HH方程式(Hodgkin-Huxley Equations)

code:HHmodel.py

# HH: Hodgkin-Huxley (1952) model

C = 1. # 膜容量（membrane capacitance) (uF/cm^2)

# maximum conductances (uS/cm^2)

gna = 120. # sodium

gk = 36. # potassium

gl = 0.3 # leak

# reversal potentials (mV)

Ena = 50. # sodium

Ek = -77. # potassium

El = -54.4 # leak

def hh(y, t, stim=0.):

# state variables: potential and activation/inactivation

v, m, h, n = y

# membrane potential

if callable(stim):

I = stim(t) # time-dependent

else:

I = stim # constant

dv = (gna*m**3*h*(Ena-v) + gk*n**4*(Ek-v) + gl*(El-v) + I)/C

# sodium current activation

am = 0.1*(v+40)/(1-np.exp(-(v+40)/10))

bm = 4*np.exp(-(v+65)/18);

dm = am*(1-m) - bm*m

# sodium current inactivation

ah = 0.07*np.exp(-(v+65)/20)

bh = 1/(1+np.exp(-(v+35)/10))

dh = ah*(1-h) - bh*h

# potassium current activation

an = 0.01*(v+55)/(1-np.exp(-(v+55)/10))

bn = 0.125*np.exp(-(v+65)/80)

dn = an*(1-n) - bn*n