| Bifurcation analysis and numerical simulations are performed on the FitzHugh-Nagumo (FHN) equations. These equations model the electrical properties of a nerve cell. They are a nonlinear system of two differential equations in two variables. In this thesis there is a parameter in the equations which represents an applied current. There are three parts to the analysis and simulation. The special solutions are determined first on the FHN system without diffusion. These include time-periodic solutions. Then the one-dimensional diffusion FHN equations are analyzed to find rotating wave solutions. The domain is a ring. In the last part, the two-dimensional diffusion FHN equations are analyzed to find rotating wave solutions on an annulus. |
