{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# Animation\n",
    "from matplotlib import animation, rc\n",
    "rc('animation', html='html5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'recovery variable, W')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 5))\n",
    "v, w = np.meshgrid(np.linspace(-2.5, 2.5, 10), np.linspace(-1.2, 1.2, 8))\n",
    "vd = v-v*v*v/3-w+0.325\n",
    "wd = 0.08*(v+0.7-0.8*w)\n",
    "plt.quiver(v, w, vd, wd)\n",
    "plt.ylim([-1.3, 1.3])\n",
    "\n",
    "x = np.linspace(-2.5, 2.5)\n",
    "plt.plot(x, x-x*x*x/3+0.325)\n",
    "plt.plot(x, (x+0.7)/0.8)\n",
    "plt.xlabel(\"membrane potential, V\")\n",
    "plt.ylabel(\"recovery variable, W\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 1.4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vd = lambda v, w: v-v*v*v/3-w\n",
    "wd = lambda v, w: 0.08*(v+0.7-0.8*w)\n",
    "\n",
    "u = np.array([-2., -0.])\n",
    "dt = 0.1\n",
    "\n",
    "# I_threshold = 0.325\n",
    "#I = lambda: 0.32\n",
    "I = lambda: 0.31 + 0.1 * np.random.randn()\n",
    "\n",
    "x = np.linspace(-2.5, 2.5)\n",
    "plt.plot(x, x-x*x*x/3+I())\n",
    "plt.plot(x, (x+0.7)/0.8)\n",
    "plt.xlabel(\"membrane potential, V\")\n",
    "plt.ylabel(\"recovery variable, W\")\n",
    "\n",
    "result = [u.copy()]\n",
    "for _ in range(10000):\n",
    "    u += dt * np.asarray([vd(*u)+I(), wd(*u)])\n",
    "    result.append(u.copy())\n",
    "\n",
    "result = np.asarray(result)\n",
    "plt.scatter(*result.T, s=2., alpha=0.3, c='g')\n",
    "plt.xlim([-2.2, 2])\n",
    "plt.ylim([-0.5, 1.4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3a01518588>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uS3fJBxvOP/98nnvuOSIR5QXYsmULO3bs4NRTT91vaZbUzFPTLwyUhyzKVsTgKcEAVcEqehLFWOwqG+sqlJ+yS/bRNMKJJ5qIEjBmH4aCFYTjYWTAj9ATX4pc7CmaiBIwXDHlgQp29e2GQCBv2YTjYYKGmtaW17GqY/WgGphSRCwZI2Dofb3RU+2gh8mR6pxyemAaoKLCQuyg8jeQfTVONfZh1DXDiOrzGI1BOAqVw5Narn7+apbtWjakz5w9bjb3nH1P1uv19fWceOKJPP/885x33nk89thjXHjhhft1H9aSsthjiRh+oRRKE3ufiCkLIocVkRo8BQJ+qgJVdMd7wJvfVx5NRPELpeA1mtjpL2jG63CGsrAVEYeCatwh6kd90wB6I+bzhKDC6rPP44oJx8PKYvd5qSvTFnvA9bFboHRQ6X1VRS1gjBHFE2qyXA65gEdZ+qYrRmpiz9+TChh6X1Zu+NiFIeM2uhmwumP2txsGStBi9wnDKjS6h30ei7KVlznL6Wga6YGAn3J/Ob3R3oK6/FZrqaxMKXjYa1gu0ZgioRGIWCKmXCdCEDLWtw97kwRB5UkR35WUSRIyoSz2oF/52KO96hn7sq+ZL6UkEo8oYg/4qQvVsTe8l2TAhyc6sJ5DKcJqPYdMHTQIPRLJqvdWOdNil0VEK2kjSlvsorBG4WAil2W9P/Hxj3+ca6+9lrfffpv+/n6OP/74/ZpeaVnsyZRbpEz7/YRhqedYcEpb7EERgICfoC+oQsEK6PLHkjH8RmMSNCzbiEfmTXO4w7SwA37KNLH7NFkUV3F1wxkwGs4Kf4Xa6SekBt+yhZTGkjEkkpD0KblABRJJxC8H3HMoRcSSMUWyQhAKqnDdsCe/3tuIvVxZ+r3JcEGD03ZiN+oarsWeDZWVlSxYsIDLLrtsv1vrUGrErl0xQlCmQ7C0FZFHwQGl5AE/QW9QbTBRQJff7JL6fQT8ak/PqO4HjXRiNyxsvVdpvyaLSHHfZeZv0psi9mgvlAWN5znnsd7RJ2g0MHqA0Mxfl0AAiysm6CdolFVEW+x59D5ouGLKyhU598b6lG+9UGK3NPx98X53YDsHLrroIpYvX86nP/3p/Z5WSblizEiOgJ+AT5FGTCTB68m5IqA5eGooatAXpKevRxG7nvbucW4DVWOiCDDoVfdEvUll9fQXvtXYcEOK2AOEEooswsRUPoSLs5RTxO4xLe9IIkIi6FNe/P4IlIUy5CJxVWahpA/8LrFnQyQeISj8EAgQ8ikLPEwsr96b5Oz34fF4lQsy1gu1+XuqkXiEAGWm6xIwxk3cge1s+MQnPnHAts4sLYtdu0Ws1l0ypkgjB8mmLHZfpsUOOV0PagKNPc1IIgqhwIheXtYk9kDKYg/rPCmy4pr5S8piB+j15XYXaIs9JPwQ8GUSuzuAChgDzEYemWUVjxSk9wHhN6NfAt6AKqtQ/jK2uuo0sffHBhcS62LoUFrEnsgk2Vgiprr8hbhitEvFG1DWonYV9OWrHD4IBNSEDf28stDId8WgLPYyvxp8U5OUiu9qW5eHtRJBr4woqzIL+ZiuGIN8TGInoeRcAgEgkogQxA9+i9ss3l+Q3usyAbVstaovIdVo5ogkM+clBPymfvTF+vKOm7g4MCgtYnewnpUFklvZTOIJqs2azcHTCiOaIMeOSLGEMVXearHrRqE/PCJDHqWUqYE1i8XeH+uH8pBq6Ir4rvQxjIqAYbHH+3KSj95IO+QJOvfCcjS4hxKUK8YHAZ8Zl24aNHn03kbsXr8KJDD1Po9BY+i9z+PD7/ErYq8oU7oxzIyaA+UCGSoM9n2HhNiFEGcLIdYKITYIIb4zFM8cCJwsdpOgpcyqqDoqJmBEtZiuGL+h9Dn2Po3FoyoSxynNRHJEumMSMoFEGgNyAUv3PgwV5cqSK8JatvWILK6YvlifCsXLkr+mK8YTcM7fAvakPRQQiYfNiC49QU8RdHlOvbe6U8Cw2JMxqDDGO3Lkr2r4VWMCUO43ZifrRmEYlU0oFKKjo2PEkLuUko6ODkKhzHGnQjHowVMhhBe4DzgDaAHeEkL8UUr53mCfXSwisTDVngAElRUBBgnofUt7+hz3MNWDdP6gysigN2ieUxZqDgWPR6gVZaZvHgxL05qmw8DgcEa6hW0ndqPi9hjd7gE8z7TYo71Q0QCtnY77bJqumGzEvrtDhTzmmCF5KCAcCxMMKleMzWLPo/fReIRKi4/d77W4YoTIT+xCpQlQ5i8zGur8jcKBRlNTEy0tLbS1jZzNtkOhEE1NTQOWH4qomBOBDVLKTQBCiMeA84ADTuzdkX1M8I4Hvx8hRGowqDykojl6nJWtP67O64kWQV/QdANQUQY727NOhoklovhFlTPxgEqzYYg/dD/DZmEH/ZT5LD72SotFNrquyOf5bA1gNBGFagv51NmnwJtRMZ6AOfZhymmi6u0/5Ik9Eo8QKgtCwIfXmFMRT8aVK8bjUXnrgGg8QkBUZFrsQqg6k4vY49pVl7LY+2J9Kr3yEPQ6p3kw4Pf7mTp16sF+jQOKoXDFTAC2WX63GOeGHttb4b2NWS93R7qp9JapAT6UokYTUaWoFWXQ0+so1xtVsx917LvZIABUVSgfZZZGoS/WR7k3BAE/Xo8Xr/AqWY9HpdntnOZwhknEvgB4vfYBOa9XEUZ34RXXfJ5fWYJej4V8rFZlGkxXTLAcjIbafJ6153CII5KIEPT4TYPG5/GlCLqiLAexR81IMLBY7KD0vrs361hKNGm32G11prJc6ccIcX2UIoaC2J3mdGeUqBDiS0KIJUKIJQPuEsVi0LYn62h9T6yXKl+FGaZoU7bqStjX6ziQ1BvpodwTQhhyPo+PRNJIo0ZN3GBft2OavdE+Krwh03IxI2oAairVlPkRFiFgEnFAkafNFQPqu/Z2F1xxbYPTYLrJEjKhSCXod2wATVeMMfaRCieNKLmyIHQ5l8uhBEXsAZvlrfcYoLpCkayDDvbF+syBaSDVIIAq43jC0T+vB9eDFovdK7yqPLVsNDYix5dKBUNB7C3ARMvvJmBH+k1SygellHOllHMbGgbom6hUvtlsFkh3rIdKb7npq7URe22VIqJ9mQTS199NhbdMxe+SUlIppToXDMBe5zVNeuO9lPsrlCULqYganWYiOTytSimzEnPKUlb5nUnsVarSF+hHTRG7ImhN7Cb51FQpgk57HzMqJo3Ybfm7t+eQtwwjiahyb/mUDtos79oqReoOet8V6aLWV2mSs71BUL1XJ73Xg+sB4QefQeweb6YxlKXOuNj/GApifws4TAgxVQgRAD4N/HEInpuJaoPYHay0aCJKLBmjqqza9IX7vRZFrTUUtWtfhmxveJ8idmOxJO0qSErDyqmtgj37nK39eD8VxkqSkG71GOf3ZKZ5UNHTB2+8C0vfc+z9dPSoHlV9tVoC1hbHDio/oGBrWRN0IGTkr9UPDMq3HotnNBThmPqtF7bSER8pYq9W7+9AWgVhVzv86101eDtCEU/GiSaj5i5GYPGVQ0oH0/ReSsneaDe1gRqTnG0NQplhye/Zm5FmqkcXMuuazWIvDynjarjp/SGEQRO7lDIOfBV4AVgNPCGlXDXY5zoi4Fe+v46ujEvdYaVElcZiRqCULS4N8vD5lBXStifDwuvt26f85MaEJE08pqI21CkLNU1Roz3dxGWcikp7mqblEvCrxqi188BZlft6YEdrdvdPIgGrNqrZtL39amA4De1tasikvq4RUEQhECqOHVQ0TEWZyssC0NXbAUBtleqpma4YnU960LTdXq7hiCLsYKVaeTDDYh9lNOJtOYg5W77v64F1W1XY5vqteTeWGK7Y26/yrKZilHnO5/GlGk2/s973xfqIyzi15Sk5W4MghBoc79yX0finu9Yy0hQC6mtVPXU33TgoGJI4dinln6WUh0spp0sp/3sonpkVo2uVzzDN99fdsROAqtrR5jmbsgGMGaXkrJZhLKZcMcHKlPVhWOw24vF5Myy73q1bAKiwpOn1WCwXgLGjVZpFDDZmhY5JzkbaO9rgnTWwvhne25RJalIqMgtH4LgjlC+0ZVfG89p3bQVg9NjJAAhjwNP2XQ11ihwLmIjSsUeVTf0o1VBkuGKCAdUL2N1he+dIt2pIQ7Uq+iaD2H0+GFWjSCs9T6SEDdvgH0thxXr7uuTxBKzepBre445Qv7ftyvsdA0I8Ae17sjccPX3wxgpYtgbixTcu+1q3A1BTO8Y8Z7O8AcbWK72xuAS7jF5ZbfXo7HKja1W+pjW4Pf3Kii83dl2CNFcMqLqWSGYaYYkEbN0JO9ucG92k4boczuNSieSAyupAYuTNPB03WhFwWkXsaW4GoLIupeC2QVCAMXUqWmXrztS55l30xvtsSppBPB6Pqhxte1JE1ttPxzYVoVNXlRozsHVJdZpeL2zdnlLk9j3Kat64LVXhtR90b7cig3Ts61Wuk7dWwlurMv32uzuU5TmqBqY0qgq1NW2oY1eHapymNCoinTReWe5Wq71zL+17FFmMrkrlpa0nApZysOSlRlqF7ejciU94qRo9Tj3Lk+aKARjfoBocbX1LSXiPsvRDtWoDkwxLH6CxQQ3U7eqwp792C2zfrb6zcy+ssTR067eqGZlHTVPXx4xSEVdOywBLqQZ2t+5QeZpORj19KlJr/Va7sSGl+pa3Vqqyfmd15to2fWF4d50KCtjb49wY9/TBms0qjZ1tdt1IJtm7eQMANfXjzNM2yxtUI+zxQMtu81TXti0A1NY3ZperrVI9s+adNqJt374JgNGjU3HWGXpfW6V6wNt2p76pP6wMjy3blYHx7jq7Rd/Tp/Jp6Xvw9urMMZz2LtUIvrUy81o8roynQnpe8USKmKVUetfRlZoXoRGOqF66Piel0pPXl8GiZeo7rOXVF1buSWuj1Nuvnu1Up/cjRt7qjgE/TBijlLSmUhHu9la6O5XSVpXZCdpGHn4/TBoHW3Yo+bIQtOym1xNnbFnKT57higGYOE5ZxBuaYfJ4WLOZzTHVuEypnZKSTbdcfD6YMh42tiiySSZVAxHwQ3tMKdOYUUpp9WxOnxcax6RmzO7tUZU66IepE5SrZdkamD5RWbs9fbB5u6pMR083VpaMqAbM51M9jv6wIh9N6KDO11bBpm3q2RVlsHYLHbIHn8dHdbDa/l3W/AgGFKlub1WumbH16hu271aVa1SNSicao2PvTkYFahGGLzej4QRFPtvKVW/D54PuXsL9avBNr9TpKFdXrVwNm1ugrgqSUjWYe/bB5EZVVttb1bk1m1W+68atxvBLT2lUZbJmM0xrUmXU26/ytXOfPbqjshzGjlK607ZHlZ/Xo9Ld0aa+o6YKdrcroqksU7qzZYcqs6kTUtFSG1vUM4+fqX6v3QLL1yn99nmhtUM1WF6PypO2Peo7xtYrN0nLLvZ2q0a5piw1p8BcGsA84VPP3LZLlYsQdG1VRklt3Vi7nNViF0K978oNSu9nTIJIjI4t6wGor09FNWfovRAq/9dsVu9cWa56UAI45jCl6+u2KqKf0qhIccsO9d2Tx6u8fHs1NI1V+bWjFTr2Kl2LxpTcjInqubs61HVNstUV0DBK/e41djPzeFIzprVx5vcp69tKxEKkxnyskVp64lVfONWD37pT1c0x9aoR165ajydzPNDrUcZLQ50ayzMGuvcXRh6xg1KE7l5VEdZuAaAtqEhxVFkWX6PGpPGqwm00Qu8ry+iUPRwRsvjJ010xoIhsWpOS69wLPi9b6lQlmFqXmvyQYbkATBgL0biqWEIoxZ3cqJRu/VZFPNWV6vlej7Kgm9Ms4cYGVcl8PlWxV6xXFUOjvlZZoHp54cMnKwXeaJliUB6CmdNTE62EUDIr1iurEsDrpb0iSX1ZvW1PxgyLHdT7RmOqUdmsrHyqKhSxtXaarqvOZA/1lalejS3cUUMI9W7vrlPvA0RCHoLeoPkejsQuBBw5BZauVj0ZKVUezpikyAzU/0RCEQeo/NONGyiSnjFJlcVSy7w6r0eVy6RxKZ/xjrYUIXs86tmTG1W6LbsVwbTtUdbqYZNUZRZCkdN7mxTRmekG4egZqlw0cWzYlpqrIYQitknjFRF096r0d7ar/0LQ1aDkaoL4OAewAAAgAElEQVR2gyajrCaNU8RjpL/Xp+pLrUXvMyx2UN/dNFZ92+4OkNAeUeU6usLeU82QHTNKEd/2VvW7slyVsV5cLxhQLjGte/W1cMRkZYCNb1CNia4HHo/StwljlM6t2mjWfUCV6agaZcC0dqb0PuBX6SQNcq8sV0Ts9SiS9hoTqirUXAlaOxQZezyqvlWWqwa+q1s13oePVb1VgNp2ZVB0datGYkqjek7XPtVQJ5Kq7GoqVd617FZ/sw6D+lR57Q+MTGL3euHYw1Vm9UegooytmxcDmdZzBrELoazanW0QjZNsHM32v2ynqcrerQQyCbpprGqJe/uhvpbN/3wSn8dHY1WqO+sRnlQ0jTXNaU2qcoEZhUBlOcw5KnNWa32tUt5YHDxCKbq1hQ8G4ISZ6j0SCUCo97I+w+OB2UcoMggbO8/X12ZaCgG/um93p+qejqmn/Q9djC4fbbstw2LXaRw1Deo71fvWVSurXwiYNgFa1YBdx+YY9QHLOER6VIxGWRDmzlQEKgTh/pAZaglZiB0UMZ8wU40XBAxSsM5G1dbjuNGqspWHyEBjgxqM3der8ryiXIW6WvN0fIP66wur760st+fntCbVaMfiqoysslUVcOIsVeF7w+odairt94wbrSy6vrB6RmW5/TuqK9Xf9Cb1nlUVtK54G4AxFXYXZAbJ+nww50hl9XoEXS1r4K0CGgRQPcO6atMi7fCVw0qoL683b/F6vKmoKWu+Hz45RcY1lfZ9DUbVwEnHKj32elK6Ayr/jp6hLOzefntehIJw/FGq0QhHVK/TurzFpPFKzusxJ1AVDG1pW6F7n+lobFANSjiSmuULamzC6RlTJ6hvqcpc3mGoMTKJHVQmjk9ZDFuWbaXcX05Dud0yzCABUMrTqCpCa88uookoE2sm2uQAZyXXlQvY3LWZidUTzfvBoUtqhS9Ldjvt2xnwk3OqvBCO639k3FNdCWmb1ceTcds74/UqJTXQ3teeSexOFrtOY2x95nm/37SYO8KdtgY3K0HrdxljbAoe3ktVsKowubIgHDY587wVafu07u7ZzdjKlCuCULCw9W+sFrbT+3uzdLOFUL2Zmirn61q+yoFcrPD7VSMN7O5VLkgrsdvi0a3weFTDAXRtUiRttdiz1hdQxDRKNQLtLWpAtL4sVe45ZSvKUjOF0+HzplxiTggGnPfXFcIIu3XISyEKXsdo0NANUiEoVL+GACNv8DQLNndtZnLNZJv7wOfxZVqZaXhp00sAHFF/hHnOcXDPAYuaFzGpZpLtnKMrZhjhmTXP4P8vP4f972FZ7/ln8z9t+QhZLPYC0dHXkUECkKXhtGB953pmjJqRIZevXArB69teZ9xd4zjvsfMG/ayDiea9zTSUN5h7AUAekjXQFTbCJEM5xqSyoKOvg+pgtbngGAx/vT/UUDLE/s6ud2y+bihMUd/a/hYAcxvnmueyumIsSCQTbNu3jQaLnxHyWOzDABc8eQEAGzo3sG3vtozr+lxnvz20M6vFXgA6+u3EXmjDuXjbYqbWpsp0qIj9vjfv45SHTwHg7Z1vD+pZBxubuzY76r1tENQBHX0dlPnKbK4ur3BwXTqgvd+hRzfM9f5QQ0kQeywRY0vXFt5rsy8oWQixL9q2iAVTFlBniSpwHDxNwwkPngBgrnxoyh4ky0VKyc7unSxqXpT1njsX32nzvT649MGMez722McAuOHUG2znHccOCkB/rJ9wPJwxqA25CfpvW/4GKOIqRq6Q9/nqX75q/t4bzpxZeaAgpeTLz32ZN7e/OWD5lza9lKGnthnXWXD3v+42VzXVKNRi/+2K37JpzybbOddiH14oCWLXVteFR19oO5/PAtnTv4elO5cyf+L8DDnIbbEv370cgOvmX2eXPUiWS8WtFTTe3cipj5zKT976Scb13mgv33rxWwCcOf1MvMKLzFyrjWW7lgFw1oyzbOcH6orp6Ffx5daBNseomDRo4vjpR35qnvMIpa75yCeRTDDuznGIhYL73rzPdu3d3e+ax0fUH0F3tDs1o/YA4zsvfYcHlj7ASQ+dNKBNIHQenTjhRNv5QgnaNs5SoJx+z7EVY23nC9X7v2/5O3ctvivr9aFws7koEWJ/fNXjAHx61qdt5/Mp6qV/uBSApmr7gvb5LENrJZw1Zpbtmld4c1q20USUG1++McPVkQ+d/Z1ZrfHuSLfN+krvuQD8ZcNfzOPf/PtvqC+vp63Xvsqm/j2haoJtUA0GbpE9seoJIDNqA3JX4uW7llPhr+Dw+sPNc7YlaXPg4XceNgcVrdY5wP+88T8A/Okzf+Ib874BpBqfocbLm15GLBSsaV/jeP32xbebx39a/6ein/+D134AwOeO+5ztfL48Wr5LGSXf/cB3M+TylfHOnp0Dln1y1ZMs+OUCvvniN9m+b3vG9SuevQL/f/mz5tejKx7lmTXP5Exjf0MsFJz+q9MP6jsUgpIg9pWtK5k1Zhazx822nc8avmXgj2vVWmX/cex/2M7nc8Xs6Fbx0PeefW/GNY/w5FTwK5+7kltfu5X62+2RJHMfnMuSHUscZap+UEX97fWc+sipiIWZETTVt6mwl7mNczl27LEZ3WRQJAPQd0Mfo8tHUxuqZW/E7ob46RJlHT983sMZ8oVYZG9ufzOjUl7/8vUAHDv2WPNcIcR+75v30hvrNa10q2wuOSklX3ruS7ZzVov8sZWPAXDW9LNMP3F7X+Z6OYWgL9aHWCgQCwUdffbGQUrJh3/9YQCOuu+oDFndM9LQg/hW/N+7/8fYO8ciFgpHi/7n7/wcgJkNM23n8+XRI8seAeDkppOLkgO4f8n9gL08IX/v+GdLf8YFT11g/v5Xy79s13+74rc8+LZyDabnl5SSM399Jp95+jN84vFPZDQKr297nZWtK3O+91BAGz6vbH5FbSpiQSwRyxjXeHXzq4iFYsCutsFgxBN7JB7htebXOG3KaRnXcimqtbJXBuzhVvlcMQt+uQCA48cfn3EtFwE2723m4WUp0tSV9fZFt7N051Le97P3Ocr1RO3Ln1q/aVdPammFFz/7IjMbZrK6fXXGMx5Z9ghnTj/TXKmxNlRrRkZo3PS3mwA4ddKpmd9VgMV+0kMncdR9R9l6Anpdl2l108xzHuFBILKWjX6v9zVm5kc+8tHfAPDV9ylr3dqD0e4nr8ebl9jvX3K/SdzrO9bbri3ftZyKW1NhiXpMAOChtx/C83171TLX6Dcw54E5APzg9B/g9/gp99tDV3/+9s/57O8/S2uvmtzz9Oqnbdc3dqpJPXPGzbGFhEKOcEcDazvWcuToIzlz+pm284UQ+3/9478AmD8pzX2Zp+FPb2xf3fKqedwf6+fipy+2Xbc2ZBf97iJe3PSi+fuWf9xiHrf2tnLKw6dwzE+P4an3nsr57qB6vm29bRm96h3dO2z17OnVTyMWCv6yPtXTHXNnqtfZeFdq7sr1L11P4JYAgVsC7OxOTSw87VeKkx5+J9NQ2t8Y8cT+lw1/oT/ez2lTiyN27SO/+8y7M67ls9g3dKr1OY4bd1ymbA4CvPSZS22/tfXz7Ze+bZ7TvQiNVa2ZC2X+aV2q2/7bFb8F4POzP09tqJYZdTNo3tucWigL2NK1hUgiYi6iBWpiitVityp6OslA/op78kMp60+7P1a3qQbmnBnnZNyfq2z0GEF6dz+f3K6eXSbxfO8D3+PCWWrMRVvpmgz1mEo2Yv/Kn76CWCi48k9XmucO//Hh5vcAzH7A3jvc3p2yIr/47BfN49tOvw2wDwLvi6RWCf32/G8zpmIMu3tS67gAXP7s5bbf5z95vu33r5b/CoB7z8nsNeaKitnatZXnNzxvLoGcLpeL2Jv3NpvH6T2pXHpvHaBOfE/dY3VFWt2Ewti3Z0vXFvOcdrWaz7Ckc+rDKSPkU09+yjx+fsPziIWCsXeO5dXNr3LX4rv43DOfo/72esbcOYYbXr6BXy//tdlwT7h7AlU/UA3k2va1fPKJTwJw7m/PBTKNK2vduW3RbeZx492K8K35/8DSBxxyZf9ixBP7Jx7/BAAfmPyBjGuOM08N/HPrPwH42BEfy7iWa3Bv6Y6l5nG6pa/TzEaALfvUVPTXv/A6AFf9+SpbCw9w3mPnsap1Fe+1vYdYKJj1U+XDv+mDN7H+a8pq1I0SwLPrngXgf85WvuNpddNIyqSta/rqZmUdff3Er5vn0i127Qq45uRrHN89V8W9Y9EdvLH9DfP3E6ueICmTZoP1vQ9+L0MmF4n8fevfAThl4ikZ13JZo+PvSs0OXPihhcyfOJ+QL2QS6SubXwHgnrPvAZyJXSwU/GRJ5uAzwNUvXA1gc3WFfCGqg9Ws2L0CSIXPAkyqmWQaHNpFJaWk5jYVO37tydcihKCpuonmfYo0l+9azhf+8AXzGS9+NmWpXviUaqhWt63m+//4PuDcu8qVt7qncMHRF2Rc83l8JGUy6xjRwr8tBOCxTz6WcS1XOOyqNmWcPHvRs2aD8OjKR83rOjqr7VttLLpMjSNp/dWW+7ymecibJHPGzTHr0a3/vJX1nfaelHZVnvMbZUy09rZy2q9O45svftNsDAF+uOiHXPLMJRnv+vbOtznyviNt5zZ0bjBJ//6P3M+Vc1MNfrpLBmBdxzoCt9gnVXX2d7KqdRVioXAMMx5qjGhiP+LHqUlF1nBFjVwDOtolYnURaGSd8g7M/ZmKd3/2omcdn5uNAKWUphJafZu6hb98TspCm/XTWRz9k6Nt8tfNv47pddMBNYHo3d3vIhYK0wWgu+N6JmXLvhaSMolYKLjsj5cB2Ho16cR+1v+pKBir0tq+K0eDdd1L12Wcm/PAHLPROWnCSY7Py0Y+nf2dHDbqMFskjUYh7oLYd5W1JIRg9rjZbNijeljaHXDCeBWqWldWh0CYxP771b/PeNbWq7ey+5vKmv7rxr9y0kMnMf1eVQ4LFyyk/8Z+zplxDg+98xBioeDEh1SEyo/P+TFbr95qDv6u71jPm9vftDU+35qvopQm1kw0BzRnPzDb1M35E+fz4WkfNsvtiVVPsKZ9DTN/onzqE6utG5elkC3cMZFMsCes1tC/4f03ZFzPNXFsR/cO8710T8iKXFFT8x9WPSStvxpLdizhwaUP8sLGFwDV0M4aMwuv8Jp+ae3S0r3oI0YfwZr2NSoI4ZUbATi8/nBbz9tpHCofPnGkMhB1GDOoIAPANpnvirlX8M6udwA1GFx5qzLu7jrzLm7/sBoMt/LSVXOvMs9pI83aQ9lfGLHEnpRJ1nWsA2DxZYsd78lFAl7hZVrdtIwZllBYHPu5h53r/NwsBKitUI10F9D9/3Y/ye9lsZQWLKTcX26+60ubXuK4+1NuoLpQqlHTfv/mvc14v2+f2q6/C2Bc5Thae1uJJ+M218Bh9c4zUvNF+wDImyRPfupJwB5W6JTH2Qa2b190O0t2LMmwxKxyTmWqu+7f/cB3bWF80+um8/bOt20DbtZFxerK6kxi//cn/t2855vzvsn3F3yfSTWTbBE91oGwG9+viOXI0XYLD+DLc78MqJmdtaFa1nas5aSHTjKjdV6+5GXGVaq1g6oCVbT1tfHChhdsz/jH5/8BqAgeDevAYvM1zTjBJ5yjYnRPb8aoGRmuFMg9qD3h7tz702crT+ug8vRRithv/uDNAJz/xPlc8dwVAEyuUctBVAWrOKHxBG755y02gtak2VDewOauzQRvSc20XfvVtVwz7xrbJEOAS467hI7rUum3f6udlVeu5K//8Vfz3L7v7EPeJE0S13jlklf4zDGfsZ37x6WqPO46U4VrXvDUBeaYzeXHX8418zJ7u3eceYdK29Ir/OLxX8y4b6gxYoldD7Z87wPfY97EeY73+IQzCby1/S1Wta3KiF835bIo+J5+Ze2cPeNsx4oB2SfyfOiXHwJg5ZWqi/mRwz9iu+71eBFC2KzqyP+LIG+SNleG1U8OsP5r69n5jZQ7Z0zFGLzCmxEZs/RLS22/m6qbSMok6zvWm66Bz8/+vOM36e9Kt8iklPzPv5QL6PpTVfTL+TPPN60fgN9fmGkFgzNBSylN982D/5Y5eSqbHMAlv1fd6vTIqNbeVrrCXTT9SIW0fvbYz9qujy4fTVtfG//vlf9nnot/N84dZ97Bdz+Y8vEvmLLAJrfuq+vMhvJLJ9gHBu//yP22RnT2uNlmBAsoN4i1nD84+YMAnP2bs81z1cFqU8dCvlBGo69lnJAtj7Q1+peLnS3GbHqvXTAAz1/8vKNstqiY0Xcod9d1p1xn6q7W5617U6uTrrhyRUombVbr9xd836zj6aHJX3nfV8zjt774lu3aLz/+S0aVjULeJJE3SerL6zl6zNGcMf0MwjeGkTdJs6ergwpAEfiHpqr62vYtFQiw+LLFvH/y+wHnHmh1sBqfx0fLNS38+1H/zoorVyBvkpT7y6nwpwbZjx9/vKOhM9QYkYuAxZNxc0AsvcJZ4aTg4XjY7C47+ce0HGT62K978TrzGdng5IpZvC3Vozh6jHKxHF5/OFNrp7K5azOPnPeIef33F/6emttqWDBlQQaJA/Tf2G9a4jXBGttaKpAi4B/960cAXH3S1fzo7B9lPEdXEN2tB9VryPpdDj2RFza+YPqdrVby4+c/bvoYncYw9P3pZWON5f7iCc5WTbYG4Z/Naszk40d+3Hbts8d+1hZRkR7KuatnlxlrD3bCtuLVz73Kvsg+qgJVGRWzsaoReZPkD2v+wGvNr3HF3Cts16fXTTddZq9+7tUMUk5vjBZftjgjnFAIgbxJ0h/r59GVj2bErlvh5IqxDqanu0Q0shH7zX+/GYAzpp2RMXFNI98Etts+nBpgTM+/x89/3BbZs3DBQv68/s8A3HfufVz1vqvMa9ecfI3Z+H9g8gf48bk/tj1L3iTpjfZSEci9kJp1bR2NVVet4uVNL5sEDqqRkTfZQ03T9cN6fUL1BH53we9s13tu6OGORXdw9Jijs/b0hxojktgfWJIaZdYtqxOc/LjWRZ8eOz9zEAiyK3hXRPmkX/iPFzJkrGmmE6D2MVqtC4BN/5kZb14drM5QJCs8wsOkmkk0721m+ZeXZ71P4xunfMPxfLp/dmzFWMeGRMOpwbLGXt+84Gbz2O/15/wGcCbojz76UQC2XZN9cMlJTr+Hk4vh4mMvNgfJxleOz5htqcdTNLK5ogDbxiNOOO/I8zjvyMxFxX744R+aFruTIXJUQ8q9sv3a7bZloNNR5i/jsjmX5XwPp6gYHcn160/8OqvF6KT32sVV5ivjr5/9q5OYKZuth3vLh27JSLP/xn5m3DuDa+ddmzGQO7dxblb98Xv9fPKoT/K71b/j5UtedrwnH6lnw8yGmRlzArKh69td+Dy+gtPS4ykHCiOS2HU4Xde3Mze1tsLJ7/fXjUo53/riWxmV3CoHZFSOp957ikk1k4omQI3/Ped/c75vodh69dac1584/wlzMkh611XDen5sxVi2X5s5E9AKpwbrrteVrzEfiTvB5/GlNhrHPp6R7Z1NuTQCOfP/VDz2E+c/kXG/R3hIfi/J9m5nwrzv3Pv4zNPKl3rRrIuK+4gCUV9enzOPAt4APzn3J8xsmJmT1AuFUx5pC1j7srPJgZ3Yp/6PWmAsvQfhJJuuHyc9pFwW1lBQjZAvRMu1LTmfmQ1PXZA/Xn1/w7oq5nDEiCN2q/86X+amK7h1UlL6QIsVOsbXKnv8A2pQ0inE0Yp0AtRp1oXqDohvDeBTR38KeXRusrUuGXDihBMd3Q9WpO+Qk8sdVQjSy+b2RWpw7JYP3ZJNxFHud++lur1zxs9xlNEhhU6wrrNy6+m35n/x/YQr3+ccjTQQpOeRlNJcJ8i674CTHDgPnj594dMZ53KlCZgD4FY3jIsDgxE3eKqnYlsXh8qGdGV78j0VsfHQRx/KKwd2BdchTj//2M8dZTTSLXY9IPbQx3KneaBhbWT+eNEfc9ypkN5g3fCyCpdzmuBVCNLL5oZX1PMuP/7ybCKOcnriTs/1PdlEckKHu545/UzbZiAjGelb3N3zr3vM41zfmK73j69UE4MunX1p3p6Ez+NDIk0d+eFrPzSv5XNhuRh6jDiLXfurnSZmpCN9pP5zz6gBp3MOy5wJaUW6gusQsxMnnJixvkY6rBsCxxIx/rFVhUg5TaA62Eh8L2HO9MuH9AZLD85eclzmJI9Cn6fz1zqwZ9vRyAFWYrfOhByoX1UPSpYSrBONPMLDtX+9FkhNjMslBym915Oqrj7p6rxpWnu5Xo/XnG1537n35RJzsZ8w4ohduwDSV1V0gp6gJKW0kVIh1gdkKviPzsqMLkmH1VrSs+dOn3p6RgjXcEC2kE0nWC323mhq93anSUSFwErQv1j2C0Ctm1KM3OR78myFd4jCOtEoTsqwyWeUpOu9joZxWjojl2w8GjeXULBGtLg4cBhRxK4tuy8d/6U8dypoZUvKJPN+ruJg7zzjzoLlYsmYzafvNMU9HX5PymLXVkuuMMKRAmt8vo5eueese3KJ5IR1sE27yC6dfWlBcum+XL3+iAsFvWVdLBlj9v0qlHJek/NcDyus5KyXiM43aJouG0vGzAic9KWfXRw4jCgfu7acc4U4WmFVVL0k7qeO/lQukQy5H72urPRrT762oDT9XmWxSylNYndatmCkQRNqJB4xV+bTsysH87ykTJrhinomZiFyeg2RykBlUT2PQwFW/dUDmIWM8Vi3LLzodypC6L9P+++C0tSNSTwZN3362WaEu9j/GFE1Qq+Dnr6BdDZoBbeuJFeIrFVJn9+oZto5TRd2QsAbIJqI2tbbLgXi0S4mvaBTVaDKcZJHodAErcPwipGLJWNmXHj6rlkuUnpvdZkVEp+t5aKJKNv2qbkE/3b4vxWVZjwZ5zcr1PR8vYSAiwOPEcU4emnT9G25skFbIL9+99cA/OyjPytIzqqke/r3cPrU03PGVluhXTE6imbdV9cVJDfcEfQFicQjPLpCrcr3h0//YVDP08SuN9de8kXnTUayyemlcQfTayhV6IHM215TYYaFWt1a7/Wg9DFjjik4TS2re1/l/vKc8z1c7F+MKGLX278VGgGhlU1PQc61FoqT3Oq21SzduZTDRmWfjZgO7Yr5wh/V0qul4IYBCHqDRBIR7nxdjVFkW5+nUGiC1mXqtGlJLjmNXPMRDlVo/b33TbVWe/oOYfnk9OQ2pxUgs0E3Jl9+TjW0T1+QO+7dxf7FyCJ2Y7JPyBcq6P6M6eN5JuGky92/tPhBz/QNDApNc7gj4A2YrjAovAyywefxmStA3nDqDQVP3vJ5fAdkG7SRDKveN1Y1Fu261CjUDWOV7Y0p90+2NWVcHBgMitiFEHcIIdYIId4VQvxeCLFfh8F1qGOZryzPnQpWRT264egcd2aXA7jvI4XH4mr/PMB/nvSfBcsNdwS9KX/6QGPXrfB6vHRHu4HCBrQ1rGXz90v/nuPOQxfWPDp3RuGLTqXrfb5Z1tlknZYxdnFgMViL/UVglpTyWGAdcP3gXyk7dLe9UN+dVdnuPqvwGZJWuctmX1bU4Kf13Q7mFPWhhnWgdDBhjhrWPE5f3bBQueE46Ws4wGpcfP9D3y9Yzpq3z1z4TFFpWmWvOOGKHHe6OBAYFLFLKf8qpbmS07+AwkYYB4hwPEzIFyq4225due+MaWcUnI6VyAuJXbdCu2K8wuu4d2gpwGm3qmLhtJdrIdAbFpRSb2ioYSXZ8VXjc9yZXS7bcsvZYG1MvnriV4uSdTH0GEof+2XAft3zqT/WX7AbBtRa2xoDXYCrkEkzVmj3Qq61qUci9KYIevebwWLjHrWx9L1nZ27GnAs63PKjh390SN6jFNHa2zogOb3MLhRfX2qCqQX5sq2a6uLAIS+xCyFeEkKsdPg7z3LPjUAc+E2O53xJCLFECLGkra1tQC97ctPJOTcYSMfFx6pdlh4///E8d2biwqMv5Nvzv1304KdexCrXmu0jEV8/8eucNvW0rOu7FwvdXf/8nMIilTRuO/02ynxlg47KKWVoF9WyK5bludMOvavTj8/5cZ47M6GXK3j0k4/mudPFgYDQM/gG/AAhPgd8GThdSum8JVEa5s6dK5csKSxu2YULFy5cKAghlkop88b4DorYhRBnA3cDH5RSFmyGCyHagNy7RWTHaKA9712lBfebDw2433xoYDDfPFlK2ZDvpsES+wYgCOitwP8lpdyvUwGFEEsKabFKCe43Hxpwv/nQwIH45kGNckgpZ+S/y4ULFy5cHEiMqJmnLly4cOEiP0YisT94sF/gIMD95kMD7jcfGtjv3zzoqBgXLly4cDG8MBItdhcuXLhwkQMjitiFEGcLIdYKITYIIb5zsN9noBBCTBRCvCqEWC2EWCWE+E/j/CghxItCiPXG/zrjvBBC3Gt897tCiOMtz/qccf96Y07BsIYQwiuEeEcI8Zzxe6oQ4g3j/R8XQgSM80Hj9wbj+hTLM643zq8VQgzrZQSFELVCiKeMxfJWCyHmlXo5CyGuMfR6pRDiUSFEqNTKWQjxsBCiVQix0nJuyMpVCHGCEGKFIXOvEEVOBZZSjog/wAtsBKYBAWA5MPNgv9cAv2U8cLxxXIVaQG0mcDvwHeP8d4AfGsfnopZrEMDJwBvG+VHAJuN/nXFcd7C/L8+3Xwv8FnjO+P0E8Gnj+H7gSuP4KuB+4/jTwOPG8Uyj7IPAVEMnvAf7u3J87y+By43jAFBbyuUMTAA2A2WW8r201MoZ+ABwPLDScm7IyhV4E5hnyPwFOKeo9zvYGVRERs4DXrD8vh64/mC/1xB92x+AM4C1wHjj3HhgrXH8AHCR5f61xvWLgAcs5233Dbc/1CJxLwOnAc8ZStsO+NLLGHgBmGcc+4z7RHq5W+8bbn9AtUFyIu18yZazQezbDLLyGeV8VimWMzAljdiHpFyNa2ss5233FfI3klwxWmE0WoxzIxpG13MO8KAsK9EAAASySURBVAYwVkq5E8D4P8a4Ldu3j7Q8uQe4Dkgav+uBLplaIdT6/ua3Gdf3GvePpG+eBrQBjxjup4eEEBWUcDlLKbcDdwLNwE5UuS2ltMtZY6jKdYJxnH6+YIwkYnfyMY3okB4hRCXwO+BqKeW+XLc6nJM5zg87CCH+DWiVUi61nna4Vea5NmK+GWWBHg/8VEo5B+hFddGzYcR/s+FXPg/lPmkEKoBzHG4tpXLOh2K/cdDfPpKIvQWYaPndBOzIcu+whxDCjyL130gp9QaRu4UQ443r4wG9/mq2bx9JeTIf+JgQYgvwGModcw9QK4TQM6Ct729+m3G9BuhkZH1zC9AipXzD+P0UiuhLuZw/DGyWUrZJKWPA08AplHY5awxVubZg39ui6G8fScT+FnCYMboeQA20/PEgv9OAYIxw/xxYLaW0bu30R0CPjH8O5XvX5y8xRtdPBvYaXb0XgDOFEHWGpXSmcW7YQUp5vZSySUo5BVV2r0gpLwZeBc43bkv/Zp0X5xv3S+P8p41oiqnAYaiBpmEHKeUuYJsQ4gjj1OnAe5RwOaNcMCcLIcoNPdffXLLlbMGQlKtxrVsIcbKRh5dYnlUYDvYARJGDFeeiIkg2Ajce7PcZxHeciupavQssM/7ORfkWXwbWG/9HGfcL4D7ju1cAcy3PugzYYPx9/mB/W4Hfv4BUVMw0VIXdADwJBI3zIeP3BuP6NIv8jUZerKXIaIGD8K2zgSVGWT+Din4o6XIGFgJrgJXAr1GRLSVVzsCjqDGEGMrC/sJQlisw18i/jcCPSRuAz/fnzjx14cKFixLDSHLFuHDhwoWLAuASuwsXLlyUGFxid+HChYsSg0vsLly4cFFicIndhQsXLkoMLrG7GJEwVk28yvK7UQjx1H5Os16oVTl7hBA/TrvmuBqfEOJSIUTj/nwvFy7S4RK7i5GKWtTKgABIKXdIKc/Pcf9QIAx8F/imw7WfAl9CTaQ5DDjbOH8pamq9CxcHDIPazNqFi4OI24DpQohlwIuoCSDPSSlnCSEuBT6OWup5FnAXasnczwIR4FwpZacQYroh1wD0AV+UUq7JlqCUshd4TQhh28TdmD5eLaV83fj9K+DjxoJfc4HfCCH6UasT9g9ZDrhwkQWuxe5ipOI7wEYp5Wwp5bccrs8CPgOcCPw30CfVQlyvo6Zog9p78mtSyhNQVvhPBvgujqvxSSmfQs06vdh4T5fUXRwQuBa7i1LFq1LKbtSaG3uBZ43zK4BjjZU1TwGetGxOExxgWqW0EqGLEoBL7C5KFRHLcdLyO4nSew9qjfDZQ5DWoFfjc+FiKOG6YlyMVHSjthUcEKRa/36zEOJTYO5LeZxx/AkhxA+KeFau1fgG9Z4uXAwELrG7GJGQUnYAi4TaMPmOAT7mYuALQojlwCrUBhEA0wHHjU+M9eTvBi4VQrQIIWYal64EHkKt0rcRtU8lwC+A+4UQy4QQZQN8TxcuioK7uqMLF2kQQvwfcI2Usu1gv4sLFwOBS+wuXLhwUWJwXTEuXLhwUWJwid2FCxcuSgwusbtw4cJFicEldhcuXLgoMbjE7sKFCxclBpfYXbhw4aLE4BK7CxcuXJQY/j/VOpU6eO22zQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x108 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 1.5))\n",
    "plt.plot(result.T[1], 'pink')\n",
    "plt.plot(result.T[0], 'g')\n",
    "plt.ylim([-2.1, 2.1])\n",
    "plt.xlabel(\"time, 10t\")\n",
    "plt.legend([\"W\", \"V\"], loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 2.5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vd = lambda v, w: v-v*v*v/3-w\n",
    "wd = lambda v, w: 0.08*(v+0.7-0.8*w)\n",
    "\n",
    "u = np.array([-2., -0.])\n",
    "dt = 0.1\n",
    "\n",
    "# I_threshold = 0.325\n",
    "I = lambda: 1.5\n",
    "#I = lambda: 0.3 + 0.1 * np.random.randn()\n",
    "\n",
    "x = np.linspace(-2.5, 2.5)\n",
    "plt.plot(x, x-x*x*x/3+I())\n",
    "plt.plot(x, (x+0.7)/0.8)\n",
    "plt.xlabel(\"membrane potential, V\")\n",
    "plt.ylabel(\"recovery variable, W\")\n",
    "\n",
    "result = [u.copy()]\n",
    "for _ in range(10000):\n",
    "    u += dt * np.asarray([vd(*u)+I(), wd(*u)])\n",
    "    result.append(u.copy())\n",
    "\n",
    "result = np.asarray(result)\n",
    "plt.scatter(*result.T, s=2., alpha=0.3, c='g')\n",
    "plt.xlim([-2.2, 2.5])\n",
    "plt.ylim([-0.5, 2.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3a01450f60>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x108 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 1.5))\n",
    "plt.plot(result.T[1], 'pink')\n",
    "plt.plot(result.T[0], 'g')\n",
    "plt.ylim([-2.1, 2.5])\n",
    "plt.xlabel(\"time, 10t\")\n",
    "plt.legend([\"W\", \"V\"], loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7f3a0149db38>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I_threshold = 0.325\n",
    "I = lambda: 0.2\n",
    "\n",
    "vd = lambda v, w: v-v*v*v/3-w\n",
    "wd = lambda v, w: 0.08*(v+0.7-0.8*w)\n",
    "\n",
    "num_x = 1000\n",
    "x, dx = np.linspace(0, 2, num_x, endpoint=False, retstep=True)\n",
    "\n",
    "v = -1.0 * np.ones_like(x)\n",
    "w = -0.5 * np.ones_like(x)\n",
    "\n",
    "dt = 0.3\n",
    "result_v = [v.copy()]\n",
    "result_w = [w.copy()]\n",
    "\n",
    "sigma = 0.03\n",
    "m = int(1 + 2 * sigma/dx)\n",
    "xk = np.arange(-m, m+1, 1) * dx / sigma\n",
    "kernel = np.exp(-xk*xk)\n",
    "kernel /= kernel.sum()\n",
    "\n",
    "for frame in range(60):\n",
    "    for _ in range(5):\n",
    "        vp = np.pad(v, (m, m), 'constant', constant_values=(0.5, -1.0))\n",
    "        v = np.convolve(vp, kernel, 'valid')\n",
    "        v_ = v + dt * (vd(v, w) + I())\n",
    "        w_ = w + dt * (wd(v, w))\n",
    "        v, w = (v_, w_)\n",
    "    result_v.append(v.copy())\n",
    "    result_w.append(w.copy())\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 3))\n",
    "ax.set_ylim([-2, 2])\n",
    "ax.set_xlim([0, 2])\n",
    "lv, lw = ax.plot([], [], [], [], animated=True)\n",
    "ax.legend(['v', 'w'], loc='lower right')\n",
    "\n",
    "def update(frame):\n",
    "    lv.set_data(x, result_v[frame])\n",
    "    lw.set_data(x, result_w[frame])\n",
    "    return (lv, lw)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, update, frames=len(result_v), interval=100)\n",
    "plt.close()\n",
    "\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "anim.save(\"fitz-wave.gif\", writer=animation.ImageMagickWriter(fps=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7f3a013d12e8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I_threshold = 0.325\n",
    "I = lambda: 0.36\n",
    "\n",
    "vd = lambda v, w: v-v*v*v/3-w\n",
    "wd = lambda v, w: 0.08*(v+0.7-0.8*w)\n",
    "\n",
    "num_x = 1000\n",
    "x, dx = np.linspace(0, 2, num_x, endpoint=False, retstep=True)\n",
    "\n",
    "v = np.cos(np.pi*x)\n",
    "w = -0.5 * np.ones_like(x)\n",
    "\n",
    "dt = 0.1\n",
    "result_v = [v.copy()]\n",
    "result_w = [w.copy()]\n",
    "\n",
    "def gen_kernel(sigma=0.03):\n",
    "    m = int(1 + 2 * sigma/dx)\n",
    "    xk = np.arange(-m, m+1, 1) * dx / sigma\n",
    "    kernel = np.exp(-xk*xk)\n",
    "    kernel /= kernel.sum()\n",
    "    return kernel\n",
    "\n",
    "def defuse(u, kernel, pad_val=(0., 0.)):\n",
    "    m = int(len(kernel)/2)\n",
    "    up = np.pad(u, (len(kernel)-m-1, m), 'constant', constant_values=pad_val)\n",
    "    return np.convolve(up, kernel, 'valid')\n",
    "\n",
    "kernel_v = gen_kernel(0.005)\n",
    "kernel_w = gen_kernel(0.02)\n",
    "\n",
    "for frame in range(100):\n",
    "    for _ in range(15):\n",
    "        v = defuse(v, kernel_v, (1.5, -1.0))\n",
    "        w = defuse(w, kernel_w, (-0.5, 1.0))\n",
    "        v_ = v + dt * (vd(v, w) + I())\n",
    "        w_ = w + dt * (wd(v, w))\n",
    "        v, w = (v_, w_)\n",
    "    result_v.append(v.copy())\n",
    "    result_w.append(w.copy())\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 3))\n",
    "ax.set_ylim([-2, 2])\n",
    "ax.set_xlim([0, 2])\n",
    "lv, lw = ax.plot([], [], [], [], animated=True)\n",
    "ax.legend(['v', 'w'], loc='lower right')\n",
    "\n",
    "def update(frame):\n",
    "    lv.set_data(x, result_v[frame])\n",
    "    lw.set_data(x, result_w[frame])\n",
    "    return (lv, lw)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, update, frames=len(result_v), interval=100)\n",
    "plt.close()\n",
    "\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "anim.save(\"fitz-patt.gif\", writer=animation.ImageMagickWriter(fps=10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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