LIF_and_ELIF_Complex_Models.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "LIF and ELIF Complex Models",
      "provenance": [],
      "collapsed_sections": [
        "MC0K-bOCK-xk",
        "bKpoPYwmkGhz",
        "dsfmhf8CzO2j",
        "rBg5bzOg4kdr",
        "9NbsO2lF7AOO"
      ],
      "authorship_tag": "ABX9TyMi42NvyNCZgbd8lsdRCtTd",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/m-abdollahi/complete-Python-LIF-Models/blob/main/LIF_and_ELIF_Complex_Models.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v65ZA8WRcUGs"
      },
      "source": [
        "Leaky Integrate-and-Fire Full Model [ Linear , nonLinear , Threshold , Reset Model & ... ] \n",
        "\n",
        "*by : Mostafa Abdollahi*\n",
        "\n",
        "github.com/m-abdollahi\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FKkDtAEUY2_I"
      },
      "source": [
        "\n",
        "> > > ># ***Linear Leaky Integrate-and-Fire (LIF) Model ( Ordinary Model)***\n",
        "\n",
        "\n",
        "\n",
        "\n",
        " \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MC0K-bOCK-xk"
      },
      "source": [
        "\n",
        "# 1 ) Ordinary Model ( without threshold or reset and Start Point)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bVFnVq_BJ-Lz"
      },
      "source": [
        "\n",
        "*   Importing Libraries and Modules\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mEmCBCFgbiu4"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math as mt\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eNKsPiFANAvj",
        "outputId": "9d079576-660b-4491-e813-9d4e01e040b0"
      },
      "source": [
        "pip install brian2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: brian2 in /usr/local/lib/python3.6/dist-packages (2.4.2)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.7)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZanJm6iaMiTy"
      },
      "source": [
        "from brian2 import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n6cNz4ECKGjj"
      },
      "source": [
        "\n",
        "*   Set the Neuron\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C_WeWNAxFH9n"
      },
      "source": [
        "v_rest = -65 * mV        # Rest Potential \n",
        "RI = 90 * mV             # RI = I * R = membrane resistance x constant input current = I/G\n",
        "tau = 10*ms              # Tau = Memberane time Constant "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h1spAGLkKtL7"
      },
      "source": [
        "\n",
        "*   Set the LIF differential equations\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wUwiNzA3hqV4"
      },
      "source": [
        "\n",
        "eqs = '''\n",
        "dv/dt = (v_rest - v + RI)/tau : volt\n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "puT1XjUBLOrK"
      },
      "source": [
        "\n",
        "*   Set the Neuron Circuit\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z2sTz2tcLnT6"
      },
      "source": [
        "Methods = 'exact'        # set the method for the equations ( exact or euler)\n",
        "Run_Time0 = 100*ms      # Import the Run time for Record"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_XK3pBkoiwzv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "8e5a7802-1334-4db2-f70e-62b9877c7284"
      },
      "source": [
        "G = NeuronGroup(1, eqs, method=Methods)\n",
        "M = StateMonitor(G, 'v', record=0)\n",
        "run(Run_Time0)\n",
        "plot(M.t/ms, M.v[0])\n",
        "xlabel('Time (ms)')\n",
        "ylabel('v');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bKpoPYwmkGhz"
      },
      "source": [
        "\n",
        "# 2 ) Ordinary Model ( with threshold & reset Potential and Start Point)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4y1HjjwlkGh0"
      },
      "source": [
        "\n",
        "*   Importing Libraries and Modules\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L5qM-a2jkGh0"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math as mt\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_lWAT1k2kGh0",
        "outputId": "d1bcf63d-70fc-4d61-ecdb-2e3ef719bcc2"
      },
      "source": [
        "pip install brian2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: brian2 in /usr/local/lib/python3.6/dist-packages (2.4.2)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.7)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z5_0kxHUkGh1"
      },
      "source": [
        "from brian2 import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k7GwgxTmkGh1"
      },
      "source": [
        "\n",
        "*   Set the Neuron\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QciikeyBkGh1"
      },
      "source": [
        "v_rest = -65 * mV                          # Rest Potential \n",
        "v_threshold = 'v > 0*mV'                   # Threshold Potential\n",
        "v_reset = 'v = -40*mV'                     # Reset Potential\n",
        "v_initial = -70*mV                         # Initail Poteiial Value\n",
        "RI = 90 * mV                               # RI = I * R = membrane resistance x constant input current = I/G\n",
        "tau = 10*ms                                # Tau = Memberane time Constant "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F_1kMjqHkGh1"
      },
      "source": [
        "\n",
        "*   Set the LIF differential equations\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v9QzSt6WkGh1"
      },
      "source": [
        "\n",
        "eqs = '''\n",
        "dv/dt = (v_rest - v + RI)/tau : volt\n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jn-LwveXkGh1"
      },
      "source": [
        "\n",
        "*   Set the Neuron Circuit\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y22AbNYvkGh2"
      },
      "source": [
        "Methods = 'exact'        # set the method for the equations ( exact or euler)\n",
        "Run_Time0 = 100*ms      # Import the Run time for Record"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "RtI33zcokGh2",
        "outputId": "5fc6be64-d40a-45dc-e6ab-e22f168bf023"
      },
      "source": [
        "G = NeuronGroup(1, eqs, method=Methods , threshold=v_threshold , reset=v_reset)\n",
        "M = StateMonitor(G, 'v', record=0)\n",
        "G.v = v_initial # initial value\n",
        "run(Run_Time0)\n",
        "plot(M.t/ms, M.v[0])\n",
        "xlabel('Time (ms)')\n",
        "ylabel('v');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dsfmhf8CzO2j"
      },
      "source": [
        "\n",
        "# 3 ) Ordinary Model plus Refractoriness type Forced Voltage Clamp \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vqGZpvzLzO2j"
      },
      "source": [
        "\n",
        "*   Importing Libraries and Modules\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t0N-rb9BzO2j"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math as mt\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xiidf5vAzO2j",
        "outputId": "15bc0142-6ead-4ec2-dc39-6a79d562374d"
      },
      "source": [
        "pip install brian2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: brian2 in /usr/local/lib/python3.6/dist-packages (2.4.2)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.7)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_5ZGT24WzO2k"
      },
      "source": [
        "from brian2 import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SxC_zurTzO2k"
      },
      "source": [
        "\n",
        "*   Set the Neuron\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Vuftqu7zO2k"
      },
      "source": [
        "v_rest = -65 * mV                          # Rest Potential \n",
        "v_threshold = 'v > 0*mV'                   # Threshold Potential\n",
        "v_reset = 'v = -40*mV'                     # Reset Potential\n",
        "v_initial = -70*mV                         # Initail Poteiial Value\n",
        "RI = 90 * mV                               # RI = I * R = membrane resistance x constant input current = I/G\n",
        "tau = 10*ms                                # Tau = Memberane time Constant \n",
        "refactorytime = 5*ms                       # Refactory time "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqwydL2wzO2k"
      },
      "source": [
        "\n",
        "*   Set the LIF differential equations\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4qwavRNMzO2k"
      },
      "source": [
        "\n",
        "eqs = '''\n",
        "dv/dt = (v_rest - v + RI)/tau : volt (unless refractory)\n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GR1IgXS4zO2k"
      },
      "source": [
        "\n",
        "*   Set the Neuron Circuit\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vbn9TGX0zO2k"
      },
      "source": [
        "Methods = 'euler'        # set the method for the equations ( exact or euler)\n",
        "Run_Time0 = 100*ms      # Import the Run time for Record"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "q5vymvVDzO2l",
        "outputId": "239c30cf-37fb-49bf-b0ef-d908704f073a"
      },
      "source": [
        "G = NeuronGroup(1, eqs, method=Methods , threshold=v_threshold , reset=v_reset,refractory=refactorytime,)\n",
        "M = StateMonitor(G, 'v', record=0)\n",
        "G.v = v_initial # initial value\n",
        "run(Run_Time0)\n",
        "plot(M.t/ms, M.v[0])\n",
        "xlabel('Time (ms)')\n",
        "ylabel('v');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V0EpMspA47vx"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rBg5bzOg4kdr"
      },
      "source": [
        "\n",
        "# 4 ) Ordinary Model plus Refractoriness type Raised Threshold \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y0dGGKRI4kdr"
      },
      "source": [
        "\n",
        "*   Importing Libraries and Modules\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NMc74G8Y4kdr"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math as mt\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QjMP_WWb4kdr",
        "outputId": "9dbef878-083d-4524-8d99-c1d68e3caf8b"
      },
      "source": [
        "pip install brian2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: brian2 in /usr/local/lib/python3.6/dist-packages (2.4.2)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.7)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wY94xXJp4kds"
      },
      "source": [
        "from brian2 import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bsq-NSjn4kds"
      },
      "source": [
        "\n",
        "*   Set the Neuron\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Su_pgt09CLR1"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SQlMNfNu4kds"
      },
      "source": [
        "v_rest = -65 * mV                          # Rest Potential \n",
        "vth = 0*mV                                 #first Treshold Potential\n",
        "vtau = 2*ms                                # Treshold Time Constant\n",
        "Run_Time0 = 100*ms                         # Run time for Record  \n",
        "vtheqs = 0 + mt.exp(-Run_Time0/vtau)       # The exponential for The Treshold\n",
        "v_threshold = 'v > vtheqs*mV'              # Threshold Potential\n",
        "v_reset = 'v = -40*mV'                     # Reset Potential\n",
        "v_initial = -70*mV                         # Initail Poteiial Value\n",
        "RI = 90 * mV                               # RI = I * R = membrane resistance x constant input current = I/G\n",
        "tau = 10*ms                                # Tau = Memberane time Constant \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YGRpOEJ14kds"
      },
      "source": [
        "\n",
        "*   Set the LIF differential equations\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ihGnjLzC4kds"
      },
      "source": [
        "\n",
        "eqs = '''\n",
        "dv/dt = (v_rest - v + RI)/tau : volt \n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OiSYnt8P4kds"
      },
      "source": [
        "\n",
        "*   Set the Neuron Circuit\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NiW-DVM34kds"
      },
      "source": [
        "Methods = 'euler'        # set the method for the equations ( exact or euler)\n",
        "Run_Time0 = 100*ms      # Import the Run time for Record"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "vKJUQ8f24kdt",
        "outputId": "5184bace-6377-4e4b-a3ee-2eb7b01362fb"
      },
      "source": [
        "G = NeuronGroup(1, eqs, method=Methods , threshold=v_threshold , reset=v_reset,)\n",
        "M = StateMonitor(G, 'v', record=0)\n",
        "G.v = v_initial # initial value\n",
        "run(Run_Time0)\n",
        "plot(M.t/ms, M.v[0])\n",
        "xlabel('Time (ms)')\n",
        "ylabel('v');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zK_WFMn1X_XG"
      },
      "source": [
        "\n",
        "> > > ># ***Exponential Exponential Leaky Integrate-and-Fire (ELIF) Model***\n",
        "\n",
        "\n",
        "\n",
        "\n",
        " \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9NbsO2lF7AOO"
      },
      "source": [
        "\n",
        "# 1 ) Exponential Model ( with threshold or reset and Start Point)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o6ppzxST7AOO"
      },
      "source": [
        "\n",
        "*   Importing Libraries and Modules\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ORW9jRBT7AOO",
        "outputId": "d8879978-b23a-4827-c1dd-9d658b8bf3ff"
      },
      "source": [
        "pip install brian2"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: brian2 in /usr/local/lib/python3.6/dist-packages (2.4.2)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.7)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SdVEinta9z4H",
        "outputId": "63ffcd3a-86c1-4e01-8a15-08380b495375"
      },
      "source": [
        "pip install neurodynex"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting neurodynex\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/0b/9c/6405def71d1e8ad42226c8097816562cab4344f1556a36338f7a83abe99f/neurodynex-0.3.4-py2.py3-none-any.whl (69kB)\n",
            "\r\u001b[K     |████▊                           | 10kB 18.5MB/s eta 0:00:01\r\u001b[K     |█████████▍                      | 20kB 22.0MB/s eta 0:00:01\r\u001b[K     |██████████████                  | 30kB 17.4MB/s eta 0:00:01\r\u001b[K     |██████████████████▉             | 40kB 14.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████▌        | 51kB 16.5MB/s eta 0:00:01\r\u001b[K     |████████████████████████████▏   | 61kB 18.5MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 71kB 4.9MB/s \n",
            "\u001b[?25hRequirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from neurodynex) (1.4.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from neurodynex) (1.18.5)\n",
            "Requirement already satisfied: brian2>=2.0 in /usr/local/lib/python3.6/dist-packages (from neurodynex) (2.4.2)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from neurodynex) (3.2.2)\n",
            "Requirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2>=2.0->neurodynex) (2.4.7)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2>=2.0->neurodynex) (50.3.2)\n",
            "Requirement already satisfied: sympy>=1.2 in /usr/local/lib/python3.6/dist-packages (from brian2>=2.0->neurodynex) (1.7)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2>=2.0->neurodynex) (0.29.21)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2>=2.0->neurodynex) (2.11.2)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->neurodynex) (2.8.1)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->neurodynex) (1.3.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->neurodynex) (0.10.0)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2>=2.0->neurodynex) (1.1.0)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2>=2.0->neurodynex) (1.1.1)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.6/dist-packages (from python-dateutil>=2.1->matplotlib->neurodynex) (1.15.0)\n",
            "Installing collected packages: neurodynex\n",
            "Successfully installed neurodynex-0.3.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IBCmhwdF7Zin"
      },
      "source": [
        "import brian2 as b2\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from neurodynex.leaky_integrate_and_fire import LIF\n",
        "from neurodynex.tools import input_factory, plot_tools\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jnvjQsjF-XzG"
      },
      "source": [
        "V_REST = -70*b2.mV                           # Reset Potential  \n",
        "V_RESET = -60*b2.mV                          # Reset Potential\n",
        "FIRING_THRESHOLD = -50*b2.mV                 # Treshold Potential\n",
        "MEMBRANE_RESISTANCE = 10. * b2.Mohm          # Membereane R \n",
        "MEMBRANE_TIME_SCALE = 8. * b2.ms             # Time Constant\n",
        "ABSOLUTE_REFRACTORY_PERIOD = 2.0 * b2.ms     # Refactory time\n",
        "LIF.getting_started()\n",
        "LIF.print_default_parameters()"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}