.. currentmodule:: brian2

.. IF_curve_Hodgkin_Huxley:

Example: IF_curve_Hodgkin_Huxley
================================


        .. 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/IF_curve_Hodgkin_Huxley.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|_

        

Input-Frequency curve of a HH model.

Network: 100 unconnected Hodgin-Huxley neurons with an input current I.
The input is set differently for each neuron.

This simulation should use exponential Euler integration.

::

    from brian2 import *
    
    num_neurons = 100
    duration = 2*second
    
    # Parameters
    area = 20000*umetre**2
    Cm = 1*ufarad*cm**-2 * area
    gl = 5e-5*siemens*cm**-2 * area
    El = -65*mV
    EK = -90*mV
    ENa = 50*mV
    g_na = 100*msiemens*cm**-2 * area
    g_kd = 30*msiemens*cm**-2 * area
    VT = -63*mV
    
    # The model
    eqs = Equations('''
    dv/dt = (gl*(El-v) - g_na*(m*m*m)*h*(v-ENa) - g_kd*(n*n*n*n)*(v-EK) + I)/Cm : volt
    dm/dt = 0.32*(mV**-1)*4*mV/exprel((13.*mV-v+VT)/(4*mV))/ms*(1-m)-0.28*(mV**-1)*5*mV/exprel((v-VT-40.*mV)/(5*mV))/ms*m : 1
    dn/dt = 0.032*(mV**-1)*5*mV/exprel((15.*mV-v+VT)/(5*mV))/ms*(1.-n)-.5*exp((10.*mV-v+VT)/(40.*mV))/ms*n : 1
    dh/dt = 0.128*exp((17.*mV-v+VT)/(18.*mV))/ms*(1.-h)-4./(1+exp((40.*mV-v+VT)/(5.*mV)))/ms*h : 1
    I : amp
    ''')
    # Threshold and refractoriness are only used for spike counting
    group = NeuronGroup(num_neurons, eqs,
                        threshold='v > -40*mV',
                        refractory='v > -40*mV',
                        method='exponential_euler')
    group.v = El
    group.I = '0.7*nA * i / num_neurons'
    
    monitor = SpikeMonitor(group)
    
    run(duration)
    
    plot(group.I/nA, monitor.count / duration)
    xlabel('I (nA)')
    ylabel('Firing rate (sp/s)')
    show()
    

