Keywords

Discrete FitzHugh-Nagumo, Lattice Differential-Difference Equation, Standing Waves, Propagation Failure, Nerve Axon, Action Potential

Abstract

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.

Notes

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Graduation Date

2009

Advisor

Moore, Brian

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0002892

URL

http://purl.fcla.edu/fcla/etd/CFE0002892

Language

English

Release Date

November 2009

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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