.. currentmodule:: brian2

.. licklider:

Example: licklider
==================


        .. only:: html

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

        

Spike-based adaptation of Licklider's model of pitch processing (autocorrelation with
delay lines) with phase locking.

::

    from brian2 import *
    
    defaultclock.dt = .02 * ms
    
    # Ear and sound
    max_delay = 20*ms # 50 Hz
    tau_ear = 1*ms
    sigma_ear = 0.0
    eqs_ear = '''
    dx/dt = (sound-x)/tau_ear+0.1*(2./tau_ear)**.5*xi : 1 (unless refractory)
    sound = 5*sin(2*pi*frequency*t)**3 : 1 # nonlinear distortion
    #sound = 5*(sin(4*pi*frequency*t)+.5*sin(6*pi*frequency*t)) : 1 # missing fundamental
    frequency = (200+200*t*Hz)*Hz : Hz # increasing pitch
    '''
    receptors = NeuronGroup(2, eqs_ear, threshold='x>1', reset='x=0',
                            refractory=2*ms, method='euler')
    # Coincidence detectors
    min_freq = 50*Hz
    max_freq = 1000*Hz
    num_neurons = 300
    tau = 1*ms
    sigma = .1
    eqs_neurons = '''
    dv/dt = -v/tau+sigma*(2./tau)**.5*xi : 1
    '''
    
    neurons = NeuronGroup(num_neurons, eqs_neurons, threshold='v>1', reset='v=0',
                          method='euler')
    
    synapses = Synapses(receptors, neurons, on_pre='v += 0.5')
    synapses.connect()
    synapses.delay = 'i*1.0/exp(log(min_freq/Hz)+(j*1.0/(num_neurons-1))*log(max_freq/min_freq))*second'
    
    spikes = SpikeMonitor(neurons)
    
    run(500*ms)
    plot(spikes.t/ms, spikes.i, '.k')
    xlabel('Time (ms)')
    ylabel('Frequency')
    yticks([0, 99, 199, 299],
           array(1. / synapses.delay[1, [0, 99, 199, 299]], dtype=int))
    show()
    

.. image:: ../resources/examples_images/synapses.licklider.1.png