#!/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()