## Introduction

The aim of this project is to understand the characteristics
of the Fitzhugh-Nagumo model of the nerve cell.

* x' = c(y + x - x*^{3}/3)

* y' = -( (x - a + by) / c ) *

The Fitzhugh-Nagumo model is a two dimensional model where * x(t) * is
the electrical potential or voltage across the nerve cell membrane, and *
y(t) * is the current through the membrane. The constants *a*,
*b* and *c* are all positive.

In our analysis we found it necessary to use bifurcation theory.
The bifurcation diagram we created on the *a* vs. *b* axis
Consists of either three or six regions depending on the value of
*c*. If *c* is between the range 0
< *c* <= 1 the diagram has three regions with distinct
characteristics that we'll consider in detail later in the report, and if
1 < *c* < (infinity) then the bifurcation diagram consists of
six regions with some regions exhibiting the same characteristics.

The remainder of the report is organized in the following
sections. Background,
an Analysis section that gives a detailed
account of our solution methods, and Conclusions.

Mike Willock
willock@wpi.wpi.edu

Richard Demar
rdemar@wpi.wpi.edu