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The uniform bifurcation of N-front traveling waves in the singularly perturbed Fitzhugh -Nagumo equations

Daryl C Bell, University of Nebraska - Lincoln

Abstract

In this dissertation we consider traveling wave solutions of the FitzHugh-Nagumo equations, vt=vxx+fv -w,wt=ev-gw . In phase space, the FitzHugh-Nagumo equations possess n-front traveling wave solutions that correspond to n-front heteroclinic orbits. These solutions bifurcate from a heteroclinic loop. However, the FitzHugh-Nagumo equations are singularly perturbed by the parameter &epsis;. The bifurcation does not occur when the FitzHugh-Nagumo equations are in their singular state, it only occurs on the set 0cγ parameter space, where c is the propagation speed of the traveling waves, the domains of definition of the bifurcation curves are dependent on &epsis;, the singular parameter. We show that these domains can be made uniform in the parameter &epsis;, that is, the set of parameters over which the bifurcation occurs is of uniform size for all 0

Subject Area

Mathematics

Recommended Citation

Bell, Daryl C, "The uniform bifurcation of N-front traveling waves in the singularly perturbed Fitzhugh -Nagumo equations" (1999). ETD collection for University of Nebraska - Lincoln. AAI9942113.
http://digitalcommons.unl.edu/dissertations/AAI9942113

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