#S Coombes Jan 2008
#Reduction of the Hodgkin-Huxley equations
#via the method of equivalent potentials to a planar system

par J=0
par C=1,gL=0.3,gK=36,gNa=120,VL=-54.402,VK=-77,VNa=50


u(0)=0
v(0)=0

alpham(x)=0.1*(x+40)/(1-exp(-0.1*(x+40)))
alphah(x)=0.07*exp(-0.05*(x+65))
alphan(x)=0.01*(x+55)/(1-exp(-0.1*(x+55)))
betam(x)=4.0*exp(-0.0556*(x+65))
betah(x)=1.0/(1+exp(-0.1*(x+35)))
betan(x)=0.125*exp(-0.0125*(x+65))
taum(x)=1.0/(alpham(x)+betam(x))
taun(x)=1.0/(alphan(x)+betan(x))
tauh(x)=1.0/(alphah(x)+betah(x))
minfty(x)=alpham(x)*taum(x)
ninfty(x)=alphan(x)*taun(x)
hinfty(x)=alphah(x)*tauh(x)

dalphahdu(x)=-0.05*alphah(x)
dalphandu(x)=((1-exp(-0.1*(x+55)))*0.01 - 0.001*(x+55)*exp(-0.1*(x+55)))/((1-exp(-0.1*(x+55)))*((1-exp(-0.1*(x+55)))))
dbetandu(x)=-0.0125*betan(x)
dbetahdu(x)=0.1*exp(-0.1*(x+35))/((1+exp(-0.1*(x+35)))*(1+exp(-0.1*(x+35))))


dhdu(x)=tauh(x)*dalphahdu(x)*(1-hinfty(x)) - hinfty(x)*tauh(x)*dbetahdu(x)
dndu(x)=taun(x)*dalphandu(x)*(1-ninfty(x))- ninfty(x)*taun(x)*dbetandu(x)
dfdh(x)=gNa*minfty(x)*minfty(x)*minfty(x)*(x-VNa)
dfdn(x,y)=4*gK*ninfty(y)*ninfty(y)*ninfty(y)*(x-VK)



f(x,y) = gK*ninfty(y)*ninfty(y)*ninfty(y)*ninfty(y)*(x-VK) + gNa*hinfty(y)*minfty(x)*minfty(x)*minfty(x)*(x-VNa) +gL*(x-VL)
A(x,y)=dfdh(x)*(hinfty(x) - hinfty(y))/tauh(x) + dfdn(x,y)*(ninfty(x) - ninfty(y))/taun(x)
B(x,y)=dfdh(x)*dhdu(y) + dfdn(x,y)*dndu(y)
g(x,y)=A(x,y)/B(x,y)


v'=(-f(v,u))/C+J
u'=g(v,u)

aux nn=ninfty(u)
aux hh=hinfty(u)


@ meth=cvode,dt=0.01,total=100,maxstore=1000000
done