# This is an XPP realization of the noisy ring model that appears in
# Goldberg JA, Rokni U and Sompolinsky H. Patterns of Ongoing Activity and the
# Functional Architecture of the Primary Visual Cortex. Neuron, 42:489500 (2004).
# must have the file CosIntCol20.tab in the same directory as NoisyRing.ode
# In order to see the population activity do
# Viewaxes, Array and then fill out
# *Column 1:m11
# NCols:20
# Row 1:0
# NRows:4000
# RowSkip:5
# Zmin:0
# and adjust Zmax according to your simulation
# The phase diagram of this model is shown in fig. 3A of the above paper. In order to
# get a noisy "hill" of activity lambda must be larger than 1 and mu must be positive.
# parameters (gain and mean of Gaussian noise)
p lambda=1.8, mu=1
# mu here is equivalent to T/Sigma_n in the figure in the paper.
# note lambda=1.1, mu=5 are other possible defaults
# threshold linear gain function
sl(x)=max(x,0)
# stochastic integration, w is local uncorrelated Gaussian white noise
weiner w[11..30]
#the model
m[11..30]'=m[j]+sl(2*lambda*h([j11])+w[j]+mu)
#Coupling Matrix
table coscol CosIntCol20.tab
# this table is cosine coupling divided by 20
# recurrent feedback is given by h
special h=mmult(20,20,coscol,m11);
# order parameters of model
rnull=sum(0,19) of (shift(m11,i'))/20
rfundc=sum(0,19) of (shift(m11,i')*cos(2*pi*i'/20))/20
rfunds=sum(0,19) of (shift(m11,i')*sin(2*pi*i'/20))/20
aux r0=rnull
aux r1=sqrt(rfundc^2+rfunds^2)
aux phiang=atan(rfunds/rfundc)
# r1 is order 1 for a "hill of activity" and is order 1/sqrt(20) otherwise
@ total=1000,xlo=0,xhi=1000,ylo=0,yhi=10,dt=0.05,bounds=10000,meth=euler
d
