Bursting Oscillations along the Axon of a Neuron
Loading...
Authors
Smidchens, Eriks
Issue Date
1993
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
The body transfers electrical signals from one part to another by means of
neurons. The first relatively complete mathematical model of nerve conduction
was published by Hodgkin and Huxley. They. subsequently won the Nobel Prize for
this work. The focus of this paper is to reveal insight into the nature of bursting
oscillations produced by the FitzHugh-Nagumo-Rinzel equations - a simplified
version of the Hodgkin and Huxley equations.
As previously mentioned, neurons transfer electrical signals. The conveyed
signals are electrical potentials arising from the potential drop across the membrane
of the neuron. When observed at a fixed location, the electrical potential
promulgates an action potential, a single nerve impulse. If the stimuli is large
enough an oscillation reaction will arise. The oscillation reaction or bursting is
r' characterized by successive action potentials (active phase), positioned between
periods of quiescence (quiet phase).
An analysis of the FitzHugh-Nagumo-Rinzel equations was performed using·
Fourier transformations, Hopf bifurcation diagrams, and perturbation theory.
Although the Fourier analysis cannot prove the oscillations are quasiperiodic (i.e.
the ratio of the frequencies that comprise the oscillations is irrational), they did,
however, lend support to the claim.
Description
vii, 82 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.