiers one based on Izhikevich neuron model, and the other one based on Integrate-and-Fire-or-Burst neuron model have been implemented in CUDA, and allow the classification to be performed in real-time. To evaluate the performance of this proposal, we test the case of a physical robot observing air-handwritings of human gesture. The proposed approaches run in real-time, thus they are suitable for human–robot applications; they allow real-time early classifying human gestures and actions while they require a very small number of training samples. In comparing to other prominent techniques, our approaches demonstrate superior accuracy and are suitable for early classification of different types of human actions in time-sensitive mobile applications such as robotics.

A Comparative Study on Determining Nonlinear Function Parameters of the Izhikevich Neuron Model

In the literature, the parabolic function of the Izhikevich Neuron Model (IzNM) is transformed to the Piecewise Linear (PWL) functions in order to make digital hardware implementations easier. The coefficients in this PWL functions are identified by utilizing the error-prone classical step size method. In this paper, it is aimed to determine the coefficients of the PWL functions in the modified IzNM by using the stochastic optimization methods. In order to obtain more accurate results, Genetic Algorithm and Artificial Bee Colony Algorithm (GA and ABC) are used as alternative estimation methods, and amplitude and phase errors between the original and the modified IzNMs are specified with a newly introduced error minimization algorithm, which is based on the exponential forms of the complex numbers. In accordance with this purpose, GA and ABC algorithms are run 30 times for each of the 20 behaviors of a neuron. The statistical results of these runs are given in the tables in order to compare the performance of three parameter-search methods and especially to see the effectiveness of the newly introduced error minimization algorithm. Additionally, two basic dynamical neuronal behaviors of the original and the modified IzNMs are realized with a digital programmable device, namely FPGA, by using new coefficients identified by GA and ABC algorithms. Thus, the efficiency of the GA and ABC algorithm for determining the nonlinear function parameters of the modified IzNM are also verified experimentally.

Modeling dynamic behavior of striatal medium spiny neurons with point neuron models

The aim of this work is to investigate the role of network organization and the neuron model type on the collective dynamic behavior of striatal population. For that purpose, two different scale neuron models which are phenomenological Izhikevich and conductance-based Hodgkin-Huxley (HH) type are used to investigate the dynamic behavior of MS neurons. Two network architectures are proposed with inhibitory and excitatory synaptic currents. In these networks, while all MS neurons affect each other with inhibitory synaptic currents, an excitatory current is applied to all MS neurons in the first layer, to represent the cortical inputs. A mathematical model of a medium spiny neuron of striatum based on HH type neuron model is proposed using different calcium channels and its dynamical behavior is investigated. It is observed that when the original HH model is used, regular spiking type behavior is observed. Including the high threshold calcium current, after hyperpolarization calcium current and voltage gated potasium current into the model improves the modeling capabilities. With extended ion channels, in addition to regular spiking behavior, bursting with resting stage are obtained. Then, Izhikevich neuron model is used in the network structures to compare the dynamic behaviors and computational time.

Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network.

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). However, STDP was not considered in previous works on stochastic burst synchronization (SBS) between noise-induced burstings of sub-threshold neurons. Here, we study the effect of additive STDP on SBS by varying the noise intensity D in the Barabási-Albert scale-free network (SFN). One of our main findings is a Matthew effect in synaptic plasticity which occurs due to a positive feedback process. Good burst synchronization (with higher bursting measure) gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization (with lower bursting measure) gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing D, in contrast to a relatively smooth transition in the absence of STDP. We also investigate the effects of network architecture on SBS by varying the symmetric attachment degree [Formula: see text] and the asymmetry parameter [Formula: see text] in the SFN, and Matthew effects are also found to occur by varying [Formula: see text] and [Formula: see text]. Furthermore, emergences of LTP and LTD of synaptic strengths are investigated in details via our own microscopic methods based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic instantaneous individual burst rates (IIBRs). Finally, a multiplicative STDP case (depending on states) with soft bounds is also investigated in comparison with the additive STDP case (independent of states) with hard bounds. Due to the soft bounds, a Matthew effect with some quantitative differences is also found to occur for the case of multiplicative STDP.

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model

Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar’e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.

Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking

The firing activities of multiple timescale dynamics for single neurons can be treated with fractional-order derivative. It has been shown in previous studies (theoretical and experimental) that the passive properties of membranes may be considered by fractional-order dynamics as it can produce various types of memory-dependent dynamics. Spiking and bursting play major role in information processing for cortical neurons. However, it is not completely clear to what extent the dynamics of fractional-order excitable systems may redesign the properties of excitable cells. It is demonstrated that the fractional dynamics of Izhikevich neuron model is capable to exhibit various oscillations for cortical neurons such as regular spiking and various bursting patterns, mixed mode oscillations, chattering, fast spiking. It characterizes various firing modes (hence the firing frequency) better than the classical-order model. It shows the dynamical differences between the integer-order and fractional-order system. The firing frequency is increased with the decrease of fractional exponents. Further, the responses of a network of excitatory and inhibitory Izhikevich neurons with a controlled parameter set show different dynamical behavior at various fractional orders and it controls the long-term interactions.

Capturing Spike Variability in Noisy Izhikevich Neurons Using Point Process Generalized Linear Models.

To understand neural activity, two broad categories of models exist: statistical and dynamical. While statistical models possess rigorous methods for parameter estimation and goodness-of-fit assessment, dynamical models provide mechanistic insight. In general, these two categories of models are separately applied; understanding the relationships between these modeling approaches remains an area of active research. In this letter, we examine this relationship using simulation. To do so, we first generate spike train data from a well-known dynamical model, the Izhikevich neuron, with a noisy input current. We then fit these spike train data with a statistical model (a generalized linear model, GLM, with multiplicative influences of past spiking). For different levels of noise, we show how the GLM captures both the deterministic features of the Izhikevich neuron and the variability driven by the noise. We conclude that the GLM captures essential features of the simulated spike trains, but for near-deterministic spike trains, goodness-of-fit analyses reveal that the model does not fit very well in a statistical sense; the essential random part of the GLM is not captured.

Statistical complexity is maximized in a small-world brain.

In this paper, we study a network of Izhikevich neurons to explore what it means for a brain to be at the edge of chaos. To do so, we first constructed the phase diagram of a single Izhikevich excitatory neuron, and identified a small region of the parameter space where we find a large number of phase boundaries to serve as our edge of chaos. We then couple the outputs of these neurons directly to the parameters of other neurons, so that the neuron dynamics can drive transitions from one phase to another on an artificial energy landscape. Finally, we measure the statistical complexity of the parameter time series, while the network is tuned from a regular network to a random network using the Watts-Strogatz rewiring algorithm. We find that the statistical complexity of the parameter dynamics is maximized when the neuron network is most small-world-like. Our results suggest that the small-world architecture of neuron connections in brains is not accidental, but may be related to the information processing that they do.

Mode-locking behavior of Izhikevich neurons under periodic external forcing.

Many neurons in the auditory system of the brain must encode periodic signals. These neurons under periodic stimulation display rich dynamical states including mode locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated sounds can lead to various forms of n:m mode-locked states, in which a neuron fires n action potentials per m cycles of the stimulus. Here, we study mode-locking in the Izhikevich neurons, a reduced model of the Hodgkin-Huxley neurons. The Izhikevich model is much simpler in terms of the dimension of the coupled nonlinear differential equations compared with other existing models, but excellent for generating the complex spiking patterns observed in real neurons. We obtained the regions of existence of the various mode-locked states on the frequency-amplitude plane, called Arnold tongues, for the Izhikevich neurons. Arnold tongue analysis provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. We find these tongues for both class-1 and class-2 excitable neurons in both deterministic and noisy regimes.

Biomimetic neural network for modifying biological dynamics during hybrid experiments

Electrical stimulation of nerve tissue and recording of neural electrical activity are the basis of emerging prostheses and treatments for many neurological disorders. Here we present closed-loop bio-hybrid experiment using in vitro biological neuronal network (BNN) with an artificial neural network (ANN) implemented in a neuromorphic board. We adopted a neuromorphic board which is able to perform real-time event detection and trigger an electrical stimulation of the BNN. This system embeds an ANN, based on Izhikevich neurons which can be put in uni- and bi-directional communication with the BNN. The ANN used in the following experiments was made up of 20 excitatory neurons with inhibition synapse and with synaptic plasticity to design central pattern generator. Open-loop and closed-loop hybrid experiments show that the biological dynamics can be modified. This work can be seen as the first step towards the realization of an innovative neuroprosthesis.

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Chaotic resonance (CR), in which a system responds to a weak signal through the effects of chaotic activities, is a known function of chaos in neural systems. The current belief suggests that chaotic states are induced by different routes to chaos in spiking neural systems. However, few studies have compared the efficiency of signal responses in CR across the different chaotic states in spiking neural systems. We focused herein on the Izhikevich neuron model, comparing the characteristics of CR in the chaotic states arising through the period-doubling or tangent bifurcation routes. We found that the signal response in CR had a unimodal maximum with respect to the stability of chaotic orbits in the tested chaotic states. Furthermore, the efficiency of signal responses at the edge of chaos became especially high as a result of synchronization between the input signal and the periodic component in chaotic spiking activity.

Recognizing tactile surface roughness with a biomimetic fingertip: A soft neuromorphic approach

Surface roughness is an important object property and can significantly affect the friction characteristics, wear resistance, and fatigue life of components. Although some work has been done on demonstrating the capability of specific tactile sensors for surface roughness discrimination, the soft neuromorphic approach by taking inspirations from neuroscience for tactile surface roughness discrimination is exceptionally rare. This paper aims to fill this gap, and presents a soft neuromorphic method for tactile surface roughness discrimination with a biomimetic fingertip. The analog tactile signals generated from polyvinylidene difluoride (PVDF) films are fed as input to the Izhikevich neurons in order to obtain spike trains. Two distinct decoding schemes based on k-nearest neighbors (kNN) in both spike feature space and spike train space are used for surface roughness discrimination. We thoroughly examined the different spike train distance based kNN (STD-kNN) algorithms for decoding spike trains. Eight standard rough surfaces with roughness values (Ra) of 50μm, 25μm, 12.5μm, 6.3μm 3.2μm, 1.6μm, 0.8μm, and 0.4μm are explored. The highest classification accuracy of (77.6±13.7) % can be achieved with kNN (k=11) classifier and the Victor−Purpura distance (q=0.024ms−1).

A spiking network that learns to extract spike signatures from speech signals

Spiking neural networks (SNNs) with adaptive synapses reflect core properties of biological neural networks. Speech recognition, as an application involving audio coding and dynamic learning, provides a good test problem to study SNN functionality. We present a simple, novel, and efficient nonrecurrent SNN that learns to convert a speech signal into a spike train signature. The signature is distinguishable from signatures for other speech signals representing different words, thereby enabling digit recognition and discrimination in devices that use only spiking neurons. The method uses a small, nonrecurrent SNN consisting of Izhikevich neurons equipped with spike timing dependent plasticity (STDP) and biologically realistic synapses. This approach introduces an efficient and fast network without error-feedback training, although it does require supervised training. The new simulation results produce discriminative spike train patterns for spoken digits in which highly correlated spike trains belong to the same category and low correlated patterns belong to different categories. The proposed SNN is evaluated using a spoken digit recognition task where a subset of the Aurora speech dataset is used. The experimental results show that the network performs well in terms of accuracy rate and complexity.

Modeling influences of dopamine on synchronization behavior of striatum

ABSTRACTA network model of striatum that comprises medium spiny neurons (MSNs) and fast spiking interneurons (FSIs) is constructed following the work of Humphries et al. (2009). The dynamic behavior of striatum microcircuit is investigated using a dopamine-modulated modified Izhikevich neuron model. The influences of dopamine on the synchronization behavior of the striatal microcircuit and the dependence on receptor type are investigated with and without time delay. To investigate the role of two types of dopamine receptors, D1 and D2, on the overall activity of the striatum microcircuit, the activities of two groups are considered as disconnected and connected. When the connection exists between D1 and D2 sub-networks with zero dopamine and time delay, neuronal activity decreases because of an inhibitory effect of the connected neurons of the other sub-network. In the presence of dopamine, an increase in the activity of D1 type MSNs and quiescent behavior of D2 type MSNs are observed when the time delay is zero. However, the diversity in synchronization of D1 and D2 type MSNs is observed for different synaptic time delays and synaptic strengths in the case that dopamine is present.

Modeling of time delay-induced multiple synchronization behavior of interneuronal networks with the Izhikevich neuron model

Modeling of time delay-induced multiple synchronization behavior of interneuronal networks with the Izhikevich neuron model