{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,y,z): \n",
    "    fxy = J[x,y]*(1/g[z] - J[z,z]) + J[x,z]*J[z,y]\n",
    "    return(fxy)\n",
    "\n",
    "def h(x,y,z):\n",
    "    hx = 1/(g[y]*g[z])-J[y,y]/g[z]-J[z,z]/g[y]-J[y,z]*J[z,y]+J[y,y]*J[z,z]\n",
    "    return(hx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "save = 0\n",
    "\n",
    "g = [1,4,1] #ge, gi, ga\n",
    "J = np.array([[5,-1,1],[10,-0.5,0.5],[0.5,0.5,0.1]])   # Jee, Jei, Jea #Jie, Jii, Jia # Jae, Jai, Jaa\n",
    "Ti = 25\n",
    "Te = np.arange(-10,40) \n",
    "Ta = -3.5\n",
    "tau = [10,2,20]\n",
    "\n",
    "fig, ax = plt.subplots(3,figsize=(12,12),sharex=True, gridspec_kw={'hspace': 0})\n",
    "#without astrocytes\n",
    "ax[0].axvline(0, color='gray',ls='--')\n",
    "ax[0].plot(Te,-J[1,0]/Ti*Te + J[0,0]-1/g[0],linestyle='--', color='gray',label='No A')\n",
    "ax[0].axvline((J[0,0]-1/g[0])/J[1,0]*Ti, linestyle='--',color='gray')\n",
    "ax[0].plot(Te,((J[0,0]-1/g[0])*(-J[1,1]-1/g[1])+J[1,0]*J[0,1])/(-Ti*J[0,1])*Te, linestyle='--',color='gray')\n",
    "\n",
    "# with astrocytes\n",
    "##Jai = 0.5, Jae = 0.5\n",
    "if Ta>0:\n",
    "    ax[1].axvline(0, ls='-',color='b') \n",
    "else:\n",
    "    ax[1].axvline(-g[2]*J[0,2]*Ta/(1-g[2]*J[2,2]), ls='-',color='b')\n",
    "\n",
    "ax[1].plot(Te,(f(1,0,2)*Te+h(1,0,2)*Ti+f(1,2,0)*Ta)/((J[2,2]-1/g[2])*Ti-J[1,2]*Ta),color='b')\n",
    "\n",
    "ax[1].axvline(-(h(1,0,2)*Ti+f(1,2,0)*Ta)/f(1,0,2),label=r'$J_{AE}=0.5$, $J_{AI}=0.5$',color='b')\n",
    "ax[1].plot(Te,-Te*(J[2,0]*f(0,2,1)+J[2,1]*f(1,2,0)+(J[2,2]-1/g[2])*h(2,0,1))/(f(0,1,2)*Ti+f(0,2,1)*Ta+Te*(h(0,1,2)-(J[2,2]-1/g[2])*(J[1,1]-1/g[1])-J[2,1]*J[1,2])),'b')\n",
    "\n",
    "###\n",
    "##Jai = 0, Jae = 1\n",
    "J = np.array([[5,-1,1],[10,-0.5,0.5],[1,0,0.1]])   # Jee, Jei, Jea #Jie, Jii, Jia # Jae, Jai, Jaa\n",
    "if Ta>0:\n",
    "    ax[2].axvline(0, ls='-',color='g') \n",
    "else:\n",
    "    ax[2].axvline(-g[2]*J[0,2]*Ta/(1-g[2]*J[2,2]), ls='-',color='g')\n",
    "\n",
    "ax[2].plot(Te,(f(1,0,2)*Te+h(1,0,2)*Ti+f(1,2,0)*Ta)/((J[2,2]-1/g[2])*Ti-J[1,2]*Ta),label=r'$J_{AE}=1$, $J_{AI}=0$',color='g')\n",
    "ax[2].axvline(-(h(1,0,2)*Ti+f(1,2,0)*Ta)/f(1,0,2),color='g')\n",
    "ax[2].plot(Te,-Te*(J[2,0]*f(0,2,1)+J[2,1]*f(1,2,0)+(J[2,2]-1/g[2])*h(2,0,1))/(f(0,1,2)*Ti+f(0,2,1)*Ta+Te*(h(0,1,2)-(J[2,2]-1/g[2])*(J[1,1]-1/g[1])-J[2,1]*J[1,2])),'g')\n",
    "\n",
    "####\n",
    "ax[0].scatter([10.5],[1], c='r',marker='*',s=100)\n",
    "ax[1].scatter([10.5],[1], c='r',marker='*',s=100)\n",
    "ax[2].scatter([10.5],[1], c='r',marker='*',s=100)\n",
    "\n",
    "ax[0].legend(fontsize=20)\n",
    "ax[1].legend(fontsize=20)\n",
    "ax[2].legend(fontsize=20,loc='upper right')\n",
    "\n",
    "plt.xticks(fontsize=25)\n",
    "ax[0].set_yticks([0,2,4,6,8,10])\n",
    "ax[1].set_yticks([0,2,4,6,8,10])\n",
    "ax[2].set_yticks([0,2,4,6,8,10])\n",
    "ax[0].tick_params(axis='y', labelsize=25)\n",
    "ax[1].tick_params(axis='y', labelsize=25)\n",
    "ax[2].tick_params(axis='y', labelsize=25)\n",
    "plt.xlim(-10,20)\n",
    "ax[0].set_ylim(0,11)\n",
    "ax[1].set_ylim(0,11)\n",
    "ax[2].set_ylim(0,11)\n",
    "plt.xlabel(r'$\\theta_E$',fontsize=30)\n",
    "ax[0].set_ylabel(r'$\\beta$',fontsize=30)\n",
    "ax[1].set_ylabel(r'$\\beta$',fontsize=30)\n",
    "ax[2].set_ylabel(r'$\\beta$',fontsize=30)\n",
    "\n",
    "if save==1:\n",
    "    plt.savefig('./figures/bifurcdiagram.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-9.4375 52.75 3.5\n"
     ]
    },
    {
     "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": [
    "g = [1,4,1] #ge,gi,ga\n",
    "J = np.array([[5,-1,0.5],[10,-0.5,0.5],[0.5,0.5,0.1]])   # Jee, Jei, Jea #Jie, Jii, Jia # Jae, Jai, Jaa\n",
    "Ti = 25\n",
    "Te = np.arange(10,20) \n",
    "Ta = -3.5\n",
    "beta = 1\n",
    "\n",
    "Te = np.arange(10,20) \n",
    "be = (f(0,1,2)*Ti+f(0,2,1)*Ta)/(-h(0,1,2))\n",
    "bi = (f(1,0,2)*Te+h(1,0,2)*Ti+f(1,2,0)*Ta)/((J[2,2]-1/g[2])*Ti-J[1,2]*Ta)\n",
    "ba = (f(2,0,1)*Te+f(2,1,0)*Ti+h(2,0,1)*Ta)/((J[1,1]-1/g[1])*Ta-J[2,1]*Ti)\n",
    "plt.figure()\n",
    "plt.axvline(be)\n",
    "plt.plot(Te,bi)\n",
    "plt.plot(Te,ba)\n",
    "\n",
    "# Numerators values\n",
    "Te = 15\n",
    "Nre = h(0,1,2)*Te+f(0,1,2)*Ti+f(0,2,1)*Ta\n",
    "Nri = f(1,0,2)*Te+(h(1,0,2)-beta*(J[2,2]-1/g[2]))*Ti+(f(1,2,0)+J[1,2]*beta)*Ta\n",
    "Nra = f(2,0,1)*Te+(f(2,1,0)+J[2,1]*beta)*Ti+(h(2,0,1)-beta*(J[1,1]-1/g[1]))*Ta\n",
    "print(Nre,Nri,Nra)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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