Brody and Hopfield model

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This script reproduces the spike synchronization behavior of integrate-and-fire neurons in response to a subthreshold oscillation. This phenomenon is shown in Fig. 1 of

C.D. Brody and J.J. Hopfield (2003) Simple Networks for Spike-Timing-Based Computation, with Application to Olfactory Processing Neuron 37, 843-852

Neurons receive a weak 35Hz oscillation, a gaussian noise current and an increasing DC. The time-locking capability is shown to depend on the input current given. The result is then plotted using pylab. All parameters are taken from the above paper.

Units are the usual NEST units: pA,pF,ms,mV,Hz

#! /usr/bin/env python

# This script reproduces the spike synchronization
# behavior of integrate-and-fire neurons in response to a subthreshold
# oscillation. This phenomenon is shown in Fig. 1 of

#   C.D. Brody and J.J. Hopfield
#   Simple Networks for Spike-Timing-Based Computation,
#   with Application to Olfactory Processing
#   Neuron 37, 843-852 (2003)

# Neurons receive a weak 35Hz oscillation, a gaussian noise current
# and an increasing DC. The time-locking capability is shown to
# depend on the input current given. The result is then plotted using pylab.
# All parameters are taken from the above paper.
#
# units are the usual NEST units: pA,pF,ms,mV,Hz
#
# Sven Schrader

import nest
import nest.raster_plot
import pylab
import numpy

N=1000 # number of neurons

bias_begin=140. # bias current from...
bias_end=200.   # ...to (ms) 
T=600 # simulation time (ms)

def bias(n):
    # constructs the dictionary with current ramp
    return { 'I_e': (n * (bias_end-bias_begin)/N + bias_begin) }

driveparams  = {'amplitude':50., 'frequency':35.}
noiseparams  = {'mean':0.0, 'std':200.}
sdparams     = { 'to_file':False, 'to_screen':False}
neuronparams = { 'tau_m':20., 'V_th':20., 'E_L':10.,
                 't_ref':2., 'V_reset':0., 'C_m':200., 'V_m':0.}

neurons = nest.Create('iaf_psc_alpha',N)
sd      = nest.Create('spike_detector')
noise   = nest.Create('noise_generator')
drive   = nest.Create('ac_generator')

nest.SetStatus(drive,   [driveparams] )
nest.SetStatus(noise,   [noiseparams] )
nest.SetStatus(sd,      [sdparams]    )
nest.SetStatus(neurons, [neuronparams])
nest.SetStatus(neurons, map(bias, neurons))

nest.DivergentConnect(drive, neurons)
nest.DivergentConnect(noise, neurons)
nest.ConvergentConnect(neurons, sd)

nest.Simulate(T)

nest.raster_plot.from_device(sd)
nest.raster_plot.show()