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) show()