The aim of this project is to understand the characteristics
of the Fitzhugh-Nagumo model of the nerve cell.
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.
x' = c(y + x - x3/3)
y' = -( (x - a + by) / c )
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
an Analysis section that gives a detailed
account of our solution methods, and Conclusions.