Random currents through nerve membranes. I. Uniform Poisson or white noise current in one-dimensional cables
type: Item
instance of: scholarly article
title: Random currents through nerve membranes. I. Uniform Poisson or white noise current in one-dimensional cables
zbMATH Open document ID: 0536.92019
DOI: 10.1007/BF00320390
author: Henry C. Tuckwell
author: John B. Walsh
published in: Biological Cybernetics
publication date: 1983-01-01T00:00:00Z
review text: The linear cable equation with uniform Poisson or white noise input is studied. The solutions of these stochastic equations are derived from Green's function representation of the solution of a corresponding deterministic cable equation. The mean, variance and covariance are computed for various cable length and boundary conditions. The spectral density is examined in the fixed point of the cable to infinite as well as finite cable. The first passage time problem is solved for the diffusion model. Numerical ad simulation techniques are employed to illustrate the derived results. The authors propose the theory as a model for the voltage across the membrane of a one- dimensional nerve cylinder.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 65C20
zbMATH DE Number: 3852858
zbMATH Keywords: random currents
zbMATH Keywords: nerve membranes
zbMATH Keywords: Fourier series representation
zbMATH Keywords: linear cable equation
zbMATH Keywords: uniform Poisson or white noise input
zbMATH Keywords: Green's function representation
zbMATH Keywords: mean
zbMATH Keywords: variance
zbMATH Keywords: covariance
zbMATH Keywords: spectral density
zbMATH Keywords: first passage time problem
zbMATH Keywords: diffusion model
zbMATH Keywords: voltage across the membrane of a one-dimensional nerve cylinder
Wikidata QID: Q52433819
reviewed by: Petr Lansky
MaRDI profile type: Publication
cites work: Q5822308
cites work: Q5533727
cites work: Q5342182
cites work: Q4275389
cites work: Ionic channel density of excitable membranes can act as a bifurcation parameter
cites work: The interspike interval of a cable model neuron with white noise input
cites work: A stochastic model of neural response
cites work: The response of a spatially distributed neuron to white noise current injection
full work available at URL: https://doi.org/10.1007/bf00320390
OpenAlex ID: W1981254512
description: scientific article; zbMATH DE number 3852858