.. currentmodule:: brian2

.. Brunel_Hakim_1999:

Example: Brunel_Hakim_1999
==========================


        .. only:: html

            .. |launchbinder| image:: file:///usr/share/doc/python-brian-doc/docs/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Brunel_Hakim_1999.ipynb

            .. note::
               You can launch an interactive, editable version of this
               example without installing any local files
               using the Binder service (although note that at some times this
               may be slow or fail to open): |launchbinder|_

        

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()
    

