The Fitzhugh-Nagumo Model is a a two dimensional approximation
of the four dimensional Hodgkin-Huxley equations which describe
the changes in the membrane potential and ion conductances at a
point in an axon. The Fitzhugh-Nagumo equations are

x' = c*(y+x-1/3*x^3)

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

where x is the membrane potential and y is the recovery variable.

Because our model is an approximation of the actual Fitzhugh-Nagumo equations, we feel justified in analyzing negative solutions, which would be unphysical in the actual equations.

Given an electrical stimulus, the membrane potential (x) changes
based on the recovery variable and the cube of the potential. The
change in the recovery variable (y) is dependent on the membrane
potential and the recovery variable. The coefficents, a, b, and c
are positive. The first equation usually has an additional term I,
which is an arbitrary function of time that describes the
membrane current. For the purposes of this project I is assumed
to be zero. In the original Hodgkin-Huxley model, the
coefficients represent the conductunce of sodium and potassium.
As the Fitzhugh-Nagumo Model is only a mathematical
simplification, the coefficients do not have a specific
physiological meaning.

Introduction

Analysis

Conclusions

Andrea Sereny

Karen J. Hirst