 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.