= Planar reduction of the Hodgkin-Huxley model
Replacing the fast activation gate by $m=m_\infty(V)$, taking $\tau_n(V)=\tau_h(V)$ and assuming $n_\infty(V)+h_\infty(V)=K$ constant reduces the <Hodgkin-Huxley model> to equations for $V,n$ when $n(0)+h(0)=K$. Indeed $q=n+h$ satisfies $\tau(V)\dot q=K-q$, so $q=K$ and $h=K-n$. The <FitzHugh-Nagumo model> additionally simplifies the two resulting response functions to a cubic activation equation and a linear recovery equation.
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