1# -*- coding: utf-8 -*- 2# 3# BrodyHopfield.py 4# 5# This file is part of NEST. 6# 7# Copyright (C) 2004 The NEST Initiative 8# 9# NEST is free software: you can redistribute it and/or modify 10# it under the terms of the GNU General Public License as published by 11# the Free Software Foundation, either version 2 of the License, or 12# (at your option) any later version. 13# 14# NEST is distributed in the hope that it will be useful, 15# but WITHOUT ANY WARRANTY; without even the implied warranty of 16# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 17# GNU General Public License for more details. 18# 19# You should have received a copy of the GNU General Public License 20# along with NEST. If not, see <http://www.gnu.org/licenses/>. 21 22 23""" 24Spike synchronization through subthreshold oscillation 25------------------------------------------------------ 26 27This script reproduces the spike synchronization behavior 28of integrate-and-fire neurons in response to a subthreshold 29oscillation. This phenomenon is shown in Fig. 1 of [1]_ 30 31Neurons receive a weak 35 Hz oscillation, a gaussian noise current 32and an increasing DC. The time-locking capability is shown to 33depend on the input current given. The result is then plotted using 34matplotlib. All parameters are taken from the above paper. 35 36References 37~~~~~~~~~~ 38 39.. [1] Brody CD and Hopfield JJ (2003). Simple networks for 40 spike-timing-based computation, with application to olfactory 41 processing. Neuron 37, 843-852. 42 43""" 44 45################################################################################# 46# First, we import all necessary modules for simulation, analysis, and plotting. 47 48import nest 49import nest.raster_plot 50import matplotlib.pyplot as plt 51 52############################################################################### 53# Second, the simulation parameters are assigned to variables. 54 55N = 1000 # number of neurons 56bias_begin = 140. # minimal value for the bias current injection [pA] 57bias_end = 200. # maximal value for the bias current injection [pA] 58T = 600 # simulation time (ms) 59 60# parameters for the alternating-current generator 61driveparams = {'amplitude': 50., 'frequency': 35.} 62# parameters for the noise generator 63noiseparams = {'mean': 0.0, 'std': 200.} 64neuronparams = {'tau_m': 20., # membrane time constant 65 'V_th': 20., # threshold potential 66 'E_L': 10., # membrane resting potential 67 't_ref': 2., # refractory period 68 'V_reset': 0., # reset potential 69 'C_m': 200., # membrane capacitance 70 'V_m': 0.} # initial membrane potential 71 72############################################################################### 73# Third, the nodes are created using ``Create``. We store the returned handles 74# in variables for later reference. 75 76neurons = nest.Create('iaf_psc_alpha', N) 77sr = nest.Create('spike_recorder') 78noise = nest.Create('noise_generator') 79drive = nest.Create('ac_generator') 80 81############################################################################### 82# Set the parameters specified above for the generators using ``set``. 83 84drive.set(driveparams) 85noise.set(noiseparams) 86 87############################################################################### 88# Set the parameters specified above for the neurons. Neurons get an internal 89# current. The first neuron additionally receives the current with amplitude 90# `bias_begin`, the last neuron with amplitude `bias_end`. 91 92neurons.set(neuronparams) 93neurons.I_e = [(n * (bias_end - bias_begin) / N + bias_begin) 94 for n in range(1, len(neurons) + 1)] 95 96############################################################################### 97# Connect alternating current and noise generators as well as 98# `spike_recorder`s to neurons 99 100nest.Connect(drive, neurons) 101nest.Connect(noise, neurons) 102nest.Connect(neurons, sr) 103 104############################################################################### 105# Simulate the network for time `T`. 106 107nest.Simulate(T) 108 109############################################################################### 110# Plot the raster plot of the neuronal spiking activity. 111 112nest.raster_plot.from_device(sr, hist=True) 113plt.show() 114