{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "input.good:checked + label {color: green}\n",
       "input.bad:checked + label {color: red}\n",
       "input.good:checked + label::after {color: green; content: ' Õige vastus!'}\n",
       "input.bad:checked + label::after {color: red; content: ' Vale vastus!'}\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<style type=\"text/css\">\n",
    "input.good:checked + label {color: green}\n",
    "input.bad:checked + label {color: red}\n",
    "input.good:checked + label::after {color: green; content: ' Õige vastus!'}\n",
    "input.bad:checked + label::after {color: red; content: ' Vale vastus!'}\n",
    "</style>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mittelineaarse süsteemi püsipunktid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See tööleht näitab, kuidas ja millisel juhul saab uurida mittelineaarse süsteemi püsipunktide stabiilsust lineariseermise abil."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Süsteemi lineariseerimine püsipunkti ümbruses\n",
    "\n",
    "Kui on antud üldine (mittelineaarne) n-mõõtmeline dünaamiline süsteem $\\underline{\\dot{x}} = f(\\underline{x})$, see tähendab funktsioonid\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\dot{x}_1 &=& f_1(x_1, \\ldots, x_n)\\\\\n",
    "\\vdots &=& \\vdots\\\\\n",
    "\\dot{x}_n &=& f_n(x_1, \\ldots, x_n)\n",
    "\\end{eqnarray}\n",
    "\n",
    "ja püsipunkt $\\underline{x}_*$, kus kehtib $f(\\underline{x}_*) = (0, \\ldots, 0)$, siis saab püsipunkti stabiilsust uurida lineariseermise abil. Selleks vaatame funktsiooni $f$ Taylori arengut püsipunkti ümbruses:\n",
    "\n",
    "$$\\begin{split}\n",
    "\\dot{x}_i &= f_i(\\underline{x})\\\\\n",
    "&= \\underbrace{f_i(\\underline{x}_*)}_{= 0} + \\sum_{j = 1}^{n}\\left.\\frac{\\partial f_i}{\\partial x_j}\\right|_{\\underline{x}_*}(x_j - x_{*j}) + \\ldots\\\\\n",
    "&= \\left[\\underline{\\underline{J}}(\\underline{x}_*) \\cdot (\\underline{x} - \\underline{x}_*)\\right]_i + \\ldots\n",
    "\\end{split}$$\n",
    "\n",
    "Maatriks $\\underline{\\underline{J}}(\\underline{x}_*) = \\left(\\left.\\frac{\\partial f_i}{\\partial x_j}\\right|_{\\underline{x}_*}\\right)_{ij}$ on **Jacobi maatriks**. Süsteem, millest on kõik liikmed peale lineaarse liikme ära jäetud, on **lineariseeritud süsteem püsipunkti ümbruses**. Seost mittelineaarse ja lineariseeritud süsteemi vahel kirjeldab **Hartman-Grobmani teoreem**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hartman-Grobmani teoreem\n",
    "\n",
    "Mittelineaarse süsteemi püsipunktide uurida aitab **Hartman-Grobmani teoreem**:\n",
    "\n",
    "Kui on antud üldine (mittelineaarne) $N$-mõõtmeline dünaamiline süsteem $\\underline{\\dot{x}} = f(\\underline{x})$ ja hüperboolne püsipunkt $\\underline{x}_*$ (see tähendab, et kõikide Jacobi maatriksi $\\underline{\\underline{J}}$ omaväärtuste reaalosad on nullist erinevad), siis on olemas püsipunkti ümbrus $U \\ni \\underline{x}_*$, hulk $V \\subset \\mathbb{R}^n$ ja homöomorfism $\\phi: U \\to V$, niiet kehtib\n",
    "\n",
    "* $\\phi(\\underline{x}_*) = (0, \\ldots, 0)$\n",
    "* $(d\\phi \\circ f)(\\underline{x}) = \\underline{\\underline{J}} \\cdot \\phi(\\underline{x})$\n",
    "\n",
    "kui $\\underline{x} \\in U$.\n",
    "\n",
    "Hartman-Grobmani teoreemist järeldub, et hüperboolse püsipunkti stabiilsust määrab ainult Jacobi maatriks selles punktis, täpsemalt tema omaväärstuste reaalosad.\n",
    "\n",
    "Kui Jacobi maatriksil on ka omaväärtus, mille reaalosa on null (ehk püsipunkt ei ole hüperboolne), siis tuleb ka kõrgemaid liikmeid Taylori arengust arvesse võtta, ja ainult Jacobi maatriksist ei piisa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interaktiivne näide: süsteemi lineariseerimine püsipunkti ümbruses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Me rakendame üleval selgitatud teooriat praktilisele näitele. Sümboolseks arvutamiseks kasutame SymPy, numbriliseks arvutamiseks NumPy ja joonistamiseks PyPlot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "from sympy.interactive.printing import init_printing\n",
    "init_printing(use_unicode=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Süsteemi definitsioon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kõigepealt defineerime oma dünaamilist süsteemi. Siin valime kahemõõtmelist süsteemi, mille faasiruum on $Q = \\mathbb{R}^2$, ja muutujad tähistame $x$ ja $y$-ga. Dünaamikaks valime\n",
    "\n",
    "$$f(x, y) = \\begin{pmatrix}\n",
    "(x - 1)(x + 1)\\\\\n",
    "xy\n",
    "\\end{pmatrix}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAI8AAAAyBAMAAACXGZULAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n58GKoLzApiYJmtjfrEn98fsHf06qXcscrz0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\left(x - 1\\right) \\left(x + 1\\right)\\\\x y\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡(x - 1)⋅(x + 1)⎤\n",
       "⎢               ⎥\n",
       "⎣      x⋅y      ⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y = sp.symbols('x y', real=True)\n",
    "f = sp.Matrix([(x + 1) * (x - 1), x * y])\n",
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Faasiportree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Järgmisena joonistame faasiportreet. Selleks konverteerime funktsiooni NumPy funktsioonideks, et neid oleks lihtsam joonistada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fx, fy = [sp.lambdify((x, y), ff, 'numpy') for ff in f]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Joonistamiseks kasutame quiver ja streamplot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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5k/zwnXdSZ36HD0PbTOWDffs4LpDFee9ejtu3z+JEdDisyrx++sng3H//Rfzj1SACLF9u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x9eTG7dUwxMzTr5/I+OCDzL+t3imLGAkJsljrZfZ54gTzVVfxiRsa8pVI8e4CPW6c2PNMgjEX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd7ef780cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_aspect('equal', 'box')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "\n",
    "X = np.linspace(-1.9, 1.9, 101)\n",
    "Y = np.linspace(-1.9, 1.9, 101)\n",
    "XX, YY = np.meshgrid(X, Y)\n",
    "DX = fx(XX, YY)\n",
    "DY = fy(XX, YY)\n",
    "ax.streamplot(XX, YY, DX, DY, color='b')\n",
    "\n",
    "X = np.linspace(-1.8, 1.8, 21)\n",
    "Y = np.linspace(-1.8, 1.8, 21)\n",
    "XX, YY = np.meshgrid(X, Y)\n",
    "DX = fx(XX, YY)\n",
    "DY = fy(XX, YY)\n",
    "ax.quiver(XX, YY, DX, DY, color='r')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Püsipunktid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Püsipunktide leidmiseks lahendame süsteemi $f(x_*, y_*) = 0$. Esimene tingimus $(x_* - 1)(x_* + 1) = 0$ näitab, et $x_*$ peab olema kas $x_* = 1$ või $x_* = -1$. Teisest tingimusest siis järeldub et $y_* = 0$. Seega on püsipunktid (1, 0) ja (-1, 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fp1 = [(x, 1), (y, 0)]\n",
    "fp2 = [(x, -1), (y, 0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kontrollime, et püsipunktides tõepoolest kehtib $f(x_*, y_*) = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAyBAMAAACqpzYoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhCZZs3dIrur\nRHbLQ9+lAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAg0lEQVQoFWOQ//+JAQT0/39kEHZxBbNDXAwZ\nRMAsEOEIZoepq8DZzQyRC6Di7AIMTA1QNvcBBuavUDb/AQbez1B2fAID7z8oe70CAwvQQrCZ6xMQ\nbGQ1QL3MML3cGxjYYWYC7WKD2cUwmSHQAWoOQ9C7IwwwNpAx4OyRFFbIaQYpLQEA+F9EPf/QavQA\nAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\\\0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0⎤\n",
       "⎢ ⎥\n",
       "⎣0⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(fp1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAyBAMAAACqpzYoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhCZZs3dIrur\nRHbLQ9+lAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAg0lEQVQoFWOQ//+JAQT0/39kEHZxBbNDXAwZ\nRMAsEOEIZoepq8DZzQyRC6Di7AIMTA1QNvcBBuavUDb/AQbez1B2fAID7z8oe70CAwvQQrCZ6xMQ\nbGQ1QL3MML3cGxjYYWYC7WKD2cUwmSHQAWoOQ9C7IwwwNpAx4OyRFFbIaQYpLQEA+F9EPf/QavQA\nAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\\\0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0⎤\n",
       "⎢ ⎥\n",
       "⎣0⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(fp2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jacobi maatriks ja püsipunktide stabiilsus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lõpuks arvutame Jacobi maatriksi teatud valemi järgi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAAyBAMAAAD1mnskAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nbZs28hVK+GY2GowM8LP5/Zf1AYeybE/lTtsrAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2 x & 0\\\\y & x\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⋅x  0⎤\n",
       "⎢      ⎥\n",
       "⎣ y   x⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J = f.jacobian([x, y])\n",
    "J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Püsipunkt $(x_*, y_*) = (1, 0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esimese püsipunkti juures on Jordani maatriks selline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAyBAMAAAAOzY77AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2 & 0\\\\0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  1⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J1 = J.subs(fp1)\n",
    "J1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Omaväärtused on positiivsed, nende kordsus on 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHwAAAAVBAMAAAB2y5cfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZpkQ3Ynvq81UMrtE\ndiLw+n06AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABXUlEQVQ4EWNgYGBUZCALLLoM0sbsSpZmoKZj\nC4AE4weitD/S3oWujqkBKMKaABKeZgAioYAzGcaC08wFDPEH4DwGsApWB6AASDtzUT2SdnP1zwiF\nUBa7AQMbUCEUQFSALYbYfh9JOwMvpnY2Bwb2XzDdDBAVJGjn+EyMdnewBVhsB4qzgN2EpAJsO3sD\nSAvE8cwZIDY2xwNFzwcACWQV4DibtgAoCtUOYgEBdtsh9iKraGJgWJ0FFiAUdAwMTAoQnWASYgG7\nLzTtEGH7JSTdUPe1A4WQ/Q5Vgc3xnAoM7xAGgFWA/c7qABIl6PhFDAz30LRjxDtSuNo3IBQDWXyu\noeoOQBpJBSS5g81Qz28XACkHhy5T2Y9CBhZnEB8OOP7//+8A4iFUIGmHK0Mw5iGYOFhIjsdUAUok\n+AFYO478znwBv16gLFMDSEkriMAAjBgiGALHDoCEOMkt64IZGAC9SljmepOSnAAAAABJRU5ErkJg\ngg==\n",
      "text/latex": [
       "$$\\left \\{ 1 : 1, \\quad 2 : 1\\right \\}$$"
      ],
      "text/plain": [
       "{1: 1, 2: 1}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J1.eigenvals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tulemus näitab, et püsipunkt $(x_*, y_*) = (1, 0)$ on **ebastabiilne sõlm**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Püsipunkt $(x_*, y_*) = (-1, 0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Teise püsipunkti juures on Jordani maatriks selline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFYAAAAyBAMAAAA0HTGIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-2 & 0\\\\0 & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-2  0 ⎤\n",
       "⎢      ⎥\n",
       "⎣0   -1⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J2 = J.subs(fp2)\n",
    "J2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Omaväärtused on negatiivsed, nende kordsus on 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAVBAMAAACu6/FQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nH6oGDAwAWMpZb+GgE+oAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ -2 : 1, \\quad -1 : 1\\right \\}$$"
      ],
      "text/plain": [
       "{-2: 1, -1: 1}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J2.eigenvals()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tulemus näitab, et püsipunkt $(x_*, y_*) = (-1, 0)$ on **stabiilne sõlm**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Küsimused"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polünoomse süsteemi püsipunktid\n",
    "\n",
    "Uurige süsteemi $(x, y) \\in Q = \\mathbb{R}^2$, mille dünaamika on\n",
    "\n",
    "$$\\begin{pmatrix}\n",
    "\\dot{x}\\\\\n",
    "\\dot{y}\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "x^2 - y^2\\\\\n",
    "x^2 + y^2 - 1\n",
    "\\end{pmatrix}.$$\n",
    "\n",
    "### Sadulad\n",
    "\n",
    "Mitu sadulat on süsteemil?\n",
    "\n",
    "* <input id=\"sad0\" name=\"sad\" class=\"bad\" type=\"radio\"><label for=\"sad0\">0</label>\n",
    "* <input id=\"sad1\" name=\"sad\" class=\"bad\" type=\"radio\"><label for=\"sad1\">1</label>\n",
    "* <input id=\"sad2\" name=\"sad\" class=\"good\" type=\"radio\"><label for=\"sad2\">2</label>\n",
    "* <input id=\"sad3\" name=\"sad\" class=\"bad\" type=\"radio\"><label for=\"sad3\">3</label>\n",
    "* <input id=\"sad4\" name=\"sad\" class=\"bad\" type=\"radio\"><label for=\"sad4\">4</label>\n",
    "\n",
    "### Atraktor\n",
    "\n",
    "Kus asub süsteemi atraktor?\n",
    "\n",
    "* <input id=\"atrA\" name=\"atr\" class=\"bad\" type=\"radio\"><label for=\"atrA\">(0, 0)</label>\n",
    "* <input id=\"atrB\" name=\"atr\" class=\"bad\" type=\"radio\"><label for=\"atrB\">(1, 1)</label>\n",
    "* <input id=\"atrC\" name=\"atr\" class=\"bad\" type=\"radio\"><label for=\"atrC\">(1, -1)</label>\n",
    "* <input id=\"atrD\" name=\"atr\" class=\"bad\" type=\"radio\"><label for=\"atrD\">(-1, 1)</label>\n",
    "* <input id=\"atrE\" name=\"atr\" class=\"good\" type=\"radio\"><label for=\"atrE\">(-1, -1)</label>\n",
    "* <input id=\"atrF\" name=\"atr\" class=\"bad\" type=\"radio\"><label for=\"atrF\">Atraktorit ei ole.</label>\n",
    "\n",
    "### Repeller\n",
    "\n",
    "Kus asub süsteemi repeller?\n",
    "\n",
    "* <input id=\"repA\" name=\"rep\" class=\"bad\" type=\"radio\"><label for=\"repA\">(0, 0)</label>\n",
    "* <input id=\"repB\" name=\"rep\" class=\"good\" type=\"radio\"><label for=\"repB\">(1, 1)</label>\n",
    "* <input id=\"repC\" name=\"rep\" class=\"bad\" type=\"radio\"><label for=\"repC\">(1, -1)</label>\n",
    "* <input id=\"repD\" name=\"rep\" class=\"bad\" type=\"radio\"><label for=\"repD\">(-1, 1)</label>\n",
    "* <input id=\"repE\" name=\"rep\" class=\"bad\" type=\"radio\"><label for=\"repE\">(-1, -1)</label>\n",
    "* <input id=\"repF\" name=\"rep\" class=\"bad\" type=\"radio\"><label for=\"repF\">Repellerit ei ole.</label>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Kompleksne dünaamika\n",
    "\n",
    "Uurige süsteemi $z \\in Q = \\mathbb{C}$, mille dünaamika on\n",
    "\n",
    "$$\\dot{z} = (z^2 + 1)e^z.$$\n",
    "\n",
    "### Püsipunktide arv\n",
    "\n",
    "Mitu püsipunkti on süsteemil?\n",
    "\n",
    "* <input id=\"fp0\" name=\"fp\" class=\"bad\" type=\"radio\"><label for=\"fp0\">0</label>\n",
    "* <input id=\"fp1\" name=\"fp\" class=\"bad\" type=\"radio\"><label for=\"fp1\">1</label>\n",
    "* <input id=\"fp2\" name=\"fp\" class=\"good\" type=\"radio\"><label for=\"fp2\">2</label>\n",
    "* <input id=\"fp3\" name=\"fp\" class=\"bad\" type=\"radio\"><label for=\"fp3\">3</label>\n",
    "* <input id=\"fp4\" name=\"fp\" class=\"bad\" type=\"radio\"><label for=\"fp4\">4</label>\n",
    "\n",
    "### Püsipunktide reaalosad\n",
    "\n",
    "Mis on püsipunktide reaalosad $\\Re z_*$?\n",
    "\n",
    "* <input id=\"reA\" name=\"re\" class=\"bad\" type=\"radio\"><label for=\"reA\">-1</label>\n",
    "* <input id=\"reB\" name=\"re\" class=\"good\" type=\"radio\"><label for=\"reB\">0</label>\n",
    "* <input id=\"reC\" name=\"re\" class=\"bad\" type=\"radio\"><label for=\"reC\">1</label>\n",
    "\n",
    "### Püsipunktide stabiilsus\n",
    "\n",
    "Millised on püsipunktide tüübid?\n",
    "\n",
    "* <input id=\"stA\" name=\"st\" class=\"good\" type=\"radio\"><label for=\"stA\">Kõik püsipunktid on atraktorid.</label>\n",
    "* <input id=\"stB\" name=\"st\" class=\"bad\" type=\"radio\"><label for=\"stB\">Kõik püsipunktid on repellerid.</label>\n",
    "* <input id=\"stC\" name=\"st\" class=\"bad\" type=\"radio\"><label for=\"stC\">Kõik püsipunktid on sadulad.</label>\n",
    "* <input id=\"stD\" name=\"st\" class=\"bad\" type=\"radio\"><label for=\"stD\">Süsteemil on atraktorid ja repellerid.</label>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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