Izhikevich Neuron Model Research Articles

Spiking Neural Network Pressure Sensor.

Von Neumann architecture requires information to be encoded as numerical values. For that reason, artificial neural networks running on computers require the data coming from sensors to be discretized. Other network architectures that more closely mimic biological neural networks (e.g., spiking neural networks) can be simulated on von Neumann architecture, but more important, they can also be executed on dedicated electrical circuits having orders of magnitude less power consumption. Unfortunately, input signal conditioning and encoding are usually not supported by such circuits, so a separate module consisting of an analog-to-digital converter, encoder, and transmitter is required. The aim of this article is to propose a sensor architecture, the output signal of which can be directly connected to the input of a spiking neural network. We demonstrate that the output signal is a valid spike source for the Izhikevich model neurons, ensuring the proper operation of a number of neurocomputational features. The advantages are clear: much lower power consumption, smaller area, and a less complex electronic circuit. The main disadvantage is that sensor characteristics somehow limit the parameters of applicable spiking neurons. The proposed architecture is illustrated by a case study involving a capacitive pressure sensor circuit, which is compatible with most of the neurocomputational properties of the Izhikevich neuron model. The sensor itself is characterized by very low power consumption: it draws only 3.49 μA at 3.3 V.

The Effects of Omeprazole on the Neuron-like Spiking of the Electrical Potential of Proteinoid Microspheres.

This study examines a new approach to hybrid neuromorphic devices by studying the impact of omeprazole-proteinoid complexes on Izhikevich neuron models. We investigate the influence of these metabolic structures on five specific patterns of neuronal firing: accommodation, chattering, triggered spiking, phasic spiking, and tonic spiking. By combining omeprazole, a proton pump inhibitor, with proteinoids, we create a unique substrate that interfaces with neuromorphic models. The Izhikevich neuron model is used because it is computationally efficient and can accurately simulate the various behaviours of cortical neurons. The results of our simulations show that omeprazole-proteinoid complexes have the ability to affect neuronal dynamics in different ways. This suggests that they could be used as adjustable components in bio-inspired computer systems. We noticed a notable alteration in the frequency of spikes, patterns of bursts, and rates of adaptation, especially in chattering and triggered spiking behaviours. The findings indicate that omeprazole-proteinoid complexes have the potential to serve as adaptable elements in neuromorphic systems, presenting novel opportunities for information processing and computation that have origins in neurobiological principles. This study makes a valuable contribution to the expanding field of biochemical neuromorphic devices and establishes a basis for the development of hybrid bio-synthetic computational systems.

Neuromodulation effect of temporal interference stimulation based on network computational model.

Deep brain stimulation (DBS) has long been the conventional method for targeting deep brain structures, but noninvasive alternatives like transcranial Temporal Interference Stimulation (tTIS) are gaining traction. Research has shown that alternating current influences brain oscillations through neural modulation. Understanding how neurons respond to the stimulus envelope, particularly considering tTIS's high-frequency carrier, is vital for elucidating its mechanism of neuronal engagement. This study aims to explore the focal effects of tTIS across varying amplitudes and modulation depths in different brain regions. An excitatory-inhibitory network using the Izhikevich neuron model was employed to investigate responses to tTIS and compare them with transcranial Alternating Current Stimulation (tACS). We utilized a multi-scale model that integrates brain tissue modeling and network computational modeling to gain insights into the neuromodulatory effects of tTIS on the human brain. By analyzing the parametric space, we delved into phase, amplitude, and frequency entrainment to elucidate how tTIS modulates endogenous alpha oscillations. Our findings highlight a significant difference in current intensity requirements between tTIS and tACS, with tTIS requiring notably higher intensity. We observed distinct network entrainment patterns, primarily due to tTIS's high-frequency component, whereas tACS exhibited harmonic entrainment that tTIS lacked. Spatial resolution analysis of tTIS, conducted via computational modeling and brain field distribution at a 13 Hz stimulation frequency, revealed modulation in deep brain areas, with minimal effects on the surface. Notably, we observed increased power within intrinsic and stimulation bands beneath the electrodes, attributed to the high stimulus signal amplitude. Additionally, Phase Locking Value (PLV) showed slight increments in non-deep areas. Our analysis indicates focal stimulation using tTIS, prompting further investigation into the necessity of high amplitudes to significantly affect deep brain regions, which warrants validation through clinical experiments.

A Novel Coupled Memristive Izhikevich Neuron Model and Its Complex Dynamics

This paper proposes a novel, five-dimensional memristor synapse-coupled Izhikevich neuron model under electromagnetic induction. Firstly, we analyze the global exponential stability of the presented system by constructing an appropriate Lyapunov function. Furthermore, the Hamilton energy functions of the model and its corresponding error system are derived by using Helmholtz’s theorem. In addition, the influence of external current and system parameters on the dynamical behavior are investigated. The numerical simulation results indicate that the discharge pattern of excitatory and inhibitory neurons changes significantly when the amplitude and frequency of the external stimulus current are applied at different degrees. And the crucial dynamical behavior of the neuronal system is determined by the intensity of modulation of the induced current and the gain in the electromagnetic induction. Moreover, the amount of Hamilton energy released by the model could be evaluated during the conversion between the distinct dynamical behaviors.

Posit and floating-point based Izhikevich neuron: A Comparison of arithmetic

Reduced precision number formats have become increasingly popular in various fields of computational science, as they offer the potential to enhance energy efficiency, reduce silicon area, and improve processing speed. However, this is often at the expense of introducing arithmetic errors that can impact the accuracy of a system. The optimal balance must be struck, judiciously choosing a number format using as few bits as possible, while minimising accuracy loss.In this study, we examine one such format, posit arithmetic as a replacement for floating-point when conducting spiking neuron simulations, specifically using the Izhikevich neuron model. This model is capable of simulating complex neural firing behaviours, 20 of which were originally identified by Izhikevich and are used in this study. We compare the accuracy, spike count, and spike timing of the two arithmetic systems at different bit-depths against a 64-bit floating-point gold-standard. Additionally, we test a rescaled set of Izhikevich equations to mitigate against arithmetic errors by taking advantage of posit arithmetic’s tapered accuracy.Our findings indicate that there is no difference in performance between 32-bit posit, 32-bit floating-point, and our 64-bit reference for all but one of the tested firing types. However, at 16-bit, both arithmetic systems diverge from the 64-bit reference, albeit in different ways. For example, 16-bit posit demonstrates an 18× improvement in accumulated spike timing error over a 1000ms simulation compared to 16-bit floating-point when simulating regular (tonic) spiking. This finding holds particular importance given the prevalence of this particular firing type in specific regions of the brain. Furthermore, when we rescale the neuron equations, this error is eliminated altogether. Although current Posit Arithmetic Units are no smaller than Floating Point Units of the same bit-width, our results demonstrate that 64-bit floating-point can be replaced with 16-bit posit which could enable significant area savings in future systems.

Correction: Alkabaa et al. An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach. Mathematics 2022, 10, 612

In the original paper [...]

SC-IZ: A Low-Cost Biologically Plausible Izhikevich Neuron for Large-Scale Neuromorphic Systems Using Stochastic Computing

Neurons are crucial components of neural networks, but implementing biologically accurate neuron models in hardware is challenging due to their nonlinearity and time variance. This paper introduces the SC-IZ neuron model, a low-cost digital implementation of the Izhikevich neuron model designed for large-scale neuromorphic systems using stochastic computing (SC). Simulation results show that SC-IZ can reproduce the behaviors of the original Izhikevich neuron. The model is synthesized and implemented on an FPGA. Comparative analysis shows improved hardware efficiency; reduced resource utilization, which is a 56.25% reduction in slices, 57.61% reduction in Look-Up Table (LUT) usage, and a 58.80% reduction in Flip-Flop (FF) utilization; and a higher operating frequency compared to state-of-the-art Izhikevich implementation.

FPGA Implementation of Nerve Cell Using Izhikevich Neuronal Model as Spike Generator (SG)

FPGA Implementation of Nerve Cell Using Izhikevich Neuronal Model as Spike Generator (SG)

Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model

This study investigates a structurally unstable synchronization phenomenon observed in the two-coupled Izhikevich neuron model. As the result of varying the system parameter in the region of parameter space close to where the unstable synchronization is observed, we find significant changes in the stability of its periodic motion. We derive a discrete-time dynamical system that is equivalent to the original model and reveal that the unstable synchronization in the continuous-time dynamical system is equivalent to border-collision bifurcations in the corresponding discrete-time system. Furthermore, we propose an objective function that can be used to obtain the parameter set at which the border-collision bifurcation occurs. The proposed objective function is numerically differentiable and can be solved using Newton’s method. We numerically generate a bifurcation diagram in the parameter plane, including the border-collision bifurcation sets. In the diagram, the border-collision bifurcation sets show a novel bifurcation structure that resembles the “strike-slip fault” observed in geology. This structure implies that, before and after the border-collision bifurcation occurs, the stability of the periodic point discontinuously changes in some cases but maintains in other cases. In addition, we demonstrate that a border-collision bifurcation set successively branches at distinct points. This behavior results in a tree-like structure being observed in the border-collision bifurcation diagram; we refer to this structure as a border-collision bifurcation tree. We observe that a periodic point disappears at the border-collision bifurcation in the discrete-time dynamical system and is simultaneously replaced by another periodic point; this phenomenon corresponds to a change in the firing order in the continuous-time dynamical system.

A Novel Approach for Target Attraction and Obstacle Avoidance of a Mobile Robot in Unknown Environments Using a Customized Spiking Neural Network

In recent years, implementing reinforcement learning in autonomous mobile robots (AMRs) has become challenging. Traditional methods face complex trials, long convergence times, and high computational requirements. This paper introduces an innovative strategy using a customized spiking neural network (SNN) for autonomous learning and control of mobile robots (AMR) in unknown environments. The model combines spike-timing-dependent plasticity (STDP) with dopamine modulation for learning. It utilizes the Izhikevich neuron model, leading to biologically inspired and computationally efficient control systems that adapt to changing environments. The performance of the model is evaluated in a simulated environment, replicating real-world scenarios with obstacles. In the initial training phase, the model faces significant challenges. Integrating brain-inspired learning, dopamine, and the Izhikevich neuron model adds complexity. The model achieves an accuracy rate of 33% in reaching its target during this phase. Collisions with obstacles occur 67% of the time, indicating the struggle of the model to adapt to complex obstacles. However, the model’s performance improves as the study progresses to the testing phase after the robot has learned. Its accuracy surges to 94% when reaching the target, and collisions with obstacles reduce it to 6%. This shift demonstrates the adaptability and problem-solving capabilities of the model in the simulated environment, making it more competent for real-world applications.

Effects of electric field on vibrational resonance in Izhikevich neuronal systems

In this paper, based on the Izhikevich neuron model, the effects of electric field (EF) on vibrational resonance (VR) of single neuron and bidirectionally coupled neurons system are investigated. It is found that multiple vibrational resonances (MVR) can be observed in a single Izhikevich neuron model whether EF is considered or not. After the introduction of EF, the system exhibits worse MVR and local vibrational anti-resonance can be observed. In coupled neuronal system, the effect of bidirectional coupling causes MVR to disappear and the system only exhibits the phenomenon of VR. When EF is not considered, the vibrational anti-resonance is also observed. Interestingly, the introduction of EF weakens both VR and anti-resonance in the system. In addition, the effects of system parameters such as the EF strength controller and coupling strength on the Fourier coefficients are also investigated, and it is found that these parameters can also cause changes in the number of resonance peaks, resulting in vibrational bi-resonance and vibrational triple-resonance. The EF plays an important role in attenuating VR in neuronal systems. Therefore, this study can provide new insights for further control of abnormal electrical activities and information transmission in neurons.

A Hardware-Friendly Real-Time Implementation of the Auditory Attention Based on a Novel Spiking Winner-Take-All Network

In recent decades, the modeling and designing of neuromorphic systems have received considerable attention, leading to the development of electrophysiological devices that can mimic the dynamic behavior of cortical networks. Some features such as parallel processing, real-time performance, reconfigurability, low production cost, and good accuracy, make field programmable gate arrays (FPGAs) an ideal hardware platform for implementing spiking neural networks (SNN), which has become very popular in the field of neural computing. In this work, we investigated a high-performance FPGA design of the auditory attention to simulate the on-chip ‘cocktail party’ effect similar to what happens in the brain. In the first step, we introduce a novel spiking winner-take-all (SWTA) network consisting of a hardware-friendly Izhikevich neuron model and explore its biological characteristics and stability. We then use this network as a receptive field in the primary auditory cortex, which is tuned by attention signals. The desired sound frequency will be selected as the target and transmitted to the higher layers of the auditory cortex for further processing, while other frequencies are severely suppressed. Experimental results show that the proposed network accurately follows the dynamic behavior defined in the auditory attention theory, and emphasizes the resource consumption after post place and routes on a fully efficient hardware implementation, where less than 4% of the resources were used to implement a network with 1856 neurons.

Specific neural coding of fMRI spiking neural network based on time coding

Specific neural coding is the key to achieving advanced cognitive function in a bio-brain, which can form an identifying coding pattern for external stimulation. The performance of specific neural coding depends extremely on brain-like models. However, the bio-interpretability of the topology of a brain-like model is still insufficient. The purpose of this paper is to investigate a more biological interpretative brain-like model verified by the performance of specific neural coding. In this study, we used the topology constrained by human brain functional magnetic resonance imaging (fMRI) to construct a new spiking neural network (SNN) as a brain-like model called fMRI-SNN. In the fMRI-SNN, the nodes are Izhikevich neuron models, and the edges are synaptic plasticity models with time-delay. Then, we investigated the specific neural coding of fMRI-SNN, and discussed its mechanism. Our results indicated that: (i) fMRI-SNN has obvious specific neural coding based on time coding for different external stimulations. Furthermore, our discussion on relevance analysis implies that the intrinsic element of specific neural coding is synaptic plasticity. (ii) The specific neural coding of fMRI-SNN outperforms that of scale-free SNN and small-world SNN. Furthermore, our discussion on dynamic topological characteristics implies that the network topology is an element that impacts the performance level of the specific neural coding. (iii) Taking a speech recognition task as a case study, the performance of fMRI-SNN outperforms that of scale-free SNN and small-world SNN in terms of speech recognition accuracy.

Neural and axonal heterogeneity improves information transmission

The complexity of the brain lies in an intricate, not homogeneous structure; however, it is not clear how important is the heterogeneity at neural and structural levels and how it may play an important constituent in the brain’s functionality. Here we show the role of cellular and axonal delay heterogeneity in the brain’s performance. We simulated, at different scales, the spiking activity on a toroidal network realized in multiple dimensions with varying degrees of heterogeneity on a network of Izhikevich neuron models. We found that increasing the heterogeneity and network dimension improved the robustness and propagation speed of the spiking activity. Our results demonstrate that the behavior of the spiking activity depends on both the cellular neural and axonal delay heterogeneity. We developed a simple theoretical framework compatible with the results of the simulations, putting forward a novel method to strategically analyze any similar networks.

Comparison of spiking neural networks with different topologies based on anti-disturbance ability under external noise

The research on robustness of brain-like models contributes to promoting its neural information processing ability, and the understanding of bio-brain function. However, the biological rationality of the current brain-like models is inadequate. In addition, the effect of network topologies on the robustness of brain-like models has not been clarified. In this study, inspired by the topological characteristics of biological functional brain networks, we construct five kinds of spiking neural networks (SNNs), which have the same Izhikevich neuron model and the same synaptic plasticity model with time-delay, but different network topologies. Then, the robustness of the SNNs with different topologies is comparatively assessed based on the anti-disturbance ability under different noise. Further, by taking a speech recognition task as the case study, we investigate the anti-disturbance ability of these SNNs in application. Finally, the anti-disturbance mechanism of the SNNs is discussed. Our simulation consistently certifies that: (i) In terms of anti-disturbance indicators, the complex SNN outperforms the small-world SNN, the small-world SNN outperforms the scale-free SNN, and all of them outperform the random SNN and the regular SNN, which indicates that the SNNs with more biological rationality have the better anti-disturbance ability. (ii) In terms of speech recognition accuracy, the performance of SNNs with different topologies presents the consistent order with the anti-disturbance ability above. And the recognition accuracy of these SNNs under disturbance still remains almost the same, compared with these SNNs without disturbance. (iii) The evolution process of neural information is clarified, which hints that the synaptic plasticity is the intrinsic factor of anti-disturbance ability, and the network topology is a factor that affects the anti-disturbance ability at the level of performance. Our simulation results are conducive to the design of neuromorphic algorithms with robustness on analog or mixed-signal neuromorphic chips under complex noise environment.

A Power-Efficient Neuromorphic Digital Implementation of Neural–Glial Interactions

Throughout the last decades, neuromorphic circuits have incited the interest of scientists, as they are potentially a powerful tool for the treatment of neurological diseases. To this end, it is essential to consider the biological principles of the CNS and develop the appropriate area- and power-efficient circuits. Motivated by studies that outline the indispensable role of astrocytes in the dynamic regulation of synaptic transmission and their active contribution to neural information processing in the CNS, in this work we propose a digital implementation of neuron–astrocyte bidirectional interactions. In order to describe the neuronal dynamics and the astrocytes’ calcium dynamics, a modified version of the original Izhikevich neuron model was combined with a linear approximation of the Postnov functional neural–glial interaction model. For the implementation of the neural–glial computation core, only three pipeline stages and a 10.10 fixed point representation were utilized. Regarding the results obtained from the FPGA implementation and the comparisons to other works, the proposed neural–glial circuit reported significant savings in area requirements (from 22.53% up to 164.20%) along with considerable savings in total power consumption of 28.07% without sacrificing output computation accuracy. Finally, an RMSE analysis was conducted, confirming that this particular implementation produces more accurate results compared to previous studies.

Rich spike patterns from a periodically forced Izhikevich neuron model

Physiological experiments have described the electrophysiological properties of a single neuron, and mathematical models formulating neuronal activity have been proposed to elucidate the mechanism of information processing by the brain. In the present study, we investigated one such model, the Izhikevich neuron model, stimulated by sinusoidal inputs, with the parameter sets of four principal neuron types: regular spiking, fast spiking, intrinsically bursting, and chattering neurons. We adopted three measures: the diversity index, the coefficient of variation, and the local variation, to quantify interspike intervals from different viewpoints. The combined evaluation of these three measures clarified that the positional relationship of the nullclines, which is determined by the amplitude of sinusoidal forcing, plays a crucial role in the intrinsic properties of a periodically forced Izhikevich neuron model. Moreover, we used stroboscopic plots to clarify qualitative differences between attractors. The results also imply that such combined evaluation is applicable to the classification of neurons.

Small-world spiking neural network with anti-interference ability based on speech recognition under interference

The external interference can hamper the normal function of neuromorphic hardware under complex noise environment. Therefore, the study of brain-like models with anti-interference ability is a crucial issue. A bio-brain has the advantage of self-adaptability. The existing brain-like models are lack of bio-interpretability. Drawing from the advantage of bio-brain, the purpose of this paper is to investigate the anti-interference ability of brain-like models with bio-interpretability. In this study, we construct a spiking neural network with a small-world topology (SWSNN) as a brain-like model, in which Izhikevich neuron models and synaptic plasticity models with time-delay are used to represent the nodes and edges of the network, respectively. Then, the anti-interference ability of our SWSNN against different external noise is investigated, and its mechanism is explored. Further, by taking the speech recognition task as the case study, we verify the anti-interference ability of the SWSNN. Our simulation results indicate that: (i) The anti-interference ability of SWSNN is better than that of SNNs with other topologies. (ii) The discussion of neural information processing of the SWSNN under interference implies that the dynamic regulation of synaptic plasticity is an intrinsic factor of the anti-interference, and the topology is a factor that affects the anti-interference at the level of performance. (iii) Taking the speech recognition task as a case study, the SWSNN under different external noises still have almost the same high speech recognition accuracy, compared with the SWSNN without interference, and SWSNN yields better anti-interference ability than SNNs with other topologies in terms of the speech recognition accuracy. In addition, the anti-interference ability of our SWSNN framework is superior to that of existing liquid state machine (LSM) framework. Our simulation results lay a preliminary foundation for the neuromorphic hardware with robustness under complex noise environment.

Modeling and Signal Integrity Analysis of RRAM-Based Neuromorphic Chip Crossbar Array Using Partial Equivalent Element Circuit (PEEC) Method

This paper provides a comprehensive study of signal integrity issues in RRAM-based neuromorphic chip crossbar arrays due to interconnect parasitic. First, the parasitic parameters of the crossbar array are calculated by the partial equivalent element circuit (PEEC) method with an efficient unit-cell approach. Numerical experiments show that for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50\times 50$ </tex-math></inline-formula> array scale, this method consumes only 1.5% of the calculation time of the commercial software based 3D model, which translates to a calculation speed up of 72 times. Moreover, the PEEC circuit simulation results match well with those of the 3D model. Then, we investigate the effects of parasitic parameters such as capacitance and inductance, as well as the feature size of the crossbar array on signal integrity. All of them will lead to corresponding changes in parasitic effects, which in turn result in the most common signal integrity issues such as crosstalk, time delay and mutual capacitive coupling induced sneak path problem. Different from other studies, the excitation used in this paper is the neural spike signal generated by the Izhikevich neuron model, which is both rich in dynamic characteristics and high in computational efficiency. Finally, based on the study we propose a simple but effective design scheme for reduction of signal distortion, which can provide valuable design guidance for neuromorphic systems to achieve high performance and high computational accuracy.

Dynamical response of Autaptic Izhikevich Neuron disturbed by Gaussian white noise.

Using the improved memristive Izhikevich neuron model, the effects of autaptic connection as well as electromagnetic induction are studied on the dynamical behavior of neuronal spiking. Using bifurcation analysis for membrane potentials, the effects of autaptic and electromagnetic parameters on the mode transition in electrical activities of the neuron model are investigated. Furthermore, white Gaussian noise is considered in the neuron model, to evaluate the effect of electromagnetic disturbance on the firing pattern of the neuron using the coefficient of variation. The bifurcation diagram versus autaptic conductance and time delay has been extensively studied. The results show that the effects of autaptic connection as well as electromagnetic induction on the spiking behavior of neurons can be well demonstrated by using the Izhikevich model. The electrical activities of the Izhikevich neuron model become more complex when the effects of autaptic connection and electromagnetic induction are considered in the neuron model. Using the Izhikevich neuron model, the high variety of spiking/bursting patterns is represented in the bifurcation diagram of inter-spike interval versus autaptic or electromagnetic parameters. Noise can have distinct effects on the spiking activity of the neuron, for the subthreshold input current, increasing the intensity of the electromagnetic noise increases the regularity of the neuron spiking, but for the suprathreshold input current, the regularity of spiking decreases with noise.