XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6.

# Ermentrout 1998 type I oscillator

p gl=.2,gkdr=80,gna=80
p iapp=0.67
p C=1.

p amphi=.32,amhalf=-54,amwidth=4
p bmphi=.28,bmhalf=-27,bmwidth=5
p ahphi=.128,ahhalf=-50,ahwidth=18
p bhphi=4,bhhalf=-27,bhwidth=5
p anphi=.032,anhalf=-52,anwidth=5
p bnphi=.5,bnhalf=-57,bnwidth=40

# functions
am(v)=amphi*(v-amhalf)/(1-exp(-(v-amhalf)/amwidth))
bm(v)=bmphi*(v-bmhalf)/(exp((v-bmhalf)/bmwidth)-1)
ah(v)=ahphi*exp(-(v-ahhalf)/ahwidth)
bh(v)=bhphi/(1+exp(-(v-bhhalf)/bhwidth))
an(v)=anphi*(v-anhalf)/(1-exp(-(v-anhalf)/anwidth))
bn(v)=bnphi*exp(-(v-bnhalf)/bnwidth)
Isyn(y,V)=gsyn*y*(V-Esyn)


#currents
ina(v,m,h)=gna*m^3*h*(v-Vna)
ikdr(v,n)=gkdr*n^4*(v-Vk)
il(v)=gl*(v-Vl)

#diff. equ.

v1'=(iapp-(ina(v1,m1,ha)+ikdr(v1,n1)+il(v1))+eps*(ua1-v1)/dx-p0*Isyn(y2,v1))/C
v2'=(iapp-(ina(v2,m2,hb)+ikdr(v2,n2)+il(v2))+eps*(ub1-v2)/dx-p0*Isyn(y1,v2))/C
m1'=am(v1)*(1-m1)-bm(v1)*m1
m2'=am(v2)*(1-m2)-bm(v2)*m2
n1'=an(v1)*(1-n1)-bn(v1)*n1
n2'=an(v2)*(1-n2)-bn(v2)*n2
ha'=ah(v1)*(1-ha)-bh(v1)*ha
hb'=ah(v2)*(1-hb)-bh(v2)*hb

## synapse
par taur=1,taud=3,thresh=-30, gsyn=1 Esyn=0
x1'=(-x1+.5*(1+tanh((v1-thresh)/3.0)))/taur
x2'=(-x2+.5*(1+tanh((v2-thresh)/3.0)))/taur
y1'=(-y1+x1)/taud
y2'=(-y2+x2)/taud
init x1=0,y1=0,x2=0,y2=0



par Vna=50,Vk=-100,Vl=-67,Vh=-65,Vrh=-40,Vsh=6,gld=0.1,gh=0.02,tauh=400




hinf(V)=1/(1+exp((V-Vh)/Vsh))
Ild(V)=V-Vl
Ih(V,y)=gh*y*(V-Vrh)/gld

ha[1..50]'=(hinf(ua[j])-ha[j])/tauh
hb[1..50]'=(hinf(ub[j])-hb[j])/tauh

# cable equation


p p[0..50]=0


ua1'=((lambda/dx)^2*(ua2-2*ua1+v1)-Ild(ua1)-Ih(ua1,ha1)-p1*Isyn(y2,ua1)/gld)/tau 
ua[2..50]'= ((lambda/dx)^2*(ua[j+1]-2*ua[j]+ua[j-1])-Ild(ua[j])-Ih(ua[j],ha[j])-p[j]*Isyn(y2,ua[j])/gld)/tau
ua51=(c1+b1*ua50/dx)/(a1+b1/dx)

ub1'=((lambda/dx)^2*(ub2-2*ub1+v2)-Ild(ub1)-Ih(ub1,hb1)-p1*Isyn(y1,ub1)/gld)/tau 
ub[2..50]'= ((lambda/dx)^2*(ub[j+1]-2*ub[j]+ub[j-1])-Ild(ub[j])-Ih(ub[j],hb[j])-p[j]*Isyn(y1,ub[j])/gld)/tau
ub51=(c1+b1*ub50/dx)/(a1+b1/dx)


par lambda=1,tau=10,dx=.1,c1=0,a1=0,b1=1,c0=0,a0=0,b0=1,eps=.025
@ total=1000,dt=.05,xlo=0,xhi=1000,ylo=-100,yhi=50,bounds=1e6

i ua[1..50]=-60
i ha[1..50]=.1
i ub[1..50]=-60
i hb[1..50]=.1

d
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Access SBML model  L3V1

FunctionDefinitions [17] name math sbo cvterm
max minimum x y x x y y
min maximum x y x x y y
heav heavyside x 0 x 0 0.5 x 0 1 x 0 0
mod modulo x y x y x y x 0 y 0 x y x y
am v amhalf amphi amwidth amphi v amhalf 1 v amhalf amwidth
bm v bmhalf bmphi bmwidth bmphi v bmhalf v bmhalf bmwidth 1
ah v ahhalf ahphi ahwidth ahphi v ahhalf ahwidth
bh v bhhalf bhphi bhwidth bhphi 1 v bhhalf bhwidth
an v anhalf anphi anwidth anphi v anhalf 1 v anhalf anwidth
bn v bnhalf bnphi bnwidth bnphi v bnhalf bnwidth
isyn y v esyn gsyn gsyn y v esyn
ina v m h gna vna gna m 3 h v vna
ikdr v n gkdr vk gkdr n 4 v vk
il v gl vl gl v vl
hinf v vh vsh 1 1 v vh vsh
ild v vl v vl
ih v y gh gld vrh gh y v vrh gld

Parameters [73] name constant value unit derived unit sbo cvterm
gl gl = .2 0.2 None
gkdr gkdr = 80 80.0 None
gna gna = 80 80.0 None
iapp iapp = 0.67 0.67 None
c c = 1. 1.0 None
amphi amphi = .32 0.32 None
amhalf amhalf = -54 -54.0 None
amwidth amwidth = 4 4.0 None
bmphi bmphi = .28 0.28 None
bmhalf bmhalf = -27 -27.0 None
bmwidth bmwidth = 5 5.0 None
ahphi ahphi = .128 0.128 None
ahhalf ahhalf = -50 -50.0 None
ahwidth ahwidth = 18 18.0 None
bhphi bhphi = 4 4.0 None
bhhalf bhhalf = -27 -27.0 None
bhwidth bhwidth = 5 5.0 None
anphi anphi = .032 0.032 None
anhalf anhalf = -52 -52.0 None
anwidth anwidth = 5 5.0 None
bnphi bnphi = .5 0.5 None
bnhalf bnhalf = -57 -57.0 None
bnwidth bnwidth = 40 40.0 None
taur taur = 1 1.0 None
taud taud = 3 3.0 None
thresh thresh = -30 -30.0 None
gsyn gsyn = 1 1.0 None
esyn esyn = 0 0.0 None
x1 x1 = 0 0.0 None
y1 y1 = 0 0.0 None
x2 x2 = 0 0.0 None
y2 y2 = 0 0.0 None
vna vna = 50 50.0 None
vk vk = -100 -100.0 None
vl vl = -67 -67.0 None
vh vh = -65 -65.0 None
vrh vrh = -40 -40.0 None
vsh vsh = 6 6.0 None
gld gld = 0.1 0.1 None
gh gh = 0.02 0.02 None
tauh tauh = 400 400.0 None
p[0..50] = 0 0.0 None
lambda lambda = 1 1.0 None
tau tau = 10 10.0 None
dx dx = .1 0.1 None
c1 c1 = 0 0.0 None
a1 a1 = 0 0.0 None
b1 b1 = 1 1.0 None
c0 c0 = 0 0.0 None
a0 a0 = 0 0.0 None
b0 b0 = 1 1.0 None
eps eps = .025 0.025 None
ua[1..50] = -60 -60.0 None
ha[1..50] = .1 0.1 None
ub[1..50] = -60 -60.0 None
hb[1..50] = .1 0.1 None
v1 0.0 dimensionless None
v2 0.0 dimensionless None
m1 0.0 dimensionless None
m2 0.0 dimensionless None
n1 0.0 dimensionless None
n2 0.0 dimensionless None
ha 0.0 dimensionless None
hb 0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
ua1 0.0 dimensionless None
0.0 dimensionless None
ub1 0.0 dimensionless None
0.0 dimensionless None
ua51 0.0 dimensionless None
ub51 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [21]   assignment name derived units sbo cvterm
d v1/dt = iapp ina v1 m1 ha gna vna ikdr v1 n1 gkdr vk il v1 gl vl eps ua1 v1 dx p0 isyn y2 v1 esyn gsyn c None
d v2/dt = iapp ina v2 m2 hb gna vna ikdr v2 n2 gkdr vk il v2 gl vl eps ub1 v2 dx p0 isyn y1 v2 esyn gsyn c None
d m1/dt = am v1 amhalf amphi amwidth 1 m1 bm v1 bmhalf bmphi bmwidth m1 None
d m2/dt = am v2 amhalf amphi amwidth 1 m2 bm v2 bmhalf bmphi bmwidth m2 None
d n1/dt = an v1 anhalf anphi anwidth 1 n1 bn v1 bnhalf bnphi bnwidth n1 None
d n2/dt = an v2 anhalf anphi anwidth 1 n2 bn v2 bnhalf bnphi bnwidth n2 None
d ha/dt = ah v1 ahhalf ahphi ahwidth 1 ha bh v1 bhhalf bhphi bhwidth ha None
d hb/dt = ah v2 ahhalf ahphi ahwidth 1 hb bh v2 bhhalf bhphi bhwidth hb None
d x1/dt = x1 0.5 1 v1 thresh 3 taur None
d x2/dt = x2 0.5 1 v2 thresh 3 taur None
d y1/dt = y1 x1 taud None
d y2/dt = y2 x2 taud None
= None None
= None None
d ua1/dt = lambda dx 2 ua2 2 ua1 v1 ild ua1 vl ih ua1 ha1 gh gld vrh p1 isyn y2 ua1 esyn gsyn gld tau None
= None None
d ub1/dt = lambda dx 2 ub2 2 ub1 v2 ild ub1 vl ih ub1 hb1 gh gld vrh p1 isyn y1 ub1 esyn gsyn gld tau None
= None None
ua51 = c1 b1 ua50 dx a1 b1 dx None
ub51 = c1 b1 ub50 dx a1 b1 dx None
t = time None