XPP model

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

# This is a a morris-lecar system with IA and depression.
# The interesting phase plane for
# the "middle" branch is the v vs. ha. Note also that the v vs w phase plane
# can have a quintic v nullcline.

#dv/dt = ( I - gca*minf(V)*(V-Vca)-gk*w*(V-VK)-GL*(v-vL))/c
#dw/dt = (winf(V)-w)/(tauwleft +(tauwright - tauwleft)*Heav(v-0))
v=-50+50*heav(TA-mod(t,per))
dvf/dt = ( Ipost - gca*minf(Vf)*(Vf-Vca)-gk*wf*(Vf-VK)-ga*mainf(vf)*ha*(Vf-VK)-gl*(Vf-Vl)-ginh* s*(vf-Vsyn))/c1
dwf/dt = (wfinf(Vf)-wf)/tauw(Vf)
dha/dt = (hainf(vf) - ha)/tauha(vf)
d'=(1-d)*Heav(vtheta-v)/taua -d*Heav(v-vtheta)/taub
s'=-s*(Heav(vtheta-v)/tauk + Heav(v-vtheta)*sdecayup)
y'=1
tf'=0
period'=0

minf(v)=.5*(1+tanh((v-v1)/v2))
winf(v)=.5*(1+tanh((v-v3)/v4))
wfinf(v)=.5*(1+tanh((v-v5)/v4))
tauw(v)=tauwflo+(tauwfhi-tauwflo)*winf(v)
hainf(v)=1/(1+exp((v-vha)/kha))
mainf(v)=1/(1+exp(-(v-vma)/kma))
#tauha(v)=tauhhi+(tauhlo-tauhhi)*hainf(v)
tauha(v)=tauhhi+(tauhlo-tauhhi)*hainf(v) + (tauhmed-tauhhi)*(Heav(v-vha) - Heav(v-vma-k))
p ipost=45 v5=20 k=2
p ga=2 vma=-10 kma=0.5
p ginh=1.85
p vha=-15 kha=0.5
p tauhlo=465 tauhhi=10 tauhmed=1200
p tauwflo=15 tauwfhi=2
# p tauwleft=200 tauwright=100
p taua=400 taub=5 tauk=125 c1=2
p TA=5
p per=500
# flags

global 1 v-vtheta {s=d}
global 1 v-vtheta {y=0}
global 1 vf-0 {tf=y}
global 1 v+24.99 {period=y}

# auxilary functions
aux phase=tf/per
aux v=v
aux window=Heav(vf-vha) - Heav(vf-vma-k)
#ma=mainf(V)
v1=-1.2
v2=18
v3=0
v4=5
gk=8
gl=2
gca=4
vk=-84
vl=-60
vca=120
c=40
vsyn=-80
vtheta=-25
sdecayup=0


ha(0)=1

@ total=5000,dt=1,xlo=-60,xhi=60,ylo=-.125,yhi=.6,
# xp=vf,yp=wf
@ nmesh=200,maxstor=100000,bounds=10000
done








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Copyright © 2017 Matthias Koenig

Redistribution and use of any part of this model, with or without modification, are permitted provided that the following conditions are met:

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This model is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


Model :

id
name
time
substance
extent
volume
area
length
Access SBML model  L3V1

FunctionDefinitions [11] 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
minf v v1 v2 0.5 1 v v1 v2
winf v v3 v4 0.5 1 v v3 v4
wfinf v v4 v5 0.5 1 v v5 v4
tauw v tauwfhi tauwflo v3 v4 tauwflo tauwfhi tauwflo winf v v4 v3
hainf v kha vha 1 1 v vha kha
mainf v kma vma 1 1 v vma kma
tauha v k kha tauhhi tauhlo tauhmed vha vma tauhhi tauhlo tauhhi hainf v vha kha tauhmed tauhhi heav v vha heav v vma k

Parameters [46] name constant value unit derived unit sbo cvterm
ipost ipost = 45 45.0 None
v5 v5 = 20 20.0 None
k k = 2 2.0 None
ga ga = 2 2.0 None
vma vma = -10 -10.0 None
kma kma = 0.5 0.5 None
ginh ginh = 1.85 1.85 None
vha vha = -15 -15.0 None
kha kha = 0.5 0.5 None
tauhlo tauhlo = 465 465.0 None
tauhhi tauhhi = 10 10.0 None
tauhmed tauhmed = 1200 1200.0 None
tauwflo tauwflo = 15 15.0 None
tauwfhi tauwfhi = 2 2.0 None
taua taua = 400 400.0 None
taub taub = 5 5.0 None
tauk tauk = 125 125.0 None
c1 c1 = 2 2.0 None
ta ta = 5 5.0 None
per per = 500 500.0 None
ha ha = 1 1.0 None
vf 0.0 dimensionless None
wf 0.0 dimensionless None
d 0.0 dimensionless None
s 0.0 dimensionless None
y 0.0 dimensionless None
tf 0.0 dimensionless None
period 0.0 dimensionless None
v 0.0 dimensionless None
phase 0.0 dimensionless None
window 0.0 dimensionless None
v1 0.0 dimensionless None
v2 0.0 dimensionless None
v3 0.0 dimensionless None
v4 0.0 dimensionless None
gk 0.0 dimensionless None
gl 0.0 dimensionless None
gca 0.0 dimensionless None
vk 0.0 dimensionless None
vl 0.0 dimensionless None
vca 0.0 dimensionless None
c 0.0 dimensionless None
vsyn 0.0 dimensionless None
vtheta 0.0 dimensionless None
sdecayup 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [26]   assignment name derived units sbo cvterm
d vf/dt = ipost gca minf vf v1 v2 vf vca gk wf vf vk ga mainf vf kma vma ha vf vk gl vf vl ginh s vf vsyn c1 None
d wf/dt = wfinf vf v4 v5 wf tauw vf tauwfhi tauwflo v3 v4 None
d ha/dt = hainf vf kha vha ha tauha vf k kha tauhhi tauhlo tauhmed vha vma None
d d/dt = 1 d heav vtheta v taua d heav v vtheta taub None
d s/dt = s heav vtheta v tauk heav v vtheta sdecayup None
d y/dt = 1 None
d tf/dt = 0 None
d period/dt = 0 None
v = 50 50 heav ta mod t per None
phase = tf per None
window = heav vf vha heav vf vma k None
v1 = 1.2 None
v2 = 18 None
v3 = 0 None
v4 = 5 None
gk = 8 None
gl = 2 None
gca = 4 None
vk = 84 None
vl = 60 None
vca = 120 None
c = 40 None
vsyn = 80 None
vtheta = 25 None
sdecayup = 0 None
t = time None

Events [4] name trigger priority delay assignments sbo cvterm
e0 v vtheta 0
initialValue = False
persistent = True
s = d
e1 v vtheta 0
initialValue = False
persistent = True
y = 0
e2 vf 0 0
initialValue = False
persistent = True
tf = y
e3 v 24.99 0
initialValue = False
persistent = True
period = y