.. currentmodule:: brian2

.. Brette_Gerstner_2005:

Example: Brette_Gerstner_2005
=============================


        .. only:: html

            .. |launchbinder| image:: http://mybinder.org/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Brette_Gerstner_2005.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|_

        

Adaptive exponential integrate-and-fire model.

http://www.scholarpedia.org/article/Adaptive_exponential_integrate-and-fire_model

Introduced in Brette R. and Gerstner W. (2005), Adaptive Exponential
Integrate-and-Fire Model as an Effective Description of Neuronal Activity,
J. Neurophysiol. 94: 3637 - 3642.

::

    from brian2 import *
    
    # Parameters
    C = 281 * pF
    gL = 30 * nS
    taum = C / gL
    EL = -70.6 * mV
    VT = -50.4 * mV
    DeltaT = 2 * mV
    Vcut = VT + 5 * DeltaT
    
    # Pick an electrophysiological behaviour
    tauw, a, b, Vr = 144*ms, 4*nS, 0.0805*nA, -70.6*mV # Regular spiking (as in the paper)
    #tauw,a,b,Vr=20*ms,4*nS,0.5*nA,VT+5*mV # Bursting
    #tauw,a,b,Vr=144*ms,2*C/(144*ms),0*nA,-70.6*mV # Fast spiking
    
    eqs = """
    dvm/dt = (gL*(EL - vm) + gL*DeltaT*exp((vm - VT)/DeltaT) + I - w)/C : volt
    dw/dt = (a*(vm - EL) - w)/tauw : amp
    I : amp
    """
    
    neuron = NeuronGroup(1, model=eqs, threshold='vm>Vcut',
                         reset="vm=Vr; w+=b", method='euler')
    neuron.vm = EL
    trace = StateMonitor(neuron, 'vm', record=0)
    spikes = SpikeMonitor(neuron)
    
    run(20 * ms)
    neuron.I = 1*nA
    run(100 * ms)
    neuron.I = 0*nA
    run(20 * ms)
    
    # We draw nicer spikes
    vm = trace[0].vm[:]
    for t in spikes.t:
        i = int(t / defaultclock.dt)
        vm[i] = 20*mV
    
    plot(trace.t / ms, vm / mV)
    xlabel('time (ms)')
    ylabel('membrane potential (mV)')
    show()
    

.. image:: ../resources/examples_images/frompapers.Brette_Gerstner_2005.1.png