Hodgkin-Huxley Equations

\[ \begin{align} C_m \dot{v} &= -(g_{Na}m^3h(V - V_{Na}) + g_K n^4 (V - V_K) + g_\ell (V - V_\ell)) + I_{app}\\ \dot{m} &= \frac{m_\infty(v) - m}{\tau_m}\\ \dot{h} &= \frac{h_\infty(v) - h}{\tau_h}\\ \dot{n} &= \frac{n_\infty(v) - n}{\tau_n}\\ \end{align} \]

Note: There is also a spatial effect on \(v\) that is omitted in the above equations.