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#!/usr/bin/env python
"""
Dynamics of a network of sparsely connected inhibitory current-based
integrate-and-fire neurons. Individual neurons fire irregularly at
low rate but the network is in an oscillatory global activity regime
where neurons are weakly synchronized.
Reference:
"Fast Global Oscillations in Networks of Integrate-and-Fire
Neurons with Low Firing Rates"
Nicolas Brunel & Vincent Hakim
Neural Computation 11, 1621-1671 (1999)
"""
from brian2 import *
N = 5000
Vr = 10*mV
theta = 20*mV
tau = 20*ms
delta = 2*ms
taurefr = 2*ms
duration = .1*second
C = 1000
sparseness = float(C)/N
J = .1*mV
muext = 25*mV
sigmaext = 1*mV
eqs = """
dV/dt = (-V+muext + sigmaext * sqrt(tau) * xi)/tau : volt
"""
group = NeuronGroup(N, eqs, threshold='V>theta',
reset='V=Vr', refractory=taurefr, method='euler')
group.V = Vr
conn = Synapses(group, group, on_pre='V += -J', delay=delta)
conn.connect(p=sparseness)
M = SpikeMonitor(group)
LFP = PopulationRateMonitor(group)
run(duration)
subplot(211)
plot(M.t/ms, M.i, '.')
xlim(0, duration/ms)
subplot(212)
plot(LFP.t/ms, LFP.smooth_rate(window='flat', width=0.5*ms)/Hz)
xlim(0, duration/ms)
show()
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