% Reduced HH equations

\documentclass ex{article}
\setlength{\topmargin}{-0.35in}
\setlength{\textheight}{9.in}
\setlength{\evensidemargin}{-.2in}
\setlength{\oddsidemargin}{-.2in}
\setlength{\textwidth}{6.5in}
\setlength{\parskip}{0.5in}
\pagestyle{plain}
\pagenumbering{arabic}
\def\beq{\begin{equation}}
\def\eeq{\end{equation}}

\begin{document}
\Large

\noindent
FitzHugh's Reduction of Hodgkin Huxley Equations

\begin{itemize}
\item Set $m = m_\infty(\phi)$

\item Set $h+n\approx N = 0.85$
\end{itemize}
Then we have a two variable system
\begin{eqnarray}
    C{d\phi\over dt} &=& \bar g_{Na}
    m_\infty^3(\phi)(N-n)(\phi-v_{Na})+ \bar g_Kn^4(\phi-v_K) + \bar g_l(\phi-v_L),   \\
    {dn \over dt} &=& \alpha_n(1-n) - \beta_n n.       
\end{eqnarray}
where
\begin{eqnarray}
    \alpha_m &=& 0.1\, {25 - \phi \over \exp\left({25 -\phi \over
                                  10}\right)-1},      \label{eq:am}\\ 
    \beta_m &=& 4\, \exp\left({-\phi \over 18}\right),      \label{eq:bm}\\
    \alpha_n &=& 0.01\, {10-\phi\over \exp({10-\phi\over
                        10})-1},                    \label{eq:an}\\ 
    \beta_n &=& 0.125\, \exp\left({-\phi\over 80}\right).  \label{eq:bn}
\end{eqnarray}
and
\beq
m_\infty(\phi) = {\alpha_m\over \alpha_m+\beta_m}
\eeq

\end{document}
