You are here

STANDING WAVES OF SPATIALLY DISCRETE FITZHUGH-NAGUMO EQUATIONS

Download pdf | Full Screen View

Date Issued:
2009
Abstract/Description:
We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infinite one-dimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1-pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.
Title: STANDING WAVES OF SPATIALLY DISCRETE FITZHUGH-NAGUMO EQUATIONS.
9 views
5 downloads
Name(s): Segal, Joseph, Author
Moore, Brian, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2009
Publisher: University of Central Florida
Language(s): English
Abstract/Description: We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infinite one-dimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1-pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.
Identifier: CFE0002892 (IID), ucf:48021 (fedora)
Note(s): 2009-12-01
M.S.
Sciences, Department of Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Discrete FitzHugh-Nagumo
Lattice Differential-Difference Equation
Standing Waves
Propagation Failure
Nerve Axon
Action Potential
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0002892
Restrictions on Access: private 2009-11-01
Host Institution: UCF

In Collections