{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9ab8478e",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: brian2 in /opt/app-root/lib/python3.6/site-packages (2.4.2)\n",
      "Requirement already satisfied: numpy>=1.15 in /opt/app-root/lib/python3.6/site-packages (from brian2) (1.18.1)\n",
      "Requirement already satisfied: cython>=0.29 in /opt/app-root/lib/python3.6/site-packages (from brian2) (0.29.15)\n",
      "Requirement already satisfied: jinja2>=2.7 in /opt/app-root/lib/python3.6/site-packages (from brian2) (3.0.3)\n",
      "Requirement already satisfied: setuptools>=24.2 in /opt/app-root/lib/python3.6/site-packages (from brian2) (28.8.0)\n",
      "Requirement already satisfied: sympy>=1.2 in /opt/app-root/lib/python3.6/site-packages (from brian2) (1.5.1)\n",
      "Requirement already satisfied: pyparsing in /opt/app-root/lib/python3.6/site-packages (from brian2) (3.0.6)\n",
      "Collecting py-cpuinfo\n",
      "  Downloading py-cpuinfo-8.0.0.tar.gz (99 kB)\n",
      "     |████████████████████████████████| 99 kB 5.8 MB/s             \n",
      "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25hRequirement already satisfied: MarkupSafe>=2.0 in /opt/app-root/lib/python3.6/site-packages (from jinja2>=2.7->brian2) (2.0.1)\n",
      "Requirement already satisfied: mpmath>=0.19 in /opt/app-root/lib/python3.6/site-packages (from sympy>=1.2->brian2) (1.2.1)\n",
      "Building wheels for collected packages: py-cpuinfo\n",
      "  Building wheel for py-cpuinfo (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for py-cpuinfo: filename=py_cpuinfo-8.0.0-py3-none-any.whl size=22473 sha256=9216530d0b1d2c78008cd227a6cdf14924f9ec24dcf85fd017cc0384f438dd80\n",
      "  Stored in directory: /tmp/pip-ephem-wheel-cache-rigal4jo/wheels/3e/e1/d9/9b782b170e5272d6500cee4d29dd6c724598b22dc399d81d01\n",
      "Successfully built py-cpuinfo\n",
      "Installing collected packages: py-cpuinfo\n",
      "Successfully installed py-cpuinfo-8.0.0\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install brian2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "76f2efad",
   "metadata": {},
   "outputs": [],
   "source": [
    "from brian2 import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9351f5a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "42c8caa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_scope()\n",
    "# Parameters\n",
    "num_inputs = 100\n",
    "input_rate = 10*Hz\n",
    "weight = 0.1\n",
    "# Range of time constants\n",
    "tau_range = linspace(1, 10, 30)*ms\n",
    "# Use this list to store output rates\n",
    "output_rates = []\n",
    "# Iterate over range of time constants\n",
    "for tau in tau_range:\n",
    "    # Construct the network each time\n",
    "    P = PoissonGroup(num_inputs, rates=input_rate)\n",
    "    eqs = '''\n",
    "    dv/dt = -v/tau : 1\n",
    "    '''\n",
    "    G = NeuronGroup(1, eqs, threshold='v>1', reset='v=0', method='exact')\n",
    "    S = Synapses(P, G, on_pre='v += weight')\n",
    "    S.connect()\n",
    "    M = SpikeMonitor(G)\n",
    "    # Run it and store the output firing rate in the list\n",
    "    run(1*second)\n",
    "    output_rates.append(M.num_spikes/second)\n",
    "# And plot it\n",
    "plot(tau_range/ms, output_rates)\n",
    "xlabel(r'$\\tau$ (ms)')\n",
    "ylabel('Firing rate (sp/s)');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}