.. currentmodule:: brian

.. index::
   pair: example usage; NeuronGroup
   pair: example usage; run
   pair: example usage; TimedArray
   pair: example usage; raster_plot
   pair: example usage; Synapses
   pair: example usage; SpikeMonitor
   pair: example usage; StateMonitor

.. _example-synapses_jeffress:

Example: jeffress (synapses)
============================

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).

Romain Brette

::

    from brian import *
    from time import time
    
    defaultclock.dt = .02 * ms
    dt = defaultclock.dt
    
    # Sound
    sound = TimedArray(10 * randn(50000)) # 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:", max_delay
    angular_speed = 2 * pi * radian / 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
    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, model=eqs_ears, threshold=1, reset=0, refractory=2.5 * ms)
    ears.distance = [-.5 * max_delay, .5 * max_delay]
    traces = StateMonitor(ears, 'x', record=True)
    
    # Coincidence detectors
    N = 300
    tau = 1 * ms
    sigma = .1
    eqs_neurons = '''
    dv/dt=-v/tau+sigma*(2./tau)**.5*xi : 1
    '''
    neurons = NeuronGroup(N, model=eqs_neurons, threshold=1, reset=0)
    
    synapses = Synapses(ears,neurons,model='w:1',pre='v+=w')
    synapses[:,:]=True
    synapses.w=.5
    synapses.delay[0, :] = linspace(0 * ms, 1.1 * max_delay, N)
    synapses.delay[1, :] = linspace(0 * ms, 1.1 * max_delay, N)[::-1]    
    
    spikes = SpikeMonitor(neurons)
    
    run(1*ms)
    t1=time()
    run(1000 * ms)
    t2=time()
    print "It took",t2-t1,"s"
    raster_plot(spikes)
    show()