Thesis Defense: Standing Waves of Spatially Discrete Fitzhugh-Nagumo Equations
MAP 318 November 6, 2009
10:00 AM - 11:00 AM
Announcing the Final Examination of Joe Segal for the degree of Master of Science, Mathematics
We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infnite 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.
Graduate Students
Thesis Defense: Standing Waves of Spatially Discrete Fitzhugh-Nagumo Equations
