Reaction and Diffusion on the Sierpinski Gasket

In this thesis we study non-linear dynamical systems on complex domains. Although the systems we consider are mathematical abstractions, our motivation is to gain insights into neurobiological systems. The mathematical techniques we employ concern analysis on a particular class of fractal sets. This theory allows one to construct a Laplacian and to study the spectrum and eigenfunctions given a variety of boundary conditions. This thesis uses these results to define and study the cable equation and the FitzHugh-Nagumo system on the Sierpinski Gasket