FitzHugh Nagumo

This is the model that started the whole business and is a variant of the van der Pol equation.

$$F(v,w) = Av(v-\alpha)(1-v) -w,$$ (3)

$$G(v,w) = \epsilon(v-\gamma w).$$ (4)

with $0 < \alpha < {1\over 2}$, and $\epsilon$ ``small''. Also, $\gamma$ is chosen so that $Ag(1-\alpha)^2 <4$, so that $A(v-\alpha)(1-v) -{1\over \gamma}= 0$ has no real roots, that is, so that there is only one steady state solution. (movie)