add to favorites : reference url back to results : previous : next
 

STANDING WAVES OF SPATIALLY DISCRETE FITZHUGH-NAGUMO EQUATIONS
Access this item.
TitleSTANDING WAVES OF SPATIALLY DISCRETE FITZHUGH-NAGUMO EQUATIONS
AuthorSegal, Joseph
KeywordsDiscrete FitzHugh-Nagumo
Lattice Differential-Difference Equation
Standing Waves
Propagation Failure
Nerve Axon
Action Potential
AbstractWe 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.
AdviserMoore, Brian
PublisherUniversity of Central Florida
DegreeM.S.
Degree DisciplineDepartment of Mathematics
Degree GrantorSciences
Degree ProgramMathematical Science MS
Graduation Date2009-01-01
TypeMaster's thesis
Access LevelPublic - Allow Worldwide Access
Release Date2009-11-01
RepositoryUniversity Archives
Repository CollectionElectronic Theses and Dissertations
IdentifierCFE0002892
Access Linkhttp://purl.fcla.edu/fcla/etd/CFE0002892

add to favorites : reference url back to results : previous : next
powered by CONTENTdm ® | contact us  ^ to top ^