ArticlePublisher preview available

Lévy noise-induced near-death spikes and phase transitions of a biological neural network

March 2020
Nonlinear Dynamics 99(12)

March 2020
99(12)

Authors:

Near-death spikes or near-death surges are a sudden increase in neuron activity in the human brain before neurons end their firings. Just before a person is clinically dead, such spikes are observed in certain cases, so the name is near-death spikes. The reason for this behavior is the lack of oxygen in brain (Chawla et al. in J Palliat Med 12(12):1095–1100, 2009). In this study, it is demonstrated that a particular type of noise called Lévy noise can generate such activity in the neural network of the worm Caenorhabditis elegans. The study identified different parameter regions of noise at which the network makes transitions from one synchronous state to another and the mechanism behind them. Such transitions are already reported in cortical regions of brain (Canavero et al. in Surg Neurol Int 7(Suppl 24):S623–S625, 2016). During the transition period between asynchronous and synchronous firing states, network is more susceptible to changes in firing pattern of individual neurons (Zandt et al. in PLoS ONE 6(7):e22127, 2011; Uzuntarla et al. Neural Netw 110:131–140, 2019). In this work, it is demonstrated that the recognized parameter regions can be used to control the network dynamics. The study also identified Lévy noise values at which the network displays generation of waves of different frequencies. This result suggests a new method for neurostimulation in the case of traumatic brain injury. The study reveals that the characteristic exponent ($\alpha $) of the noise has better influence on the network dynamics than the scale parameter of noise (D) and the synaptic coupling constant (Gsyn) of the network. The neuronal network even displayed Gamma oscillations for large values of $\alpha $. If the parameters of the neurons are made chaotic, the network firing rate is diminished and it displayed Delta and Theta oscillations.

a Variations of busting synchronization of the network with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and Gsyn at D=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}=0.5$$\end{document}. The system displayed two states of synchronization with an increase in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} for a given synaptic coupling. The dynamics is independent of a change in Gsyn value. b Variations of busting synchronization of the network with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and D at Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document}. When synaptic coupling strength is fixed at Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document}, the bursting synchronization is slightly increased with an increase in value of D (non-chaotic neurons)

…

Raster plot of the network at Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document}, D=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}=0.5$$\end{document} and α=1.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =1.5$$\end{document}. The network is displaying asynchronous bursting (non-chaotic neurons)

…

a Interspike interval bifurcation curve with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} value of a representative FS interneuron of the network. It indicates increased random firing for α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} values between 0.7 and 1.2 (for Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document} and D=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}=0.5$$\end{document}). For α>1.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha > 1.2$$\end{document}, with an increase in its value the firing dynamics becomes almost steady. b Irregular spiking of interneuron at α=0.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.8$$\end{document}. The firings stopped around 1000 ms with a burst, indicating near-death spikes. c When α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} is increased to 1.8, interneuron fired almost regularly

…

a ISI bifurcation curve of a non-interneuron neuron (it can be RS/IB/CH/FS neuron) of the network with an increase in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} value, at Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document}, D=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}=0.5$$\end{document}. It indicates different modes of firing. b At α=0.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.8$$\end{document}, neurons displayed irregular bursting. c At α=1.8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =1.8$$\end{document}, neuron bursting becomes almost regular

…

+14

Variations of average feedback current with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}. Average of feedback current received by a neuron from the neural network first increases with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}, reaches a maximum near α=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.7$$\end{document} and then decreases, at Gsyn=5.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Gsyn}=5.0$$\end{document}, D=0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}=0.5$$\end{document} (non-chaotic neuron)

…

Figures - available from: Nonlinear Dynamics

This content is subject to copyright. Terms and conditions apply.

A preview of this full-text is provided by Springer Nature.

Learn more

Content available from Nonlinear Dynamics

This content is subject to copyright. Terms and conditions apply.

Nonlinear Dyn (2020) 99:3265–3283

https://doi.org/10.1007/s11071-020-05472-2

ORIGINAL PAPER

Lévy noise-induced near-death spikes and phase transitions

of a biological neural network

K. K. Mineeja ·Rose P. Ignatius

Received: 28 August 2019 / Accepted: 4 January 2020 / Published online: 22 January 2020

Abstract Near-death spikes or near-death surges are

a sudden increase in neuron activity in the human brain

before neurons end their ﬁrings. Just before a person

is clinically dead, such spikes are observed in certain

cases, so the name is near-death spikes. The reason for

this behavior is the lack of oxygen in brain (Chawla et

al. in J Palliat Med 12(12):1095–1100, 2009). In this

study, it is demonstrated that a particular type of noise

called Lévy noise can generate such activity in the neu-

ral network of the worm Caenorhabditis elegans.The

study identiﬁed different parameter regions of noise

at which the network makes transitions from one syn-

chronous state to another and the mechanism behind

them. Such transitions are already reported in cortical

regions of brain (Canavero et al. in Surg Neurol Int

7(Suppl 24):S623–S625, 2016). During the transition

period between asynchronous and synchronous ﬁring

states, network is more susceptible to changes in ﬁr-

ing pattern of individual neurons (Zandt et al. in PLoS

ONE 6(7):e22127, 2011; Uzuntarla et al. Neural Netw

110:131–140, 2019). In this work, it is demonstrated

that the recognized parameter regions can be used to

control the network dynamics. The study also identiﬁed

K. K. Mineeja (B)·R. P. Ignatius

Department of Physics, St. Teresa’s College, Ernakulam,

Afﬁliated to M.G University, Ernakulam, Kerala, India

e-mail: kkmineeja@gmail.com

R. P. Ignatius

Department of Physics, Al-Ameen College, Edathala,

Kerala, India

e-mail: rosgeo@yahoo.com

Lévy noise values at which the network displays gener-

ation of waves of different frequencies. This result sug-

gests a new method for neurostimulation in the case of

traumatic brain injury. The study reveals that the char-

acteristic exponent (α) of the noise has better inﬂuence

on the network dynamics than the scale parameter of

noise (D) and the synaptic coupling constant (Gsyn)

of the network. The neuronal network even displayed

Gamma oscillations for large values of α. If the param-

eters of the neurons are made chaotic, the network ﬁr-

ing rate is diminished and it displayed Delta and Theta

oscillations.

Keywords Lévy noise ·Spatiotemporal activity ·

Network of neurons ·Chaotic neuron ·Near-death

surge ·Phase transitions

1 Introduction

Even after centuries of scientiﬁc search and validations,

mankind still lacks the capacity to unlock the mystery

behind death and related events. So near-death expe-

riences always generate curiosity and are a subject of

intense research. One such observation was reported in

2009 by Chawla et al. [1]. They found a surge in elec-

troencephalogram (EEG) activity near death, and this

phenomenon is called ‘near-death surges’ or ‘wave of

death.’ One of their postulates is that, at near death, as

the hypoxemia in patients increases beyond a thresh-

old value, most of the neurons in the brain lose Na–K

123

Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Research on Modeling and Dynamic Characteristics of Complex Biological Neural Network Model considering BP Neural Network Method

Article

Full-text available

Dec 2021
Adv Multimed

Hongyan Chen

Biological neural network system is a complex nonlinear dynamic system, and research on its dynamics is an important topic at home and abroad. This paper briefly introduces the dynamic characteristics and influencing factors of the neural network system, including the effects of time delay and noise on neural network synchronization, synchronous transition, and stochastic resonance, and introduces the modeling of the neural network system. There are irregular mixing problems in the complex biological neural network system. The BP neural network algorithm can be used to solve more complex dynamic behaviors and can optimize the global search. In order to ensure that the neural network increases the biological characteristics, this paper adjusts the parameters of the BP neural network to receive EEG signals in different states. It can simulate different frequencies and types of brain waves, and it can also carry out a variety of simulations during the operation of the system. Finally, the experimental analysis shows that the complex biological neural network model proposed in this paper has good dynamic characteristics, and the application of this algorithm to data information processing, data encryption, and many other aspects has a bright prospect.

Effects of magnetic fields on stochastic resonance in Hodgkin-Huxley neuronal network driven by Gaussian noise and non-Gaussian noise

Article

Full-text available

Nov 2021
COGN NEURODYNAMICS

Stochastic resonance is a remarkable phenomenon that can enhance signal processing by the addition of random noise. However, the effect of magnetic fields on stochastic resonance under channel noises has been inadequately studied. In this paper, the stochastic resonance in Hodgkin-Huxley neuronal network under Gaussian channel noises and non-Gaussian channel noise were studied, and the effects of electromagnetic field stimulation on stochastic resonance were considered. The results indicate that stochastic resonance in neuronal networks can be induced by Gaussian channel noise and non-Gaussian Levy channel noise, and stochastic resonance may occur more easily under Levy channel noise. The resonance amplitude was significantly improved by selecting appropriate parameters of the magnetic field, while, a too strong magnetic field can be detrimental to the resonance amplitude. Magnetic fields may induce the enhancement of the resonance amplitude by increasing the firing frequency and spiking regularity.

Infection Eradication Criterion in a General Epidemic Model with Logistic Growth, Quarantine Strategy, Media Intrusion, and Quadratic Perturbation

Article

Full-text available

Nov 2022

This article explores and highlights the effect of stochasticity on the extinction behavior of a disease in a general epidemic model. Specifically, we consider a sophisticated dynamical model that combines logistic growth, quarantine strategy, media intrusion, and quadratic noise. The amalgamation of all these hypotheses makes our model more practical and realistic. By adopting new analytical techniques, we provide a sharp criterion for disease eradication. The theoretical results show that the extinction criterion of our general perturbed model is mainly determined by the parameters closely related to the linear and quadratic perturbations as well as other deterministic parameters of the system. In order to clearly show the strength of our new result in a practical way, we perform numerical examples using the case of herpes simplex virus (HSV) in the USA. We conclude that a great amount of quadratic noise minimizes the period of HSV and affects its eradication time.

Neurons and Near-Death Spikes

Chapter

Apr 2021

Rose P. Ignatius

Near-death spikes or near-death surges represent sudden increase in neuron activity in the human brain before neurons end their firing. Just before a person is clinically dead, such spikes are observed in certain cases, so it got the name ‘near-death spikes’. The reason for this behaviour is the lack of oxygen in brain. The neural network of the worm Caenorhabditis elegans resembles that of human brain. Hence it can be used to understand the simple dynamics of human brain. Within the network, the neurons are found to exhibit chaotic nature, even though their parameters are that of normal neurons. It is observed that when the strength of synaptic conductance is increased, initially the bursting synchronization, entropy of the network and the average firing rate decrease slightly and then increase. As the neurons of the network are made chaotic, ‘near-death’-like surges of neuron activity are observed. Also, the brain dynamics changes from alert to rest state. It can be demonstrated that a particular type of noise called Lévy noise can generate ‘near-death’-like surges in the neural network of the worm Caenorhabditis elegans. Identification of different parameter regions of Lévy noise at which the network makes transitions from one synchronous state to another and the mechanism behind them is a challenging subject. Such transitions are already reported in cortical regions of brain. The Lévy noise values at which the network displays generation of waves of different frequencies can be determined. This result suggests a new method for neuro stimulation in the case of traumatic brain injury. The neuronal network even displayed Gamma oscillations. If the parameters of the neurons are made chaotic, the network firing rate is diminished and it displayed Delta and Theta oscillations.

Generating Brain Waves, the Power of Astrocytes

Article

Full-text available

Oct 2019

Synchronization of neuronal activity in the brain underlies the emergence of neuronal oscillations termed “brain waves”, which serve various physiological functions and correlate with different behavioral states. It has been postulated that at least ten distinct mechanisms are involved in the formulation of these brain waves, including variations in the concentration of extracellular neurotransmitters and ions, as well as changes in cellular excitability. In this mini review we highlight the contribution of astrocytes, a subtype of glia, in the formation and modulation of brain waves mainly due to their close association with synapses that allows their bidirectional interaction with neurons, and their syncytium-like activity via gap junctions that facilitate communication to distal brain regions through Ca²⁺ waves. These capabilities allow astrocytes to regulate neuronal excitability via glutamate uptake, gliotransmission and tight control of the extracellular K⁺ levels via a process termed K⁺ clearance. Spatio-temporal synchrony of activity across neuronal and astrocytic networks, both locally and distributed across cortical regions, underpins brain states and thereby behavioral states, and it is becoming apparent that astrocytes play an important role in the development and maintenance of neural activity underlying these complex behavioral states.

Synchronization-induced spike termination in networks of bistable neurons

Article

Full-text available

Nov 2018
NEURAL NETWORKS

We observe and study a self-organized phenomenon whereby the activity in a network of spiking neurons spontaneously terminates. We consider different types of populations, consisting of bistable model neurons connected electrically by gap junctions, or by either excitatory or inhibitory synapses, in a scale-free connection topology. We find that strongly synchronized population spiking events lead to complete cessation of activity in excitatory networks, but not in gap junction or inhibitory networks. We identify the underlying mechanism responsible for this phenomenon by examining the particular shape of the excitatory postsynaptic currents that arise in the neurons. We also examine the effects of the synaptic time constant, coupling strength, and channel noise on the occurrence of the phenomenon.

Effect of Lévy noise on the networks of Izhikevich neurons

Article

Full-text available

Oct 2018
NONLINEAR DYNAM

Lévy 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 Lévy 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 Lévy noise. Whole parameter space of Lévy noise is investigated by changing its characteristic exponent, skewness, scale and mean parameters. The simulation results show that the noise generated from $\alpha $-stable Lévy 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 Lévy noise. In all cases, neurons are found to be irregularly spiking when Lévy noise with characteristic exponent $\alpha $ equal to 0.5 is applied. Lévy 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 Lévy distribution in standard parameterisation is maximum. Other parameters of Lévy noise do not influence the way in which a particular neuron is firing. The effects of Lévy noise on the correlation between individual neurons and on the networks are investigated using statistical measures.

Spatiotemporal activities of a pulse-coupled biological neural network

Article

Full-text available

Jun 2018
NONLINEAR DYNAM

The present work is on the spatiotemporal activities and effects of chaotic neurons in a pulse-coupled biological neural network. The biological neural network used is that of Caenorhabditis elegans. Because of its similarity to human neural network, it can be used to understand the simple dynamics of human brain. Within the network the neurons are found to exhibit chaotic nature, even though their parameters are that of normal neurons. It is observed that when the strength of synaptic conductance is increased, initially the bursting synchronization, entropy of the network and the average firing rate decrease slightly and then increase. Since chaotic dynamics of neuron plays an important role in human brain functions, the neurons of the network are intentionally made chaotic and the dynamics is studied. As the neurons of the network are made chaotic, ‘near-death’-like surges of neuron activity before ending firing is observed throughout the network. Also, the brain dynamics changes from alert to rest state. When most of the neurons of the network are made chaotic, their activities become independent of the coupling strength.

UP-DOWN cortical dynamics reflect state transitions in a bistable network

Article

Full-text available

Aug 2017
eLife

In the idling brain, neuronal circuits transition between periods of sustained firing (UP state) and quiescence (DOWN state), a pattern the mechanisms of which remain unclear. Here we analyzed spontaneous cortical population activity from anesthetized rats and found that UP and DOWN durations were highly variable and that population rates showed no significant decay during UP periods. We built a network rate model with excitatory (E) and inhibitory (I) populations exhibiting a novel bistable regime between a quiescent and an inhibition-stabilized state of arbitrarily low rate. Fluctuations triggered state transitions, while adaptation in E cells paradoxically caused a marginal decay of E-rate but a marked decay of I-rate in UP periods, a prediction that we validated experimentally. A spiking network implementation further predicted that DOWN-to-UP transitions must be caused by synchronous high-amplitude events. Our findings provide evidence of bistable cortical network that exhibits non-rhythmic state transitions when the brain rests.

Lévy noise improves the electrical activity in a neuron under electromagnetic radiation

Article

Full-text available

Mar 2017
PLOS ONE

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Lévy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Lévy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Lévy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Lévy noise intensity are depicted. The increasing of Lévy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Lévy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Lévy noise distribution are detected.

Nonlinear feedback coupling in Hindmarsh–Rose neurons

Article

Full-text available

Feb 2017
NONLINEAR DYNAM

We analyse the model of neurons described by Hindmarsh–Rose (H–R) system with various coupling schemes. We have examined the scope of synchronization, anti-phase synchronization and amplitude death for linear indirect synaptic coupling of the H–R neurons. The work is extended to coupling of the form nonlinear cubic feedback. The coupling between two neurons using memristor is also examined. A memristor is now identified as the fourth fundamental circuit element which can be considered as an electrical synapse. Mutual coupling of H–R systems using cubic flux-controlled memristor exhibits the properties of bursting and amplitude death. With unidirectional coupling one neuron exhibits tonic spiking or bursting while the other neuron shows amplitude death. Mutual coupling with quadratic flux-controlled memristor model shows the possibilities of synchronization, oscillation death and other interesting dynamics like near-death rare spikes. Exponential flux-controlled memristor coupling in H–R neuron presents synchronization and oscillation death. We have examined the stability of different coupled systems and the Lyapunov exponent plots. It is shown that among different memristor couplings in H–R neurons, cubic flux-controlled memristor has got highest Lyapunov exponent. The present work summarizes the simulation results of different coupling schemes in H–R neurons which show many interesting dynamical characteristics of coupled neuron cells.

Fractional Gaussian noise-enhanced information capacity of a nonlinear neuron model with binary signal input

Article

May 2018
PRE

This paper reveals the effect of fractional Gaussian noise with Hurst exponent H∈(1/2,1) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H∈(1/2,1) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

Lévy noise-induced escape in an excitable system

Article

Jun 2017
J STAT MECH-THEORY E

This paper considers the dynamics of escape in the stochastic FitzHugh–Nagumo (FHN) neuronal model driven by symmetric α-stable Lévy noise. External or internal stimulation may make the excitable system produce a pulse or not, which can be interpreted as an escape problem. A new method to analyse the state transition from the rest state to the excitatory state is presented. This approach consists of two deterministic indices: the first escape probability (FEP) and the mean first exit time (MFET). We find that higher FEP in the rest state (equilibrium) promotes such a transition and MFET reflects the stability of the rest state directly with the selected escape region. The developed two dimensional numerical simulation method to calculate FEP and MFET can not only avoid a dimension reduction, but is also applicable for the cases with large noise. In addition, FEP provides us with a new perspective to understand the seperatrix of the stochastic FHN model. It can be seen that smaller jumps of the Lévy motion and relatively small noise intensity are conducive to the production of spikes. In order to characterize the effect of noise on the selected escape region in which the equilibrium lies, the area of higher FEP and MFET in the escape region are calculated. Meanwhile, Brownian motion as a special case is also taken into account for comparison.

Micro-connectomics: Probing the organizational principles of neuronal networks at the cellular scale

Article

Feb 2017

Defining the organizational principles of neuronal network s at the cellular scale, or $\textit{micro-connectomics}$, is a key challenge of modern neuroscience. Accelerated by methodological advances, recent experimental studies have generated rich data on anatomical, physiological and genetic factors determining the organization of neuronal networks. In this Review, we will focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originate with Ramón y Cajal’s conservation laws. First, we summarize results from experimental studies in intact small organisms and in tissue samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization and development of neuronal networks. In general, the wiring cost of neuronal networks was nearly, but not strictly, minimized by the spatial positioning and connectivity of neurons. Features that reduce the number of synaptic connections between neurons , such as hubs, were more expensive to wire than the theoretical minimum. It seems reasonable to infer from contemporary micro-connectomics that many aspects of intricately detailed neuronal network organization are indeed the outcome of competition between two fundamental selection pressures: low biological cost and high functional value. Future studies will be needed to clarify which aspects of network topology are most functionally valuable and to identify the biological mechanisms controlling expression of cost and topological pressures on the development and evolution of micro-connectomes.

Lévy noise-induced near-death spikes and phase transitions of a biological neural network

Abstract and Figures

Recommended publications

Neurons and Near-Death Spikes

Spatiotemporal activities of a pulse-coupled biological neural network

Effect of Lévy noise on the networks of Izhikevich neurons

Effects of Lévy noise on the FitzHugh-Nagumo model: A perspective on the maximal likely trajectories