130 PQN Model with Verilog

\frac{dv}{dt} = \frac{\phi}{\tau} \left( f(v) - n + I_0 + k I_{\text{stim}} \right)

\frac{dn}{dt} = \frac{1}{\tau} \left( g(v) - n \right)

f(v) =
\begin{cases}
a_{fn}(v - b_{fn})^2 + c_{fn} & (v < 0) \\
a_{fp}(v - b_{fp})^2 + c_{fp} & (v \ge 0)
\end{cases}

g(v) =
\begin{cases}
a_{gn}(v - b_{gn})^2 + c_{gn} & (v < r_g) \\
a_{gp}(v - b_{gp})^2 + c_{gp} & (v \ge r_g)
\end{cases}

b_{fp} = \frac{a_{fn} b_{fn}}{a_{fp}}

c_{fp} = a_{fn} b_{fn}^2 + c_{fn} - a_{fp} b_{fp}^2

b_{gp} = r_g - \frac{a_{gn} (r_g - b_{gn})}{a_{gp}}

c_{gp} = a_{gn}(r_g - b_{gn})^2 + c_{gn} - a_{gp}(r_g - b_{gp})^2

\frac{dv}{dt} =
\begin{cases}
f_{vv_n} v^2 + f_{vv_n} v + f_{\text{const}_n} - f_{\text{coef}} n + I_{\text{coef}} I_{\text{stim}} & (v < 0 ) \\
f_{vv_p} v^2 + f_{vv_p} p + f_{\text{const}_p} - f_{\text{coef}} n + I_{\text{coef}} I_{\text{stim}} & (v \ge 0)
\end{cases}  

\frac{dn}{dt} =
\begin{cases}
g_{vv_n} v^2 + g_{vv_n} v + g_{\text{const}_n} - g_{\text{coef}} n & (v < r_g) \\
g_{vv_p} v^2 + g_{vv_p} p + g_{\text{const}_p} - g_{\text{coef}} n & (v \ge r_g)
\end{cases}