Standing and Traveling Waves of the FitzHugh-Nagumo
Prof. Yung-Sze Choi (University of Connecticut, USA)
Abstract. Since the pioneer work of Hodgekin-Huxley in early 1950's, mathematical models have been employed by neuroscientists and mathematicians alike to understand the mechanisms governing excitation and propagation of action potentials along neurons. It is a daunting task in view of the complexity of observed phenomena. A simpler system of FitzHugh- Nagumo equations has been proposed. These latter equations support both standing and traveling waves of action potential.
We will survey some results on the FHN equations, which are valid for some parameter regime. For a different parameter range, we explain our variational method with oscillation constraints in treating standing and traveling waves. If time allows, we will briefly talk about a geometric variational formulation arising from the FHN equation.