Hodgkin-Huxley model

All cells in animal body tissues are electrically polarized. I.e. there is voltage difference V across the cell's membrane (membrane potential). This electrical polarization results from different Na, Ca and K ions consentrations inside and outside cells (due to the electrochemical gradient). Polarization is maintaining by voltage-gated protein structures embedded in the membrane called ion pumps and ion channels. The Hodgkin-Huxley model [1] describes how action potentials in neurons are initiated and propagated
dV/dt = -(iK + iNa + il )/Cm ,
where Cm = 1 μF/cm2 is membrane's capacitance, iNa , iK are Na, K ion currents, il is a small leakage current caused by other ions
iK = 36 n4(V - 12),
iNa = 120 m3h (V + 115),
il = 0.3 (V + 10.613)
,
dy/dt = αy - (αy + βy )y = (y - y)/τy ,     τy = 1/(αy + βy ),     y = αy /(αy + βy ),
y is one of potassium n, fast activation m or slow inactivation h gates.
 αn = 0.01 (V + 10) / (exp((V + 10)/10) -1), βn = 0.125 exp(V/80), αm = 0.1 (V + 25) / (exp((V + 25)/10) - 1), βm = 4 exp(V/18), αh = 0.07 exp(V/20), βh = 1 / (exp((V + 30)/10) + 1).
m(E), h(E), n(E) and 2 τm(E), τh(E)/10, τn(E)/10 (ms) are ploted below (E = -V)

here 0 ≤ E ≤ 150 (mV), 0 ≤ y ≤ 1. So the minimum time is τm (100) ~ 0.13 and the maximum one is τh (0) ~ 8.5 (ms).

You can see below action potential dynamics in the HH model. A sufficiently strong depolarization (increase in E) causes the voltage-sensitive sodium channels to open (due to fast m gate). The increasing voltage in turn causes even more sodium channels to open, which pushes V still further. This positive feedback continues until the sodium channels are fully open. However, raised voltage also slowly shuts them off by the h gate. The sodium channels become inactivated. At the same time, the raised voltage opens voltage-sensitive potassium channels, driving membrane back towards the resting E = 0 value.
E(mV) Emin Emax dt(ms)   it iNa iK il

m h n
The script makes 1000 it time steps dt. You can change initial E and gates values.

[1] Hodgkin-Huxley model Wikipedia

Heart rhythms     updated 28 May 2012