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.
Karen J. Hirst