# Example: jeffressΒΆ

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:", 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')
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')

synapses = Synapses(ears, neurons, pre='v += .5')
synapses.connect(True)

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)
show()