.. currentmodule:: brian2

.. jeffress:

Example: jeffress
=================


        .. only:: html

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

        

Jeffress model, adapted with spiking neuron models.
A sound source (white noise) is moving around the head.
Delay differences between the two ears are used to determine the azimuth of the
source. Delays are mapped to a neural place code using delay lines (each neuron
receives input from both ears, with different delays).

::

    from brian2 import *
    
    defaultclock.dt = .02*ms
    
    # Sound
    sound = TimedArray(10 * randn(50000), dt=defaultclock.dt) # white noise
    
    # Ears and sound motion around the head (constant angular speed)
    sound_speed = 300*metre/second
    interaural_distance = 20*cm # big head!
    max_delay = interaural_distance / sound_speed
    print("Maximum interaural delay: %s" % max_delay)
    angular_speed = 2 * pi / second # 1 turn/second
    tau_ear = 1*ms
    sigma_ear = .1
    eqs_ears = '''
    dx/dt = (sound(t-delay)-x)/tau_ear+sigma_ear*(2./tau_ear)**.5*xi : 1 (unless refractory)
    delay = distance*sin(theta) : second
    distance : second # distance to the centre of the head in time units
    dtheta/dt = angular_speed : radian
    '''
    ears = NeuronGroup(2, eqs_ears, threshold='x>1', reset='x = 0',
                       refractory=2.5*ms, name='ears', method='euler')
    ears.distance = [-.5 * max_delay, .5 * max_delay]
    traces = StateMonitor(ears, 'delay', record=True)
    # Coincidence detectors
    num_neurons = 30
    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', name='neurons', method='euler')
    
    synapses = Synapses(ears, neurons, on_pre='v += .5')
    synapses.connect()
    
    synapses.delay['i==0'] = '(1.0*j)/(num_neurons-1)*1.1*max_delay'
    synapses.delay['i==1'] = '(1.0*(num_neurons-j-1))/(num_neurons-1)*1.1*max_delay'
    
    spikes = SpikeMonitor(neurons)
    
    run(1000*ms)
    
    # Plot the results
    i, t = spikes.it
    subplot(2, 1, 1)
    plot(t/ms, i, '.')
    xlabel('Time (ms)')
    ylabel('Neuron index')
    xlim(0, 1000)
    subplot(2, 1, 2)
    plot(traces.t/ms, traces.delay.T/ms)
    xlabel('Time (ms)')
    ylabel('Input delay (ms)')
    xlim(0, 1000)
    tight_layout()
    show()
    

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