# Mean-field model of one population of Izhikevich neurons
# By Liang Chen, Oct. 26, 2021
#
# ref. [Nicola&Campbell2013]:Mean-field models for heterogeneous networks
#          of two-dimensional integrate and fire neurons



# parameters
par mu=0.2, hw=0.02, I=0 
par gsyn=1.2308,  er=1
par b=-0.0062, wjump=0.0189
par alpha=0.6215, sjump=1.2308, ts=2.6, a=0.0077




# initial conditions
init rm=0, vm=0, wm=b*vm, sm=0


# the model:
rm'=hw/pi+2*rm*vm-rm*(gsyn*sm+alpha)
vm'=vm^2-alpha*vm-wm+mu+I+gsyn*sm*(er-vm)-pi^2*rm^2
wm'=a*(b*vm-wm)+wjump*rm
sm'=-sm/ts+sjump*rm
Global 1 {sm-1} {sm=1}




@xplot=t, yplot=rm, xlo=0, xhi=800, ylo=0, yhi=1, bell=0
@total=5000, dt=0.001, maxstor=2000000, bounds=1000000
@ ntst=150, npr=500, nmax=2000, ds=1e-05, dsmin=1e-05, dsmax=1e-04, ncol=5
@ parmin=0, parmax=0.3, epsl=0.000001, epsu=0.000001, epss=0.000001 
@ AUTOXMIN=0, AUTOXMAX=0.3, AUTOYMIN=0, AUTOYMAX=0.2 
@ BUT=QUIT:fq, BUT=AUTO:fa

Done