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Reduced HH


$\displaystyle F(v,w)$ $\textstyle =$ $\displaystyle g_Kw^4(v-v_K)
+g_{Na}m_\infty^3(v)(0.8-w)(v-v_{Na})$  
  $\textstyle +$ $\displaystyle g_l(v-v_l)$ (14)
$\displaystyle G(v,w)$ $\textstyle =$ $\displaystyle \alpha_w(v)(1-h)-\beta_w(v)w$ (15)

where
\begin{displaymath}
\alpha_w = 0.01{10-v\over \exp({10-v\over 10})-1},\qquad \beta_w =
0.125\exp({-v\over 80})
\end{displaymath} (16)

Typical parameter values are $g_{Na} = 120$, $g_k = 36$, $g_l = 0.3$, $v_{Na} = 115$, $v_K = -12$, and $v_l = -10.5988$. The high precision of $V_l$ is to insure that $v=0$ is the rest state.

Phase portrait:

To see a derivation of this model, click here .