Izhikevich Neuron Research Articles

Tactile Surface Roughness Categorization With Multineuron Spike Train Distance

Tactile sensing with spiking neural networks (SNNs) has attracted increasing attention in the past decades. In this article, a novel SNN framework is proposed for the tactile surface roughness categorization task. In contrast to supervised SNN methods such as ReSuMe and Tempotron that require prespecifying target spike trains, the presented method performs the classification through directly comparing the distance between multineuron spike trains. Unlike simple spike train fusion methods using average pairwise spike train distance or pooled spike train distance, the proposed method merges spike trains from different neurons with the multineuron spike train distance, which can capture the complex correlation of multiple spike trains. Specifically, the spike trains are generated via the Izhikevich neurons from tactile signals. The similarity of the multineuron spike trains is computed using the multineuron Victor–Purpura spike train distance, which can be efficiently implemented in an inductive manner. The classification can be performed by incorporating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbors and the multineuron spike train distance as a similarity metric. The proposed framework is quite general, i.e., other multineuron spike train distances and spike train kernel-based methods can be readily incorporated. The effectiveness of the proposed method has been demonstrated on a tactile data set by comparing it with various feature- and spike-based methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In the soft neuromorphic implementation of biomimetic tactile sensing and the development of the tactile sensing capability in neurobotic systems, the processing and analysis of spike-like tactile signals are quite common. Inspired by human tactile perception, this article proposes a novel supervised spiking neural network method for tactile sensing tasks. The traditional methods have to prespecify target spike trains, which is still an open question. In addition, the current ways to fuse spike trains from multiple neurons are far from mature. This article tackles these two problems using spike train similarity comparison with multineuron spike train distance. The direct spike train similarity comparison avoids the need to prespecify target spike trains. The multineuron spike train distance can inherently fuse spike trains from different neurons. It is demonstrated that the proposed method is able to effectively perform classification in a tactile roughness discrimination task.

Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform, patterns that emerge due to instability in an extended homogeneous 2D spatial domain, using the excitable Izhikevich neuron model. We examine diffusive instability and perform bifurcation and fixed-point analyses to characterize the patterns and their stability. Then, we derive analytically the amplitude equations that establish the activities of reaction-diffusion structures. We report on the emergence of diverse spatial structures including hexagonal and mixed-type patterns by providing a systematic mathematical approach, including variations in correlated oscillations, pattern variations and amplitude fluctuations. Our work shows that the emergence of spatiotemporal behavior, commonly found in excitable systems, has the potential to contribute significantly to the study of diffusively-coupled biophysical systems at large.

An extensive FPGA-based realization study about the Izhikevich neurons and their bio-inspired applications

An extensive FPGA-based realization study about the Izhikevich neurons and their bio-inspired applications

Analysis of spatially extended excitable Izhikevich neuron model near instability

The article focuses on the issue of a spatiotemporal excitable biophysical model that describes the propagation of electrical potential called spikes to model the diffusion-induced dynamics based on an analytical development of amplitude equations. Considering the Izhikevich neuron model consisting of coupled systems of ODEs, we demonstrate various results of spatiotemporal architecture (PDEs) using a suitable parameter regime. We analytically perform the saddle-node bifurcation and Hopf bifurcation analysis with bifurcating periodic solutions that show the transition phases in the system dynamics. We study different firing patterns both analytically and numerically by the formation of Riccati differential equation. To examine the characteristics of diffusive instabilities, we use Turing amplitude equations by multiscaling method. The instabilities and Turing bifurcation are established using theoretical analysis and numerical simulations. The spatial dynamics has potential effects on the deterministic system as a result of the diffusive matrices with various couplings, and the coupled oscillators with this nearest-neighbor coupling show synchronization measured by the synchronization factor analysis. Our results qualitatively reproduce different phenomena of the extended excitable system based with an efficient analytical scheme.

Anti-injury function of complex spiking neural networks under targeted attack

Brain-like intelligence is to simulate the structure and function of the biological brain as much as possible based on the latest findings in brain science. The biological brain has strong robustness under external attacks. In this study, two complex spiking neural networks (CSNNs) are constructed: a spiking neural network (SNN) with small-world topology and a SNN with scale-free topology, in which the nodes are Izhikevich neuron model, and the edges are the synaptic plasticity model including excitatory and inhibitory synapses. For the targeted attack, the anti-injury function of two CSNNs is comparatively analyzed. On this basis, the anti-injury mechanism of CSNN is explored. The experimental results show that: (1) Small-world SNN (SWSNN) has better performance than scale-free SNN (SFSNN) in the anti-injury ability under targeted attack on high-degree nodes, and they are similar in the anti-injury ability under targeted attack on intermediate and low-degree nodes; the results of the robustness of topology are consistent with the results of anti-injury function of CSNNs, which indicates that the anti-injury ability of two kinds of CSNNs is affected by topology. (2) The dynamic evolutions of neuron firing, synaptic weight, and topological characteristic in the information processing of CSNN have a linkage effect under targeted attack; the dynamic evolution of synaptic weight is significantly related to the anti-injury ability of CSNNs, which clues synaptic plasticity is the intrinsic factor of the anti-injury function of CSNNs.

Reconfigurable field‐programmable gate array‐based on‐chip learning neuromorphic digital implementation for nonlinear function approximation

SummaryHardware implementations of spiking neural networks, which are known as neuromorphic architectures, provide an explicit understanding of brain performance. As a result, biological features of the brain may well inspire the next generation of computers and electronic systems used in such areas as signal processing, image processing, function approximation, and pattern recognition. Approximating nonlinear functions has many uses in computer science and applied mathematics. The sigmoid is the most universal activation function in neural networks by which the relationship between biological and artificial neurons is defined. It is a suitable option for predicting the probability of anything from 0 to 1 as output. In this paper, a spiking neural network using Izhikevich neurons and a gradient descent learning algorithm are propounded to approximate the sigmoid and other nonlinear functions. The flexibility of the spiking network is demonstrated by showing the average relative errors in the approximation process. A time‐ and cost‐efficient digital neuromorphic implementation on the base of on‐chip learning method for approximating the sigmoid function is also discussed. The paper reports the results of the hardware synthesis and the spiking network's physical implementation on a field‐programmable gate array. The maximum frequency and throughput of the implemented network were 83.209 MHz and 9.86 Mb/s, respectively.

Simulation of spiking activities neuron models using the Euler method

Simulation of neuron spiking activity models has been carried out using the Euler method. This study aims to simulate spiking activity in a neuron model. The neuron model used is the Hodgkin-Huxley neuron model, Integrate and Fire neuron model, Wilson neuron model, and Izhikevich neuron model. The research was conducted by implementing the mathematical equations of each neuron model used and then recording the membrane potential changes from time to time using the Euler method in MATLAB. The different forms of spiking activity were done by varying the variable’s value in each mathematical equation of a neuron model that describes the processing of action potentials (spikes) influenced by ion channel activity. The results showed that the Integrate and Fire neuron models produce regular spiking (RS), Hodgkin-Huxley neuron models have regular spiking (RS) forms, Wilson neuron models produce regular spiking (RS), fast-spiking (FS), and intrinsic bursting (IB), Izhikevich neuron model produces regular spiking (RS), fast-spiking (FS), intrinsic bursting (IB), chattering neurons (CH), and low threshold spiking (LTS). The complexity of the variables used and the spiking activity generated by each neuron model can provide an overview of computational efficiency and proximity to actual biological neurons.

Differential mapping spiking neural network for sensor-based robot control

In this work, a spiking neural network (SNN) is proposed for approximating differential sensorimotor maps of robotic systems. The computed model is used as a local Jacobian-like projection that relates changes in sensor space to changes in motor space. The SNN consists of an input (sensory) layer and an output (motor) layer connected through plastic synapses, with inter-inhibitory connections at the output layer. Spiking neurons are modeled as Izhikevich neurons with a synaptic learning rule based on spike timing-dependent plasticity. Feedback data from proprioceptive and exteroceptive sensors are encoded and fed into the input layer through a motor babbling process. A guideline for tuning the network parameters is proposed and applied along with the particle swarm optimization technique. Our proposed control architecture takes advantage of biologically plausible tools of an SNN to achieve the target reaching task while minimizing deviations from the desired path, and consequently minimizing the execution time. Thanks to the chosen architecture and optimization of the parameters, the number of neurons and the amount of data required for training are considerably low. The SNN is capable of handling noisy sensor readings to guide the robot movements in real-time. Experimental results are presented to validate the control methodology with a vision-guided robot.

Suppressing the spiking of a synchronized array of Izhikevich neurons

The aim of this research work is to investigate the synchronization and desynchronization of an array of non-identical Izhikevich neurons in a star-like configuration. Both regular spiking neurons and fast spiking neurons are considered in the analysis. The equilibrium points and their stability for a single neuron are determined, and an adaptive stable filter is applied to suppress the spiking of the neuron. A star coupling array configuration is applied to synchronize an array of isolated neurons. Next, the adaptive stable filter is employed to suppress the spiking of the synchronized array of coupled neurons. Appreciably, one filter is enough to suppress the entire star-like array. Numerical simulations demonstrate the success of the proposed technique. The parameters that govern the performance of the filter are specified, the limitations of the methodology are identified, and the required conditions for application are identified.

Modeling Working Memory in a Spiking Neuron Network Accompanied by Astrocytes.

We propose a novel biologically plausible computational model of working memory (WM) implemented by a spiking neuron network (SNN) interacting with a network of astrocytes. The SNN is modeled by synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons via chemicals diffused in the extracellular space. Calcium elevations occur in response to the increased concentration of the neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strength of the synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organized by the application of a cue pattern representing one from the memory set distorted by noise. We found that successful retrieval with the level of the correlation between the recalled pattern and ideal pattern exceeding 90% is possible for the multi-item WM task. Having analyzed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in the SNN leading to successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Fast Simulations of Highly-Connected Spiking Cortical Models Using GPUs.

Over the past decade there has been a growing interest in the development of parallel hardware systems for simulating large-scale networks of spiking neurons. Compared to other highly-parallel systems, GPU-accelerated solutions have the advantage of a relatively low cost and a great versatility, thanks also to the possibility of using the CUDA-C/C++ programming languages. NeuronGPU is a GPU library for large-scale simulations of spiking neural network models, written in the C++ and CUDA-C++ programming languages, based on a novel spike-delivery algorithm. This library includes simple LIF (leaky-integrate-and-fire) neuron models as well as several multisynapse AdEx (adaptive-exponential-integrate-and-fire) neuron models with current or conductance based synapses, different types of spike generators, tools for recording spikes, state variables and parameters, and it supports user-definable models. The numerical solution of the differential equations of the dynamics of the AdEx models is performed through a parallel implementation, written in CUDA-C++, of the fifth-order Runge-Kutta method with adaptive step-size control. In this work we evaluate the performance of this library on the simulation of a cortical microcircuit model, based on LIF neurons and current-based synapses, and on balanced networks of excitatory and inhibitory neurons, using AdEx or Izhikevich neuron models and conductance-based or current-based synapses. On these models, we will show that the proposed library achieves state-of-the-art performance in terms of simulation time per second of biological activity. In particular, using a single NVIDIA GeForce RTX 2080 Ti GPU board, the full-scale cortical-microcircuit model, which includes about 77,000 neurons and 3 · 108 connections, can be simulated at a speed very close to real time, while the simulation time of a balanced network of 1,000,000 AdEx neurons with 1,000 connections per neuron was about 70 s per second of biological activity.

Noise suppression ability and its mechanism analysis of scale-free spiking neural network under white Gaussian noise.

With the continuous improvement of automation and informatization, the electromagnetic environment has become increasingly complex. Traditional protection methods for electronic systems are facing with serious challenges. Biological nervous system has the self-adaptive advantages under the regulation of the nervous system. It is necessary to explore a new thought on electromagnetic protection by drawing from the self-adaptive advantage of the biological nervous system. In this study, the scale-free spiking neural network (SFSNN) is constructed, in which the Izhikevich neuron model is employed as a node, and the synaptic plasticity model including excitatory and inhibitory synapses is employed as an edge. Under white Gaussian noise, the noise suppression abilities of the SFSNNs with the high average clustering coefficient (ACC) and the SFSNNs with the low ACC are studied comparatively. The noise suppression mechanism of the SFSNN is explored. The experiment results demonstrate that the following. (1) The SFSNN has a certain degree of noise suppression ability, and the SFSNNs with the high ACC have higher noise suppression performance than the SFSNNs with the low ACC. (2) The neural information processing of the SFSNN is the linkage effect of dynamic changes in neuron firing, synaptic weight and topological characteristics. (3) The synaptic plasticity is the intrinsic factor of the noise suppression ability of the SFSNN.

An Efficient Spiking Neuron Hardware System Based on the Hardware-Oriented Modified Izhikevich Neuron (HOMIN) Model

Mathematical modifications have been made to the Izhikevich Neuron Model to allow for a simple, low-area digital hardware implementation with low computational intensity. The implemented neuron circuit only requires one input parameter to replicate all of the cortical neuron behaviours described by Izhikevich. The low hardware requirements of this neuron implementation make large, highly parallel digital spiking neural networks of this neuron feasible. Additionally, the model requires fewer external parameter changes to exhibit diverse neuron behaviours. The alterations made to create this novel model are presented in detail with a performance comparison to the original Izhikevich Neuron. Subsequently a digital hardware realization is presented and its performance is characterized.

A Multi-Scale Computational Model of Excitotoxic Loss of Dopaminergic Cells in Parkinson's Disease.

Parkinson's disease (PD) is a neurodegenerative disorder caused by loss of dopaminergic neurons in substantia nigra pars compacta (SNc). Although the exact cause of cell death is not clear, the hypothesis that metabolic deficiency is a key factor has been gaining attention in recent years. In the present study, we investigated this hypothesis using a multi-scale computational model of the subsystem of the basal ganglia comprising the subthalamic nucleus (STN), globus pallidus externa (GPe), and SNc. The proposed model is a multiscale model in that interaction among the three nuclei are simulated using more abstract Izhikevich neuron models, while the molecular pathways involved in cell death of SNc neurons are simulated in terms of detailed chemical kinetics. Simulation results obtained from the proposed model showed that energy deficiencies occurring at cellular and network levels could precipitate the excitotoxic loss of SNc neurons in PD. At the subcellular level, the models show how calcium elevation leads to apoptosis of SNc neurons. The therapeutic effects of several neuroprotective interventions are also simulated in the model. From neuroprotective studies, it was clear that glutamate inhibition and apoptotic signal blocker therapies were able to halt the progression of SNc cell loss when compared to other therapeutic interventions, which only slowed down the progression of SNc cell loss.

A Low-Cost High-Throughput Digital Design of Biorealistic Spiking Neuron

With the ability to generate different spiking patterns, Izhikevich model has well been considered a computationally efficient and biologically plausible neuron model for applications such as brain dynamic behavior study. This brief presents a low-cost, high-throughput digital hardware design for Izhikevich neuron model. The proposed design requires only addition, subtraction and logic shifts operations to achieve the low hardware cost. The dynamic behaviors of both the proposed neuron model and the original Izhikevich model were analyzed using the phase portraits. The FPGA implementation results demonstrated that the proposed design can reproduce different spiking patterns with very high throughput. Compared to existing designs, the proposed design achieves the lowest slices and LUTs utilization, which are 73% and 11% lower than the latest design (HOMIN), respectively.

A Cerebellar Computational Mechanism for Delay Conditioning at Precise Time Intervals.

The cerebellum is known to have an important role in sensing and execution of precise time intervals, but the mechanism by which arbitrary time intervals can be recognized and replicated with high precision is unknown. We propose a computational model in which precise time intervals can be identified from the pattern of individual spike activity in a population of parallel fibers in the cerebellar cortex. The model depends on the presence of repeatable sequences of spikes in response to conditioned stimulus input. We emulate granule cells using a population of Izhikevich neuron approximations driven by random but repeatable mossy fiber input. We emulate long-term depression (LTD) and long-term potentiation (LTP) synaptic plasticity at the parallel fiber to Purkinje cell synapse. We simulate a delay conditioning paradigm with a conditioned stimulus (CS) presented to the mossy fibers and an unconditioned stimulus (US) some time later issued to the Purkinje cells as a teaching signal. We show that Purkinje cells rapidly adapt to decrease firing probability following onset of the CS only at the interval for which the US had occurred. We suggest that detection of replicable spike patterns provides an accurate and easily learned timing structure that could be an important mechanism for behaviors that require identification and production of precise time intervals.

Emergence of Mixed Mode Oscillations in Random Networks of Diverse Excitable Neurons: The Role of Neighbors and Electrical Coupling.

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

Interaction of neuronal and network mechanisms on firing propagation in a feedforward network

The mammalian brain has enormously complex neuronal diversity and a highly modular structure. The propagation of information in the modular brain network can be modeled by a feedforward network (FFN). Although studies in this area have yielded many important results, neuronal diversity has rarely been considered. In the current work, we investigate the complex interactions between the intrinsic properties of neurons and the FFN structure in the propagation of spiking activity. Here, four typical types of cortical neurons reproduced by the Izhikevich neuron model are introduced. A homogeneous FFN composed of a single type of excitatory neuron (regular spiking, mixed model, or tonic bursting) can propagate spiking activity. However, an FFN with fast spiking neurons does not propagate spiking activity. By modifying the network structure and synaptic weights, the spiking propagation of the homogeneous FFNs can vary from synchronous transmission (with a high firing rate) to asynchronous transmission (with a low firing rate). Among the homogeneous FFNs, both the firing rate and the synchrony of the FFN with tonic bursting neurons are the highest, but those of the FFN with regular spiking neurons is lowest, even when implementing the same FFN structure. For the FFN with mixed neuronal types, interestingly, the spiking propagation is very sensitive to the composition of the four types of neurons. By introducing fast spiking neurons into the homogeneous FFN composed of excitatory neurons, spiking propagation can be modified from synchronous to asynchronous. Similarly, changing the proportion of any of the types of neuron affects the spiking propagation, even for very small changes. The underlying mechanism of these observed results has also been discussed.

Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction.

Energy supply plays a key role in metabolism and signal transmission of biological individuals, neurons in a complex electromagnetic environment must be accompanied by the absorption and release of energy. In this paper, the discharge mode and the Hamiltonian energy are investigated within the Izhikevich neuronal model driven by external signals in the presence of electromagnetic induction. It is found that multiple electrical activity modes can be observed by changing external stimulus, and the Hamiltonian energy is more dependent on the discharge mode. In particular, there is a distinct shift and transition in the Hamiltonian energy when the discharge mode is switched quickly. Furthermore, the amplitude of periodic stimulus signal has a greater effect on the neuronal energy compared to the angular frequency, and the average Hamiltonian energy decreases when the discharge rhythm becomes higher. Based on the principle of energy minimization, the system should choose the minimum Hamiltonian energy when maintaining various trigger states to reduce the metabolic energy of signal processing in biological systems. Therefore, our results give the possible clues for predicting and selecting appropriate parameters, and help to understand the sudden and paroxysmal mechanisms of epilepsy symptoms.

Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise

Abstract The neuron's behavior is related to the changes in its complex electrophysiological environment such as variations in ion concentration. In this paper, a three-variable memristive Izhikevich model is proposed to describe the behavior of neurons under electromagnetic induction and noise. This model can represent the effect of internal and external magnetic fields on neurons. The improved model without the external magnetic field can exhibit firing patterns such as regular spiking, resonator, chattering, fast-spiking, chaotic spiking, and chaotic bursts. The presence of the external magnetic field causes the firing pattern of the neuron to change, for example shifting from chaotic firings to the periodic ones or vice versa. Furthermore, the firing rate of the neuron is increased. It is also observed that the external field effect can stimulate the neuron to fire, while in the absence of the external field, it is at rest. Finally, in order to detect the realistic neuron's activities, we examine the effect of Gaussian white noise on the improved model. The results show that the model has more robustness against noise with considering the external magnetic field.