TP4_Portrait_de_phase_III.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# INFO-F-305 - TP 4\n",
    "# Dessin qualitiatif - Portrait de phase III\n",
    "### Jacopo De Stefani - __[jdestefa@ulb.ac.be](mailto:jdestefa@ulb.ac.be)__\n",
    "### Github: https://github.com/jdestefani/ulb-infof305\n",
    "### Slides: https://jdestefani.github.io/ulb-infof305"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Project\n",
    "\n",
    "- Analyse des systèmes ODE (ordre 1-2) avec Octave\n",
    "- Simulation des systèmes et comparaison avec des données réelles\n",
    "- 2 x Séances TP en salle machine + Travail personnel\n",
    "- Durée: Environ 4 semaines\n",
    "- A remettre: Jupyter Notebook/Rapport LaTeX sur UV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "function trace_det_condition(A)\n",
    "    printf(\"Tr(A) = %d\\n\",trace(A));\n",
    "    printf(\"det(A) = %d\\n\",det(A));\n",
    "    printf(\"Tr(A) > 4*det(A)? = %d\\n\",(trace(A) > 4*det(A)));\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Fuction to avoid repetition of phase portrait code\n",
    "function portrait_phase(A)\n",
    "    # Define grid for plotting\n",
    "    x1range=-1.5:.1:1.5;\n",
    "    x2range=-1.5:.1:1.5;\n",
    "    [x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "    x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "    x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "    #Normalize values for plotting\n",
    "    arrow=sqrt(x1p.^2+x2p.^2);\n",
    "    # Vector field plot\n",
    "    hold on;\n",
    "    quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "    # Trajectory plot\n",
    "    sys_str = sprintf('[%d*x(1)+%d*x(2);%d*x(1)+%d*x(2)]',A(1,1),A(1,2),A(2,1),A(2,2))\n",
    "    sys_ode = inline(sys_str,'t','x')\n",
    "    for x_0=0:0.1:1\n",
    "        [ts,ys] = ode45(sys_ode,[0,10],[0;x_0]);\n",
    "        plot(ys(:,1),ys(:,2))\n",
    "    end\n",
    "grid on;\n",
    "axis tight;\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "  -2  -7\n",
      "   1  -3\n",
      "\n",
      "Tr(A) = -5\n",
      "det(A) = 13\n",
      "Tr(A) > 4*det(A)? = 0\n",
      "sys_str = [-2*x(1)+-7*x(2);1*x(1)+-3*x(2)]\n",
      "sys_ode = f(t, x) = [-2*x(1)+-7*x(2);1*x(1)+-3*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAJNmlDQ1BkZWZhdWx0X3JnYi5pY2MAAHiclZFnUJSHFobP933bCwvssnRYepMqZQHpvUmvogJL7yxLEbEhYgQiiog0RZCggAGjUiRWRLEQFBSxoFkkCCgxGEVUUPLDOxPn3vHHfX49884755yZA0ARBQBARQFSUgV8Pxd7TkhoGAe+IZKXmW7n4+MJ3+X9KCAAAPdWfb/zXSjRMZk8AFgGgHxeOl8AgOQCgGaOIF0AgBwFAFZUUroAADkLACx+SGgYAHIDAFhxX30cAFhRX30eAFj8AD8HABQHQKLFfeNR3/h/9gIAKNvxBQmxMbkc/7RYQU4kP4aT6ediz3FzcOD48NNiE5Jjvjn4/yp/B0FMrgAAwCEtfRM/IS5ewPmfoUYGhobw7y/e+gICAAh78L//AwDf9NIaAbgLANi+f7OoaoDuXQBSj//NVI8CMAoBuu7wsvjZXzMcAAAeKMAAFkiDAqiAJuiCEZiBJdiCE7iDNwRAKGwAHsRDCvAhB/JhBxRBCeyDg1AD9dAELdAOp6EbzsMVuA634S6MwhMQwhS8gnl4D0sIghAROsJEpBFFRA3RQYwQLmKNOCGeiB8SikQgcUgqkoXkIzuREqQcqUEakBbkF+QccgW5iQwjj5AJZBb5G/mEYigNZaHyqDqqj3JRO9QDDUDXo3FoBpqHFqJ70Sq0ET2JdqFX0NvoKCpEX6ELGGBUjI0pYboYF3PAvLEwLBbjY1uxYqwSa8TasV5sALuHCbE57COOgGPiODhdnCXOFReI4+EycFtxpbga3AlcF64fdw83gZvHfcHT8XJ4HbwF3g0fgo/D5+CL8JX4Znwn/hp+FD+Ff08gENgEDYIZwZUQSkgkbCaUEg4TOgiXCcOEScICkUiUJuoQrYjexEiigFhErCaeJF4ijhCniB9IVJIiyYjkTAojpZIKSJWkVtJF0ghpmrREFiWrkS3I3uRo8iZyGbmJ3Eu+Q54iL1HEKBoUK0oAJZGyg1JFaadco4xT3lKpVGWqOdWXmkDdTq2inqLeoE5QP9LEado0B1o4LYu2l3acdpn2iPaWTqer023pYXQBfS+9hX6V/oz+QYQpoifiJhItsk2kVqRLZETkNYPMUGPYMTYw8hiVjDOMO4w5UbKouqiDaKToVtFa0XOiY6ILYkwxQzFvsRSxUrFWsZtiM+JEcXVxJ/Fo8ULxY+JXxSeZGFOF6cDkMXcym5jXmFMsAkuD5cZKZJWwfmYNseYlxCWMJYIkciVqJS5ICNkYW53txk5ml7FPsx+wP0nKS9pJxkjukWyXHJFclJKVspWKkSqW6pAalfokzZF2kk6S3i/dLf1UBiejLeMrkyNzROaazJwsS9ZSlidbLHta9rEcKqct5ye3We6Y3KDcgryCvIt8uny1/FX5OQW2gq1CokKFwkWFWUWmorVigmKF4iXFlxwJjh0nmVPF6efMK8kpuSplKTUoDSktKWsoByoXKHcoP1WhqHBVYlUqVPpU5lUVVb1U81XbVB+rkdW4avFqh9QG1BbVNdSD1Xerd6vPaEhpuGnkabRpjGvSNW00MzQbNe9rEbS4Wklah7XuaqPaJtrx2rXad3RQHVOdBJ3DOsOr8KvMV6Wualw1pkvTtdPN1m3TndBj63nqFeh1673WV9UP09+vP6D/xcDEINmgyeCJobihu2GBYa/h30baRjyjWqP7q+mrnVdvW92z+o2xjnGM8RHjhyZMEy+T3SZ9Jp9NzUz5pu2ms2aqZhFmdWZjXBbXh1vKvWGON7c332Z+3vyjhamFwOK0xV+WupZJlq2WM2s01sSsaVozaaVsFWnVYCW05lhHWB+1Ftoo2UTaNNo8t1WxjbZttp2207JLtDtp99rewJ5v32m/6GDhsMXhsiPm6OJY7DjkJO4U6FTj9MxZ2TnOuc153sXEZbPLZVe8q4frftcxN3k3nluL27y7mfsW934Pmoe/R43Hc09tT75nrxfq5e51wGt8rdra1LXd3uDt5n3A+6mPhk+Gz6++BF8f31rfF36Gfvl+A/5M/43+rf7vA+wDygKeBGoGZgX2BTGCwoNaghaDHYPLg4Uh+iFbQm6HyoQmhPaEEcOCwprDFtY5rTu4bircJLwo/MF6jfW5629ukNmQvOHCRsbGyI1nIvARwRGtEcuR3pGNkQtRblF1UfM8B94h3qto2+iK6NkYq5jymOlYq9jy2Jk4q7gDcbPxNvGV8XMJDgk1CW8SXRPrExeTvJOOJ60kByd3pJBSIlLOpYqnJqX2pymk5aYNp+ukF6ULMywyDmbM8z34zZlI5vrMHgFLkC4YzNLM2pU1kW2dXZv9ISco50yuWG5q7uAm7U17Nk3nOef9tBm3mbe5L18pf0f+xBa7LQ1bka1RW/u2qWwr3Da13WX7iR2UHUk7fiswKCgveLczeGdvoXzh9sLJXS672opEivhFY7std9f/gPsh4YehPav3VO/5UhxdfKvEoKSyZLmUV3rrR8Mfq35c2Ru7d6jMtOzIPsK+1H0P9tvsP1EuVp5XPnnA60BXBaeiuOLdwY0Hb1YaV9YfohzKOiSs8qzqqVat3le9XBNfM1prX9tRJ1e3p27xcPThkSO2R9rr5etL6j8dTTj6sMGloatRvbHyGOFY9rEXTUFNAz9xf2pplmkuaf58PPW48ITfif4Ws5aWVrnWsja0Latt9mT4ybs/O/7c067b3tDB7ig5BaeyTr38JeKXB6c9Tved4Z5pP6t2tq6T2VnchXRt6prvju8W9oT2DJ9zP9fXa9nb+aver8fPK52vvSBxoewi5WLhxZVLeZcWLqdfnrsSd2Wyb2Pfk6shV+/3+/YPXfO4duO68/WrA3YDl25Y3Th/0+LmuVvcW923TW93DZoMdv5m8lvnkOlQ1x2zOz13ze/2Dq8ZvjhiM3LlnuO96/fd7t8eXTs6/CDwwcOx8DHhw+iHM4+SH715nP146cn2cfx48VPRp5XP5J41/q71e4fQVHhhwnFi8Ln/8yeTvMlXf2T+sTxV+IL+onJacbplxmjm/Kzz7N2X615OvUp/tTRX9KfYn3WvNV+f/cv2r8H5kPmpN/w3K3+XvpV+e/yd8bu+BZ+FZ+9T3i8tFn+Q/nDiI/fjwKfgT9NLOcvE5arPWp97v3h8GV9JWVn5By6ikLxSF1/9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAHXRFWHRTb2Z0d2FyZQBHUEwgR2hvc3RzY3JpcHQgOS4wNmqmDDUAACAASURBVHic7Z1PiB3Xte7XES9gLjwJFHtwg5rL9eCcQTeWM4jIERgcQ0ACCcOVLU3kJzdEfmgSxbS4OARrIHNxuE+NNBNJBxohT4IjcU1r0HBtJxA4J3gSO6gH6kEgtMgkSGA/CIbAO29QUrlUf3attWuvXauqvh/GHJ3+9q69q85Zq/auvb8zWiwWBAAAALTNvrYbAAAAABAhIQEAADACEhIAAAATICEBAAAwARISAAAAEyAhAQAAMAESEgAAABP8j4blt7e3d3Z21tbWsm8eOXJkeXmZiFZWVnJ/AgAAAEpplJBWV1dns9lbb72VffPBgwfLy8ubm5vNGgYAAGBYNJqy29zczGUjItrb2ztw4MDly5fX19e/+uqrJvUDAAAYDuGfIX355ZdLS0vHjx/fv3//6upq8PoBAAD0kqbPkIocO3bs2LFjRDSdTre3t0s1k8lkd3c3eT0ej5MXuydvENF46wLzQNr6pIi2XtSkfuj5RbT1NLwum9U7imS/Vn3SVxXJfsY09NkmKdVPRPfv36/6k4NRQ3PV9fV1IsquXNjY2FhZWZlOp0R06tSp27dvF0tNJpNcc0eXPl1cfaX4fmW7L326uPoKv50eeiLiF/HWM7scrT0R9I4up5eJWX9DfW2RtNqG+qouS+tPu6CkT2UpnPpL9e4uN6/foL60y6L6pee/dT0/YjMJOUKaz+dvvvnmnTt3Ll68ePz48Xv37p05c6a2lF4ozH4Voe+EnoTXN4Ke2HczvdEzv4zZaCWqP4KeU8SaPoe2nlMkeyvjdwgpTUdIVczn86WlpUOHDpX+dTKZ7J68kfS29hbjcUN9vy3G9bU3ktrtYRYJqK+9kbQW3ZrrS6cEsv+0EA3Dhp7g9872QZebE/4ZUkIyZeemOB5sroRepFfKdtpi6IPr/YoAEBathMRB9TvW3cp7oPcrAgAYOK0lpE4nAAAAAMGBlx0AAAATICEBAAAwARISAAAAEyAhAQAAMAESEgAAABMgIQEAADBBm/uQcowufUpPO/fV6y3ZtZGfY16Xu+yn53fZmt0GDa/L3voxR82zh8h+rSzrq7qc/cxwHDSi6ZnWdg498yrz0bIOctMJc1VxavGKa/02Vx2VmZ/aMVdlGvAszJirMiOIBT3HaTRmeyLoaw2iIrenVt/cgKoz1kF89ELnyJ556ND0JLxeBvXEvjuJppcOVphF+qTnFNHW57CgF92NZTVSczJvWhsheZirFvUOzE5l5PQwV229PRH07ntnjWhLkrijAZxGh0CvRkjSrMvX69XcM73esxZVMfRKRQBol26Yq/rd69kJiNaiFaIhAMAgMFeNoQcAAFDLvrYbAAAAABAhIQEAADACEhIAAAATICEBAAAwARISAAAAEyAhBUa6JWhX4mXXD6RdjrZLXA90uRbtvXcGsbY90QLtWweljC5122mUvBzwxlsX6Cp3q7O1Lvvp+V32q59fJJqe2eUO2W3U6jldZtafcyD00zuKhNLXmqvy629FX1XEkdhgrvqUnn/ECHryCuUwV63VS+sPq8/+01tfaxDVsH6Deo65quX2e+hrzVWNt9+tLxX3yjooQS90juyZjQ5NT8LrZVDPFFvWM4tY1nOKWNPn4OgXbN/3rIb/kU41zBvu+A4AbY6QiucxrLmqVJ+8iKyHuWrr7YmgD2iuGj9G+AGn0SHQnxGSY14yVBGPQxhpSTS9UrbTFkMPQC9pecpOFBBVn4ioBghr0SpCNEQABQBIgblqDD0AAIBa9rXdAAAAAIAICQkAAIARkJAAAACYAAkJAACACZCQAAAAmMBWQuqB06h0SxC6HLx+gwzQadRalyOc0qF1WeNT1751UMqo406j5OWA1+ku++lhrtp6e5hFmugdXR6FMEu1pqfqLlfpSw+RfuaL4b6qSVWJwVF/KP1kq+qPnsBcNZieYK5aJivabbVursqP46H0MFdtvT0R9GHNVe0bYlGfrINS9ELnyJ7Z6ND0JLxecfSi8YS2nmyMb7RDubQ9EZrk0QWpXnQ3k9UwZ8P65wDQGXNVMnPX76ev+lwGN1dlFmlRD3NV7/o7ZBECp9Eh0J8RUvqFZN5RmtVrIK3cO3oq3ctri6EHoJd0yVxVqlcdG6kGFGvRzSMaIoACAKTAXDWGHgAAQC372m4AAAAAQISEBAAAwAhISAAAAEyAhAQAAMAESEgAAABMYCshwWk0eP0RsNblCKeo612OcIq63mUPvajLo0ufBmxS6Z8i6INHbCtedkQ0uvTpeOsCf9+vKSOGtIhUL+1yHIc9VT2/y3Hawy/irWd2mVN/9jMQTe8oUqWv6nL2GjHrpzKzUYN6hwVJ8/qrijiySAR9cKcGKwlpBHNVnfrb1Y+imKvy80RbeodBlHZ7sv+MqQ9urmq5swm5Lmu3h4Tnp6G+tEg/E1IahvjRWS+76IXyUZk5aW10blh/u/r0dW2ocuhr69ce3zTXu6NzkNBgTR/Kvk9PT/JLnC0VITrbpz9edmQ1oFib0xM1XpottPUJEe7dOqrnfxismY94mJX0oElNSgEOLZurlk6VOvTS+j30zBxgSm9tbKEtHqAegCHQsrmqdMTQ3bGRasAyGD0RcAEAUrphrirVGwzQAAAA3OxruwEAAAAAERISAAAAI2glpO3t7fX1daXKAQAA9A+VhLS6unrx4kWNmgEAAPQVlYS0ubn51ltvadQMAACgr7S3D2k0Sl+Px+Pkxe7JG5PJhF/J7skb460LgVvW7BAeetUu2zxFprrsoScidLlGL+myT/3yS6B+itrrcrG1cfSOLvs5OGhZByUPkNbW1kr/GspcNY7dnOgQUr12l02dopFJc1VtPdkwV2Xung6ldxtE5XbEu+tvrncUqdpB76Hn2PfFbE9zvcNeQGT2xqfljbEpycd6siXTS+tX1ZOfuSqvyzZDLcdCIhutHn+Iq7s80jcbbUVf1WWP+ikTJkT64AZRWTMRkZ7k/iPa+gjuVsHtBBs2yeZudxMJyWB20dOLQr+qx082GirpySsaijprUE/CaG4hukWIntr64q1P/DbE1Ec4RHwHAK2EVDVZlyUNcPwvvLY+edFRgyJpNhIdwk8vbQ8fs3rm9bIWSnoQPZuUAkZo38vOiD5aS6R3xFK96sjdiNiOXpqHAAAOWnb7JjPDEVHlHuJOV+5RpPcB2u8DBgBw0OYIyU6ANqgHNsGQCAA9OuP2DUC7YEgEgDYmVtkBYBYMiQCIBhISACUgDwEQHyQkAJ4CU3MAtAUSEgBEGBIBYIB9bTfgKR4b9rGRbgbyQHt/knaXPU7R0Lo8uvRpstkr+Y+pF9X/7qNnpE2yppd2WXSVPeqPoBftYhR12V1/8U9m9dLvci1a5qpuOmGu6ncIqR7mqm21x2NIJG3PB88dTl68d/Dr2i4zdyun19S43mGuKq2/+GZb+qqQneiLXXbrpfUb1MNc9Sm9tH6RnqKYk8Jctajnpwqz+ls33yais3/7Inn/vQqLfqllxsjXLq/Teo44sp5TRKrPoaEXfZhTjcetmzcmRkhp2GLm2wjZKJre3eWRSTs+pj4bzbN69w8TKDUmjj7JQ5RJRQm1987Bo1uE6OkO6O4uq36/2iL4cME+PRwhiT5t0jkZaTTX1icvRHpp/dKTKW0PUy+6l6dCQAyrl1buUeSD5w7fKuQhBxbul5vo4xyiYUHQOdpMSN4BVHoIC/poLWEmML9sJAoNemKmvslUA7NI+pSIn4oAAFV0bIREluZn+GJRzX56a3fQ7d7VelwdEchDAGjQstu3aHiEgA7cRHj6mqQi5CEANOiMuSoCOnCAIREAPaD9KTsAvMGQCIA+gYQEOgmGRAD0DyQk0CUwJAKgxyAhgW6AIREAvcdWQvKw3ZRGKGuuDdpd1vZM8jiEn7mq3oJM6ZBI2p6Tv3s0/sWc3544tk/8Ip56obkqv/5affEDINLXOkpU6iu6nDs6p/5o+uJ+x2IRlx7mqll917ORdpetZa+RJXNV6ZDIIy6fOPEiEW29fNDhsJKec2b9cfR8m58qvdtclelUVLU9XFXv6K9bzzRX9a5fQ197cd36HloHRUPPo6iJvt/mqqX6WnNVfv256MbUJ6nojXPXRPXzvSGSPHTixItbLx/k6Pmdzb5Q1YuMMLT1NBizVNGHOdXwP59+evK6+/fDyggp6TA/36re++tVngY4x12VWy+tv1afvIiprzVXZdYvbYzqkCibiop5COaquYK93CYIc9XmtDxCihBwPQK00kDBrzHaetI0V42jryUdEiX/PMsoIqr/5O8eVaWiKjTur2Pq/Yo0LAh6T/tTdn7PLfg1i/SiJkn1JAxzIqQ1a4+NPMQiPUeZGxJx8pC0JSd/94gkeQgA4KD9hETyBKD3qIMv9gvoFlruIdbWB5/D0d5LlOQhQioCIChd+vkJqVi1clMB3UNvBI/PgIMIe4kwJAJAjzYTEmL0kNFIRRgSAdBpTEzZgaERao4OQyIA+gQSEojK6NKndPJG82yEIREA/QMJCUTim73Akwld9d+7ECcVIQ8BEB8kJBCDIHN0qqkIQyIAWsdWQoK5auvtCb48vSjw6/IHzx3mOyyIuiwdEklP0U9/811+Yzzq99Pzi3jq2Ve5tv7cBfXWVxVpon9q/19Zl3NXp9YRI9c7kb64GdGhryJXpEYPc9VcEVPZxUPfdXNVUSoaeZmr3rr5NvEGRqLQLB0SecTld76/RkTvv/bH1s1VmUYY6QkU6XMk+qrveJVeWn9zfVWoFekdnljxOysyiArin9I366AmdCs6V+mZ5qrS+uPcZbu/LcVU9DhUMbrMTEW5aMv5Qi6uvsIfEmXr53+Bkzz0zvfp/df+WCsm9slvotdwHhFFt9o7/Yb1e+hz1Bbh5+msgP/hzI2i+HpiXzL7O2esjJBGlsxVtfVPRWeeuSqxv5OLts1Ys60t1TPNVWvn6KRDFtUhUTYVFfOQfXNVahzQc8BpdAhghESkmS3iBHQ7jZfWn7xwz2kUp8ul0fDWzbc/uFkzR1c7FZ6S5qG7dz9//NbLgvZwGv/T33z3ne8TlaWiKrTvVTWGCABo035CEsVoj1TErzxbREOvPYXi1xipXvQkWXTmF09+qYjzuIhTc35qjpGHRPXTkwUL/DwEAHDQ/s9PpC+Cx9xsEVECCDh/VUSpcr8EEERcemiPO3r+Ojo3ERZwpwvnkIoACEj7IyRSm47wiNFSvRFxBH0pfme4SKgNRhH2tGJIBIAe7Sekgcf07iKdPi2lK6kIQyIAItByQhp4TO8oAQdGXUlFyEMARKD9ERLoEAbn6JRSEYZEAMQHCQlwCTVH9y49Y3ZghDwEQIsgIYF6ws7RTSaTsw0qUU1FyEOgi5ja+N8EWwkJ5qqtt6d0c6t0zXeR7Bxdky5z5uhEXfYYEknT8+XD1888c4Ep9qjfT88v4qnnXeVae4iq3dYR9KVFSo1IHuM0Vy3dr5Krv3ZPi0Mvrb/qWMXdhC59j81VyV62iKC3bK5aW5xTfzYVjbzMVZNDcAZGotCcpKKf/2FdLy6/+99/IqIrX/wkuLkq0+anNBrW6nP46ZnmqnEao6TPid3mqhbcnjzcodwfy+DWQYYSkvHorKS3ad8XcGCUTUWOUOWo35GKctGZ851P7OaINyTK1s//wid5iIiufPGT5AUnOosCVvDoEzx6NozOFCXaEvuTnCsSJzrbB152kbCZvYLriwHX/f1M9cyB0Rvnrr0htIZKXnDm6EZCL77EcU46JBLZfCSp6L0fvqCdAJjt4WNw016cfYERGgb4WElII83fYvDQixBVLroj4yeAbOX8+unpxrsPxAzQ6RxdwxjqnqPjV54+Jfr5H9Y9GsM5k5cPX3+XiJ4Mia4w6jeYAABoHSsJiU/Dp/Rh9X6NEcEv4p0APNJYFbk5On6duTm62sULnGpzC+fef43TEEH9lw9fT16kU3MAgCa0n5Cyz13HkiLSo0inofk1S4voDXc8xPwEzBwYeTSDeHN0In76m+/qreFOUhHyEABhaT8hJUin7FRnMJTEHo9P9cT0JBsFGRWRJT86vR1FGBIBoIqVhGQqTFsQe+hFeGTHUkz50WmnIuQhAFRpPyGZCtMDeRRsbWBkdo4OQyIAYtIoIa2vr89mMyK6cuXK8vJy+v6RI0eSf66srKytrTVsIrDGEOboMCQCID7+CWk+n+/t7d2+fXs+n29sbFy//vhe8sGDB8vLy5ubm4FaCALTcHjU7zk6DIkAaBH/hDSbzZJh0HQ6vXjxYvr+3t7egQMHLl++fODAgfPnz+/fvz9AM4EBQg2Mxr+YG5yjw5AIGEF1p0oEfRP8rYPW19ePHj06nU6JaHV1NR0SbW9v7+zsHD169N69e9vb27dv3y6WnUwmu7u76T/H48frvXdP3hhvCWwotfUGm9RQX1s8cT7Nad599AwRvXfwa6a+ivEv5kR09+7nDbv8b//xT0R052d/Z+odpLanv/6aaxMp6jIRzf/zH0Q0/fdvadSfOtVq66uKFD9gtfr0Tzmb3eb6bO+KHr4OfRW5Iqp6julwE720PX6HSPGzFGqUkJaWlk6fPk1ER44c+eyzz4qaU6dOVSUkmKtSG/Z9tV4Mxb865uj47Unm6O7e/Zx8zVUT3HN0olu5ZEjEsfnJVs6v/9FHzycvDr7651pzVW+zVHdjRGamUr3bnLTYZdXGFPXxvQGb2/eR/GPmZ84i0lNE+z7/Kbvl5eWdnR0ievDgwdLSUvr+xsbGyspKMnICDuK7JUmzkXuOTpSNklSU6DldLv3OOObomN+x0RMHbuLZ/PiZqz586UdEdPDVP3PExD6TIn2TaMsp4hdtRXp+3s1pmOfTpnuTQZNAvyJ++CekY8eObWxsENFsNjt//jwRzefzN998886dOxcvXjx+/Pi9e/fOnDkTrKUFDA537KwaDzI2oopsxA/Q6cCo4e1e1cBIFLCSbCQdEvGzxcOXfvTwJSKib//+V9KAzmxMQkejbbQ4aOdrCKQ0WvadLLE7c+bMoUOHiGg6nSbDt48//jj7PpNk/oqudtK/XS97+fmrNq+8dKbOIxVxmpGtPIdjjk4U0xP/0/d++IK0MZzOPvro+YcvfTMkWrxaX7+p7XcAGKHpxtiqqTlTU3YG/VU9ioiUuVY5GllauSMbuWtLSPa6SocvRbF7jk70rIjvw11sRhXZp0TsigEAlbTv1JCQxCPmj1tnH+2K0ozeIIZfrahyVX9VDW+97AajJjXXbjDiZyONldxJKkIeAiAsVhJSAnPKLklF0gSjOkliWVx1oqpqrlpWVzsqIkt7XTX2FWFIBIAqthKSCGQjO5jyo9NLRchDAKhiJSHxFwRn9Rpi7cojIx1HSp2BDA6MAqYiDIkAiImVhAQ0iLMSvWE2sjlHhyERAPFBQgLf4DE8apKNDKYiDIkAaBEkpN6iPVnXkFDWqKHm6DAk6g2qW9r99pDwi/htljCib46/l10T2vKyi3AIO3rpjtokIYkMgZLhkbQL0oFRVf1VAyNpe6SpSLpN7f5fzhLR+MO/8isX1e/WF3ek8fUcfyCRPnvqOFZ1Re8+h75294W2PldEW88p0lDvV6QJwxohddoNSESEtQzp1lf+gZJUdOdnf/c2V01wpCJ+exKzH2KnImaqSM/87uvfIaL7ROMP/zqZTEo7XAy4tZXn3nHbQRVLifQccZV+Mplkt3AU9fyeenwNme5KHl55jiK5LufydO0hpPpcEZGej7tIrsvNGVZC0sYj4YnckvjbadMvj+rchXRglIyK7vxswqmcKr4MpXN0zO9wGk0S3zmO/+mCba6aVp6kotohEd/5gthJJYieU2TBdijPCaTRmU9visRplU2QkDqDXnbxmKwT+aUurr7CfGLknmYsDoz8JtwfvvQjzqhoJDRXTabmiGjyLx8ETzDaQS1aEOxN6AQa2EpI460LI7oxkI/sSPjzE6JqRY+abgkfTZ048aLoCYdo/ULpnHXpHJ3IsWkk+WEIEqa63de/cz8zJOI8lR3IhxwAEbYSUneRPr2QjnX4lUu5dfPtN85d47fkxIkX7979fHSX2553vr/28z+sv/8aq/LkRa7mJnN0KaLHRcyak6k5Yi9YAAC4sZWQEnNVkfGo6NZeWrloqOHRGBH8Jw38yj947nCSjUTZTjhZx9XzFy/w25Dw6KPnw67nZj4lAgCIsJWQEvjxyyOsiyqXDmX0xHqVi6o9ceJF/k5Y/qOjIqH2uobdXYQhEQCq2EpI460LzF+giIORbKQ0ExjZl4FPkL2uAVMR8hAAcbCVkKR0cUTi0RIOBrdMeQyPAg6MAqYi5CEA4mAuIVmLqn1Fe3jkl43sDIyQigCIj7mEBDzQnqyLQPNshFQEeoN0LRXJ7fU8ll9FGC0gIYF6IgyPGhJkjg6pyCB+0VNDr21+kdPXdrxUzy/C6U7VIdxHaYKthCRd0eDx4ETbzk6qb95l9xGLf60dHsXvsnt45K6/ODDya//u698R+Z/KQh77KteGlWzvmDGFr892rdY3r2aNa6HLtWtis/U7QmEQPVVH5yp9bf25Li+e9sqrPUTutJdehVo9Oa9ytkjp2WPqSf7BZmLL7XsymeyelDk1WEsw8fVhE1JR7x4eFfXu4dHo0qfjrQvZq++djUpTEcnnLphu3My76dQpI31ncfUVh7197h1REKxtSZzKS5W5LkuHC7lSevNXFG5BUNVV7jHBu2xrhASkhH161DwbuRG5JbkjS3GOjr/lOU0YtakoK+ZPuXD0TeZ/NOaLHPfCDj0fv4jvUSpOEaCEuYS0EJojSPV9orbjqmemtHLH8KhUXxwepTmAOTDyeAzAnKPzsPZICX7azSYAAAJiLiFp0+kE1rDloYZHVc0ozUa1CYZfPxUGRn4Ppe//5ezu6zVzdB41t74XDYCuYzEh8SdJsiilGb/GRCD4oyPp0ZuLS4dHjnqaZKNExl9HJ8pw1j4bAHQUiwlJGhxFRUTzMNLG+FUumhTSaHmpsnapt2gtA3OyrlTJr9MNfx2dG+QhAJSwmJCqlkj2tXKPqR5mWko1nJ2w2Qod2Ui66DlUgmmy0yjUBiObY2UAeoPFhETCyC5NAx6Vm4pBGu1pmDaqhkdV1QZxCeKAVARAhzCakGgYxqnJDhW6ylrIn9bMyZHZv9YOj0RLvVvBb3gUcI4OqQiACNhNSMCBqXGb1CjozDMXRMMjj2yEgREAXQQJqaswc5JBV29tggyMkIrsoOp+In0mmr7mb5Rm6qX1G9Q3Bwmpw5gaJzG5fPj6r7++cYW4IyTp8ChUNurWWQ1IhGjuEf05e8Cr/llVMFd/9k+lRRyHKC2Se1YtzU8cM6fsIZT0qVJqLuWHLS87j0CgevfUCX1tDfxBUjI84jcpGR7x9claBlGXH330/Ld//yu+fvf170z+5QPvU1obYaUjpw+eO5y84FyC2jCaPXptgHOv3Cl+itxtk+pzRaT6bJHS/hb1xSKON3N/LT20I5NVHbrqECJ9FY4vTtUhtGNRzpcyAIs2GI/HVe/T2ifS2qRFTOk9ulzUu2ugtU9uPftCbbUnfvuQU1uWdz58UaR/94VrtPZJ1dUv8vC//lV0cu6/9s8iPa19kuqzr2vFbtniyTlPT3tVl5M60/9qj84U5/S1bfbQ50oV/8S/yr0BXW6OuSm7Lk5DtU7tSTv7ty+SW3XHffrWywdFD5D8hkfvsRfcS8dGCaLppuzAqHZihznHcuvm2x/cpFt1Q6Ims/OiLWgB6wxVCoAqzCUk0vdX7brer5IkPrqn75KcxDlcd9cylE4EuZ8ZMB//3rr5NhG9ce4ap0ichAFAt9jXdgPKSR++MXeweuul7bFAVWM4jUyHSlVsvXzwxIkXG7WvDOnTI/7wSHTdcw+Zk/bUPsF2V/7Bc4c/eO7wrZtvn/3bF2f/9kVVhQCAWiyOkFKkOcAvxyg99xNV7tGY0pZwBltJTnKMk+7e/fwkvdji3tjRpU8fviQ7Fff/clb0C3uincVV1M6CAgBEGB0hUSYi8Ac9ovo9RjwiwyG9xtSunioKktFA+k/HOCmR3b37uXvu7v3X/vjT33yXOTq5fPj6ez98gd/Hhy/96Nu//xVHP3ryO3tMA++Aw5ckqSMbARAQuwmJnkQQqZ6fwKSV88X09COKsJVznk/UrpF1z90trr5S+zzp/df++M7312rbk7WtEz1XYz6690gwDZ/YJXN0SEUAhCfsoj0mjmXfkVvSOtkuS1fc1gqya5pLNcXl4LlVvOla8KpDJCu/3bz7wrXsP91X+eF//WtthVnuv/bPIr3HvoKU7EpuEQP/YA8EdLk5pkdIQyP4OKn20VRxnJQbc7jHSYurryRzdz/9zXcdLbnyxU8uH77ubm1Ck9+Y0AZzdABoY3pRA2gOc4tSk/1Jyfpv90LwJCcF/8kJqVGQ32QdFi90C+nKowTmPjO+Xlq/xyGs6ZuDEVL/qX2uxlkLXrs/KRkqOQT8cZId0sdFw8lG/LUnyUqZ3HoZjlhDny1CvF5IlzV5mCcVmxf2EB76nKlS7Qopkb45trzsqt7vMdG6XHvbWPugnuPjULthNjFXdXSZP2unPTwKuHIh1FXm7w1oeG+epXafVmmRYpdri1QdhbNIp7aIVO8uUrpkqcrYLXvVmNel9BAaen6RbNn0Nbzs8hjUe9up6TWJWTB5Yu+Qla5xyOlrlznk1jgUya1rKG2PYy1DVful71etXxCd/xO/fZj8V1VVzkyvyh2u6GUXVl9sj/vN7F+Z9bixpvdA+oR/gF2uxVxCWujHdFM5I+2yUv05vYWcNB6PRTmpqjFVOakqRFYdq/RPpdmI6Wqa/D+bh4ofeG2z1Fx74oMlZ0NgEAkpwdrtg5I+7XK3clIxLfFzUjIO1stJpff4VUcRLYivqiQVpHkod37cCcldbUdBdB4CA0pIC6e5fSld1BdzMO2MhQAAHhNJREFUsKh+Dz2nSG1OWhSGSkVxVU5KB4X8nORoSTEn8RMSJxuJRjAnfvuwVIlQNQTQ5eZ0Y5WdkqmdtzuR1AxC1SJWZE6ROopy1t2l+lJNbuldsc7m6+4OvvrnRx89/+ij5x2a8Yd/3X39O+k/mSsX0vNQ/FN2LQP/g3fixIsnTry49fJBOKsC4I3phJRddMgJDVI96eekVKa3XFK0Tjd90XwtOFXkpGy1jpyUiN/74Qu1Oengq39++NKPHJo0J1X1qKqz7jOQNWN1pJmTv3uUrD9s0Y4WgJ4QdsDFZIDWQVVzPo7fEhVVLp1IZB7l1rMv1Fae/anZUnFu7i67dCURu+fuElmtpVDyc7HuJWTudi6qV9Y5cLsrJfT4g10FujwEhvUMaQi03mVmTnJrskG5VJzNSdl1HKk4YE5y11PVwhRRTuJko4WBqxwfdHkIDPQZEtCDM3d36+bbfCuH0tmt0rm7rNL9PClRJo+UHM0Yf/jX+3856xDwfy/KIUgR/eI7AKAWFS+79fX12WxGRFeuXFleXtY4BAgIx++OeD9/7ra8K/o4FHNSld9dNic5rByS50kOB4cgv2EYhCY75LtojEZxu2zhFNHTTyJrxdSLLjch/AhpPp/v7e3dvn370qVLGxsbwesHGnCW6jW3vGOuu+MsvXMIcuvuigTpbHNyLmGqeml7mPomh9DustIp8u4y0wiuB11uRNgZwMVicfXq1V/+8pfJ6+9973ulGjxDSjHVZc7KiNpHLLWPVTx+QqkI53mSWxCnswmOq5xbalFblVSfLai06y59MpfV2+myVO99ilrsclufiuDhK7y56vr6+tGjR6fTKRGtrq5ubm4WNTBXTbHWZc4+noY2rJPJ5N/+45/cHqz09E/NllJrw1rrvsrxKg3iOSv1Bq1tlbeeeL1urufbbmp3OdopQpebo5KQlpaWTp8+TURHjhz57LPPiprJZLK7u5u8Ho/H2T/tnrxBROOtC8zD+en5RbT1FKvLHqfIUerdR88kL947+HVpl8e/mH9T4f+eFg+R/Px5wp2f/b30KGee+abC9374QrEx8//8R/p6+u/fynVhvHVh64X/m7558k//s/Qotf1NO0tE7x38mgpX2d3Z8S/md+9+fuvm20de/tuzZ5/5P/84sHzh/71x7hr/igDQOfwSVfhFDcvLyzs7O0T04MGDpaWlKllpIpxMJo+tDejxF557RyDUp0X89JxhBFMfrcs+p+jSp9lgXV7wucN08+0n/3jmjXPXil0+mYnXWy8ffNLlP2Zuyp56sFQ+eDp8nZ7kp9KR05y+ebB08NXHp3SSafnW0w+WSgdP6Vly9Zco7fIb524Q0f2XD9KTLqedPfP6Dx4Xef0Hd89de+PctWQF4LfeO7dz4+atC2+/ce5Gj20drA39I4AuN0fl95BOnTp19OjR2Wx2/vz5Y8eOFQX8KbtoY1tmkeD6bnU5S5XvTvo6TU5Zcqsetl4+WGxPduFDaXLKrXoo5qfcqodv//5XxWbvVuen0i7X9jfljXPXsv9M8tCzZ5+5fvnHRPSPd2/ee/aTu3c/73E2IkTnYdCNhERE8/l8aWnp0KFDpX/1SEgJ/VuK6u6yxjrOhoeoMk8qrva59c3IiSjzE+DZLufyUzFM51blJfkpd+h3//tP6evSwVMuP5U+ecrmp/GHfy12mbOEKbcL6tmzj+f6rl/+8T/evUlE95795MzrPyhN1T0D0XkIdCYhucGihhR3l5lWoRaoTXK5wUTpSoFsfipdKVCan7LUDp7o6fxUm5yYpLknIRkMEVGah4goSUWkv5mDCd+Ilj/4TpX4Lg8BJKS+0csuuwdtSZez+ak2OREjPwWZ3PMgzT0JSQZKyOUhipiKWI85eQur+OuvssraD7boZqsTd2a9/C67Cd5lFacGMHBysaN08JRNQqWDp1wGKh08ZZNQ6eApl4HKttz+uPAOl8e550kGStIP0f+iJysalukHb5y7dvfcteCrYx1Ifej51XqMkzht6JaY5NmxE9nUCBghtczQusx54hV88BScJ7mHKLuajogKKxqYwwUOnNUrohUuoqGPxgiJefSsnlnE+ylpk5VEVV22tuso4EY0TNn1jYF3uTY/SZ88aZNNP7nck6DxvRWFV/5EnNKYIBEzu6w0nJLqg8R0R5dt5iR+kSo9puxAr6id3MtloNJl1mcCNcZxrDT33M0koYbzMNKgwJF1bnZowfC6TZUk6aBIv8j8+LKoMcS7dovMj0Gb0jOR6r1BQgKGKK4dz1M2KPGrv0iSgb4Z9whzj8c4hiPWeHijShK8xvVC/8r53ZTmGFH90pyXvBiI3g8kJGAUjQ99zV3e02uyvR9acGTpLWftA6FuZSMP9HIM9Hw9SYbp0ulTPniGFBhpXBhgl6v0jnpK/+T4VtSmB8dUoZ/e/S2VTvGT/lIu6IPrRWspVR+JeehJv8usOq0lpHrztKcpnfpwhzZvfVrEfeWKh3AvU8l2mXMIaZO8o2fDItnmZSl2mVPKnTOCT6mR11e6ih7cdkhBl4fAsFbZcZYIZ2mob+UQwd2SPIroRfPSIqVX37tJnZinQqgaAuhyc0wnpITIaSlyNG+lyySP5gEfUeB7OwTQ5SEwxGXf0jhoTR/hEAabBAAAUva13QAAQM/hb2HRUNoRg1qQkAAAYlrPMVK9BfHo0qfSmi0020/vBxISAICIHf5EUbJzIx7VQ2TX3LbbEnqyblY1QXqAhARAP0nChyjHiHbsMxG5HmiIRUq/ItL6RWFdtXK+vrhhXAMkJAC6QZpgaiNCViMK8cxmLK6+ohqvw6K6fic5FaJxCf8Q0sr5NUfTS0FCAqAFstmFOYhJX4cdGaQL+kViDgG3CkRGmgZUK+fr0+toRO9BB5Z9A9AKTfYChx1AiGoeSM4wxULoJ7swaWenp+eDhARM4Ge9lbxgluKH9YaPkTm2UsyvtOi0aG92Vs1eSI2AOuHUEJbSz73bCC7Il9bxPlVYt4maVGs0l/tTrT6h9ElmaVVuskWkek4Rkb7WKC+7Gop/ihxIc6f76FV61ewyNL3BJhnUD8tcNWERztbTr0jD6ObWJ6dC9RDeRapKSUckpV2u0vdyugmmMkMAXW6OuYQU0HbTpj5XpLbLetM1Un2o6I/v7RBAl4cAvOxUinRdH+EQXRmLAAC6C5Z9AwAAMAESEgCg84g8ipTEuydvKNVMytZKepVLQUICAJhDmjZUG9M6SQftpA29ypGQAACe8NOGR4Lx2F7WFXHDUhqVS1ui1HIkJAAAkcSMlTIJxmOVaUBxSlg7JakyFUsrD+vo0bAxIpRWOSEhAdAZ+DljJDHKI6+tuyKxUrUR9BbWl6q2wePs6dnZdWDZNwCdQOo4l/1nWDs7Uc0kz0bJpjR+qtMbDQzHzUjPPs4USEigq4i+nxG2V3vDd7QT2d8xz4+3wYxq5RoMIaCnSBOYn57vJ8sECakneHzzSe7swC/ibTbBLJJbd+TQF2/k3ZWL9N6VS7MLv3KmuKivpev2esA+thJSupC/6JXpNlsr6otvZv+U+yvTKy8VOOJg1Z14VZHavQt8I7uqQzjqd5w9fhHpbLK0y1V+eh5XjWPZJ9IzA2LpB5uT57ob/XdP3jDVHhCcxdVXRpS3Hm2IUS87R8CqDUAcfdgiojvonN7tNFpbf1EvHY6I9EFCBiy/hgC6PASG4mVXdQNeFRD5IyTHIWqjLefe2d0wPqYWGnno/YoAAIaM0YSUJUIojBCdAQAAuME+JAAAAGI0tiIhIQEAQGCMeBRJxapWRhyQkAAAPUFkl6ckFjUjglg1xxR/4LshSEgAgHhYyBmq3nqqCSZ5eq2aY6ReU2FBQgIAfIM0B/DjV/Ifcw+DX1jX8NZTXVQltVNKTqBoia+0MaLKx1sXmJUz6cAqOwBACn9DmIfzhbQZzJZIce96dhcRHYUj89uBa8GLr4sgIQEQhiYJQKRX3aWgkQNGT8xYNcL0SOKtJ61cyqASjIZTAxISUMHPW4+8jO84paR6apBggicMb9sOfuV+jnbMxuglDGuGSaAhSEhEsZxJpXrVIqoxTlokq6w9V8W78ibWTU0qp6dPO+cq5/Rhs4W2HZRBvalspG3fNwRsJaRS283szEDx+tVOGpS6ChWpOoSj/tIiUr3babT0K+rucvFTHnaZEPMSOAJ0scvZtUO19XMMnKoujUjvoFTvKAtz1eD1D5AhDO+Mmqtm0Z5saaJvfuvqNle1E48CAg/KIYAuD4GhmKtm6YGXXQ+6AAAA2mAfEgAAABMgIQEAADABEhIAALRPdw2NAtoIISEBAAAL1bCuJNauPCwdWNQAABgs0n2ypLMNq7sJQ7VyuH0DAAzBn7EZeZmxSpvB3LbhF6ZFxqMipBaoqpXz9Ym5asAluxghAdAlRGE3fd2uOxF5xXTpVjy+t55q5WTSj7Ur2zwaJaT19fXZbEZEV65cWV5eTt8/cuRI8s+VlZW1tbWGTQSgFbwDuoae5DFdVLmfWKTnx3SPjecR7PKUEkYX/RRSpH4ctfgnpPl8vre3d/v27fl8vrGxcf369eT9Bw8eLC8vb25uBmohUCGOfV+C9I6bU0Tbv8PDu8+vco3GpBcruF1eQz2z8aY8kFSx1tnWT45/QprNZskwaDqdXrx4MX1/b2/vwIEDly9fPnDgwPnz5/fv39+8lXGip0e09XgiqlTEI9oye5GtmXOimj9E5Zi8ccRN9MxZnZxeFP1r9c0dqjj1x0lF/CKD0oMc/l526+vrR48enU6nRLS6upoOiba3t3d2do4ePXrv3r3t7e3bt28Xy04mk93d3fSf4/E4ecFZs5H7jcLaIlJ9rkjr+ob9LS0y3rqQvlmrTwTJm6U/ENlEnzsVIr0DR+86pBf9HGfV2euQniRdHuYpUtWHPYSfx504Ic3n89lstrS0tLe3t7S0dPr0aSI6cuTIZ599VhSfOnWqKiHxzVXJ91axE7d+MGQcAujyEECXmyOesptOp8moKBkJEdGDBw+WlpZSwcbGxsrKSqIJhTWn0R6vcgEAgLbwf4Z07NixjY0NIprNZufPnyei+Xz+5ptv3rlz5+LFi8ePH793796ZM2eCtRQAAECvabTsO1lid+bMmUOHDhHRdDpNhm8ff/xx9n0AAACglqZODdPptDTrVL0PAADAPq1YrMI6CAAAtDBis+3tlhRc7AbWQQCA/qBtxirVa5i3SvXalYt8ldwgIQEAGsHPAaKY7idm4q1XSjCkaa3kkTCkxoChVhEjIQHQJZTMVaX6aGasTKR+qdr+qmkRvlgU1iP4R7SyUwUJCQwCa956Zs1VpXptM1apdx+nZo+N8N31V+2WWxISUk+wZsdnLQHkyrYbc+OcTJG9nlRv04y1i+atprJX63QjITV3mWTqmUVMRVuR+WnxFtL9+Y42NZ8ibQxTz5miKer5Z16k1/4Ye5urtmvGSvaiOfRugv/8hL+5ahNqPescZPsv1XOKaOgd0bC5fvHEOrpUT4W4mX1TVV/1SfVO50pxnPRDrTU92Qttw+yyKX2cQ9RUaCohORKVtSsXChgyDgF0eQigy83ZF7AuPUw9xQUAAKBBNxISAACA3oOEBAAAwARISAAAAAIgXWRbBAkJAACsIIrpI7llKl/vUTlfXEU39iEBAIAGqsvNPcR8/CrXaEyQVJSAhAQAaIRo14ReGFXd39ZwL3zYxnjUz/dV8ijC2XXOBAkJgC7B/+ZH9h8JWznJY7S0ftKMuR4xWpozRHq/rZb8KxVq5wwSEugkptybIugpSoD2aIy0fr0pJo57k58+TS3MBOAxDbhge/c10UvbEx8kJCKrtij8IjGjoYde2iTtL0PwAK3d2WxAbF1vzQYpqxd1lq9PZVI9h6Hp3XQjIalOPiRifg7I6d1FsjLOIXKhrfbL2fzZo7RyI3rOlEhR77643vrFEztBkb6Wol5av4ZeL7WQvegJvZuhm6vmOi/VlxbJjsSD61NB1ZczoL70k1GVOB2fvNLeSfUOrOlJP9Ra05O90DbMLpvSxzlETYWmEhLcCYcAujwE0OUhMFBzVQAAAL0HCQkAAIAJkJAAAACYAAkJAACACZCQAABgKIg2ikj1I6Efa5Fu7EMCAAAlVNc6i5an++1w8Ns+H1bvsdeiFCQkAEBUjAR07wCt3Ri9xi+E7kfMxohqdoOEBEBniBbj7MRQZuUe+hRVqyppQFfSp0qRnn/JRk+8AZn6KpCQgAm8ow+zSJXDRVt6atAF7YCrodfurIee4w7VXM8Rk3DUKNV7Vy7qLF/voJ8JKY5tCb+ItejZsEka+mzB4HesMbOR3snkB0RVffbDz9fbsU3K6kUnJ4Keg4femkGRA+sJqdRKjqNn5oxs/bVXutgY98UI8hRRWr8RPWdKoajnXyyRPpFZ09dS1Evr19BnNVJ9Ldai59D0rWPLy64q/VR9sqX6YhGRPhVo66n6k6StpxBxs1t6kofOruvJXigcZpdN6T0I7mVnKyHBnXAIoMtDAF0eAjBXBQAA0E+QkAAAAJgACQkAAIAJkJAAAACYAAkJAAAGRJDtKA6xtP4s1vchAQCAKbRdFUh/R4SFxpSChAQAiIrBAO3hn6Knt9BZkrd/AS87ALoOP+Bac3tqoudgLaBzzEeqCvKVol575AC9xvudnBxISECFyNGN78BmRF8swkcvpujp/a4vxyAqV7/qcEHqIMcfC6ZKbT2TtlwhOpCQvJ1g+EW6Hj0bNklDL6LhvbNqdmk92mY/zN3Vpx5dqnoOMfWiDwOzfrKXXQJ6FJlOSLk44r5ypUGN49jm1xhvvbQ9qnrHx6ihvjZaFYN4t/TZIn56qgtDxQ889MUipkJtBD113PGvpjZTXnZVd7JVp7XqztRxGUoHT9p6qr5s2lMN7tZCnxYxFRdsdtmanobXZe1U0W42ImsJCe6EQwBdHgLo8hCAuSoAAIB+goQEAADABEhIAAAATICEBAAAwARISAAAAILhveObkJAAAEAV1S2PI6G7tkifiKV6fmOKmN4YCwDoH6LNK6L9Rt4WGxH8WezolbY8emyRLIKEBEBrRAuI1vQcmuiDZyOSm6tK9dmCSvqFsnmrVF9EKyFtb2/v7Oysra0p1Q8a4rcxPsFgdOM7sBnRU4M7yi7q/a5vrQFVQz2zMXH0cVwbpO1R0lehkpBWV1dns9lbb70VpDbpR9mjSNejp0eTSPKdMTv5QPauL/9kMqNnP/QLnt1fQz2xzz9snFrUO1BJSJubm+vr6w0rKQ1Sjp63EjQdl6FPes7kQ2Q91X0N4utrKfbRXRB6qb4Wa6F5gNmxpjYlL7skIVVN2U0mk93d3fSf4/E4ebF78sY3b25dSF/vnryR/Wf2fZE+WySm3oG2Pi0yHD05L1BbesIpalVvsEkRuiwlYJP8PO6CJaT5fD6bzZaWlk6fPk2MhARz1QR0eQigy0MAXW5OsCm76XQ6nU5D1QYAAGBoYGMsAAAAE2gt+8aCbwAAACIwQgIAAGACJCQAAAAmgHUQAAAYQnUzk5/lRDQ7OyQkAEBU9MxVSRgTVe3vYnr9GWmPXS87AAYLP+BGC3DW9BzMBmjmxeX4j8TUZwsq6f3akwUJySIebhzeN5LMUl23+4up157f6KLe7/PAtMuLrK8Vk+/3UVXfCQOhDiQkaWig7kdPaZNSMfNjaupe1XJqEemZ0W2Yeo49YHM9sa9XND0Ha9miRTs7owmpKgJWdbtn+trBeNf19HRcS9/ptJ6E/Q2rp7JQODS9G5upQtQka3oKba5KizYYj8el79PaJ8l/xferqmpF70Bbv3C2tit6nKKw+giHsKaPgLUu9+AU1aLl9u0G5qop6PIQQJeHALrcnH0B6wIAAAC8QUICAABgAiQkAAAAJkBCAgAAYAIkJAAAACYwug8JAAAGi2hzj+pmI6mfiLf/SAISEgAgKqq7TW3aA2pEc8vuX95bZZGQAAjGoAJKQ8MtVb12AA3pTeBbOccPxbK+FCQkH+IYhPCLWLN3o8bRSrULStHKe7JiCHq/88+0y+uZvlYcU88Re+ir6EZCsnavR17RJ45PVOvZCHqmnhmt+qFPZNp6Yp9/O3p6upvW9BwC2tlZTEiOHF7a7fh69+C0Su+4ZsWg5s5epXpm/Zyveny9mwh3DK3oOadISU+F0NkDvZsId4Rx5k7s6GkI5qqiqnqgN9ikTusjHMKa3gNrXeiBc2gPuiwF5qp9A10eAujyEECXm7MvYF0AAACAN0hIAAAATICEBAAAwARISAAAAEyAhAQAAMAESEgAAGALVZul0aVP9fSJWNr+FIsbYwEAPUZ196how7I1CxjvPGR597cIJCQAXPCjp+XoZk3PwVr7s1jTi2oWXQipnmCu2pw4hh8JEb7qrdu1kb1ooh09s1iLVtbOp56eaa8HvZ6+VummGwlJ9dOciPmDzVTJvAaq08FFfevZCHojemY0yX6Mrek55PTS+lvXk21zVam+IRYTUlVErupzQ/3Cy8lUVU/OayzV54rY1LuJMBtjbXo9iJ5zCZh6KoTaCHo31vQEc9XmhLXGYwJzVW+9B9a6YNBT0lqXcYq6CLrcHJirtgy6PATQ5SGALjdnX8C6AAAAAG+QkAAAAJgACQkAAIAJkJAAAACYAAkJAACACZCQAACg26juvh9pmrHmsLgxFgDQY1R3j4o2FFvboB3THlCkV9rNXQQJCQwLfjS0HH26rudgrf1ZhqNf6JuxZulAQvJzsxAV8b4RYBZp+NW1Y4/G1JO9aKIdDbNo6C2fTz09046vT/paZeT2eLS/iZNQBxJSAj9npErmNc5+Vfjmj3wa6jn2X9C3pS8WUdLXOiIW9WTPLFWqJ2F/e6DnMOqvuao566Ddkzdyb7q/iqURpEV9sYhbX+xy7Ve39GazRX22COdzme2y0tx0ND2zSJ+6zNSnXfa46x+IngZpxlpDWGs8JlXmqlXvdwip2+AAu9wDT0kp6PIQkH6Xe3CKgoevfcEyGyCisDcLHUHa5fHWBaWWmAVdBkUGGCtqQUICAABgAiQkAAAAJkBCAgAAYAIkJAAAACZAQgIAAGACJCQAAOg2kXfr14q93YNsOTXs7u623YTYoMtDAF3OorobVHXDr3tDdLHLlg2xguhzXW7iYpfQNCFtb2/v7Oysra1l3zxy5Mjy8jIRrays5P4EQCtYsxNs2KSu6zlot4fk2UtaP/RSGiWk1dXV2Wz21ltvZd988ODB8vLy5uZmk5qzNLF1YZYy/tVt3U6NbJ8i7Q2GGt9Ga+fHpn5hzzxUW1+rjNwepfZX1rNo5mW3vr5ORNlh0Hw+//Wvf71///4DBw6cP39+//79xVJVXnajUb491sw0g+tzXW69PRH02S5Ha0+tA6GqPu2ydnvo6dDAiSZK+lyX/ernYEefdNmmA56SPu1yqJvC8AkpmcQ7evTovXv3tre3b9++XSzlSEi09kn2nfRzTFVf9bKb/S7pn+5yqnF91Y2Zq4pvfjNdtvBgIIb+SZe146agScb05Nvl7upJ+XGaQX19hdKENJ/PZ7PZ0tLS6dOnqSwhZTl16lRVQpI3FQAAQDcoHXLUIn6GNJ1Op9OpQ7CxsbGysuLW+LUVAABAjwm57Hs+n7/55pt37ty5ePHi8ePH7927d+bMmYD1AwAA6DFaP9A3n8+XlpYOHTqkUTkAAID+0c4vxgIAAAA59rXdAAAAAIDIiHVQqd0DDcbxoar7fWJ9fX02mxHRlStXkmua0vur7Oh7bxjy9U0ZwhdZO1a3n5BK7R5IwfHBJlXd7xPz+Xxvb+/27dvz+XxjY+P69evpn3p/lR197w1Dvr4pQ/giR4jV7U/ZbW5ull7Fvb29AwcOXL58eX19/auvvorfsDhUdb9PzGaz5O5pOp0m99Epvb/Kjr73hiFf35QhfJEjxOr2E1IVX3755dLS0vHjx/fv37+6utp2c0AjVlZWkhe5+ZwhXOWqvveJIV9fEPAqtzNll7N7KOXYsWPHjh0joul0ur29HbF16nC63wPSbhLR3t5esld6Z2cnq+nxVU6p6nufGPL1BQGvcjsJqdbugXiODx2F0/0ekHYzeRBKRA8ePEjyU0qPr3LC8vJyVd97g6OPvb++gIJe5fYXNeRI7B7u379/9OhROD70g2PHjm1sbBDRbDY7f/48DekqF/veP4Z8fYeMxlW2vjEWjg+9wXEpe3+Ve99BGvb1BRToKltPSAAAAAaC3VV2AAAABgUSEgAAABMgIQEAADABEhIAAAATICEBAAAwwf8H326fB0gAOPYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [-2 -7; 1 -3]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "  -5  -3\n",
      "   1  -1\n",
      "\n",
      "Tr(A) = -6\n",
      "det(A) = 8\n",
      "Tr(A) > 4*det(A)? = 0\n",
      "sys_str = [-5*x(1)+-3*x(2);1*x(1)+-1*x(2)]\n",
      "sys_ode = f(t, x) = [-5*x(1)+-3*x(2);1*x(1)+-1*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [-5 -3; 1 -1]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   2   1\n",
      "   5  -2\n",
      "\n",
      "Tr(A) = 0\n",
      "det(A) = -9\n",
      "Tr(A) > 4*det(A)? = 1\n",
      "sys_str = [2*x(1)+1*x(2);5*x(1)+-2*x(2)]\n",
      "sys_ode = f(t, x) = [2*x(1)+1*x(2);5*x(1)+-2*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [2 1; 5 -2]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   0.50000   2.00000\n",
      "   1.00000   0.50000\n",
      "\n",
      "Tr(A) = 1\n",
      "det(A) = -1.75\n",
      "Tr(A) > 4*det(A)? = 1\n",
      "sys_str = [0.5*x(1)+2*x(2);1*x(1)+0.5*x(2)]\n",
      "sys_ode = f(t, x) = [0.5*x(1)+2*x(2);1*x(1)+0.5*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [1/2 2; 1 1/2]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "    0.75000   11.00000\n",
      "   -0.12500    0.50000\n",
      "\n",
      "Tr(A) = 1.25\n",
      "det(A) = 1.75\n",
      "Tr(A) > 4*det(A)? = 0\n",
      "sys_str = [0.75*x(1)+11*x(2);-0.125*x(1)+0.5*x(2)]\n",
      "sys_ode = f(t, x) = [0.75*x(1)+11*x(2);-0.125*x(1)+0.5*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [3/4 11; -1/8 1/2]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   0   1\n",
      "  -7   3\n",
      "\n",
      "Tr(A) = 3\n",
      "det(A) = 7\n",
      "Tr(A) > 4*det(A)? = 0\n",
      "sys_str = [0*x(1)+1*x(2);-7*x(1)+3*x(2)]\n",
      "sys_ode = f(t, x) = [0*x(1)+1*x(2);-7*x(1)+3*x(2)]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [0 1; -7 3]\n",
    "trace_det_condition(A)\n",
    "portrait_phase(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Système linéaire, regulier, à dimensions finies - Th 5.1\n",
    "\n",
    "$\\begin{cases}\n",
    "\\dot{\\mathbf{X}}(t) & = \\mathbf{A}(t)\\mathbf{X}(t) + \\mathbf{B}(t)\\mathbf{U}(t) \\\\\n",
    "\\mathbf{Y}(t) & = \\mathbf{C}(t)\\mathbf{X}(t) \\\\\n",
    "\\end{cases}$\n",
    "\n",
    "où $\\mathbf{A}(\\cdot),\\mathbf{B}(\\cdot),\\mathbf{C}(\\cdot)$ sont des matrices continues en $T$.\n",
    "\n",
    "Si on considère le mouvement libre (c-à-d $\\mathbf{U}(t) = 0$ $\\forall t$), et on se concentre sur l'état, avec $\\mathbf{A}(t)$ constante:\n",
    "\n",
    "$\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Rappels Théoriques - Système du second ordre\n",
    "\n",
    "$\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$\n",
    "\n",
    "$\\begin{bmatrix}\\dot{x_{1}}\\\\\n",
    "\\dot{x_{2}}\\end{bmatrix}=\\begin{bmatrix}a_{11} & a_{12}\\\\\n",
    "a_{21} & a_{22}\\end{bmatrix}\\begin{bmatrix}x_{1}\\\\\n",
    "x_{2}\\end{bmatrix}$\n",
    "\n",
    "### Equation caractéristique\n",
    "\n",
    "$\\det(A-\\lambda I) = \\lambda^{2}-\\tau\\lambda+\\Delta=0$\n",
    "\n",
    "$\\lambda_{1,2} = \\frac{\\tau \\pm \\sqrt{\\tau^2 - 4 \\Delta}}{2}$\n",
    "\n",
    "où:\n",
    "- $\\tau=a_{11}+a_{22}=tr(A)$\n",
    "- $\\Delta=a_{11}a_{22}-a_{12}a_{21}=\\det(A)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Stabilité et valeurs propres\n",
    "\n",
    "### Stabilité asymptotique - Th 5.3\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est asymptotiquement stable si la partie réelle de tous les valeurs propres de A est negative.\n",
    "\n",
    "### Stabilité simple - Th 5.4\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est (simplement) stable si la partie réelle de tous les valeurs propres de A est negative ou nulle et celles ayant partie réelle nulle ont une multiplicité égale à 1. \n",
    "\n",
    "\n",
    "### Instabilité - Th 5.5\n",
    "Un système $\\dot{\\mathbf{X}}(t) = \\mathbf{A}\\mathbf{X}(t)$ est instable s'il existe soit une valeur propre de A avec partie réelle positive soit une valeur propre ayant partie réelle nulle et une multiplicité supérieure à 1. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Points d'équilibre\n",
    "\n",
    "### Definition\n",
    "Un point d’équilibre est un point où la trajectoire coincide avec la condition initiale. \n",
    "\n",
    "- Si $\\det(\\mathbf{A}) \\neq 0$ alors le seul état d’équilibre est (0, 0) et le système corréspondant est dit *simple*\n",
    "- Si $\\det(\\mathbf{A}) = 0$ alors il existe plusieurs état d'équilibre et le système corréspondant est dit *non simple*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas 1 - Racines réelles et distinctes - $\\lambda_1,\\lambda_2$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\lambda_1 t} \\mathbf{v_1} $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\lambda_2 t} \\mathbf{v_2} $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}1 & 3\\\\\n",
    "3 & 1\\end{bmatrix}\\mathbf{x}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Stabilité - Racines réelles et distinctes - $\\lambda_1,\\lambda_2$\n",
    "\n",
    "### Noeud stable\n",
    "Si valeurs propres de $\\mathbf{A}$ sont réelles et négatives.\n",
    "\n",
    "### Noeud instable\n",
    "Si valeurs propres de $\\mathbf{A}$ sont réelles et positive.\n",
    "\n",
    "### Selle\n",
    "Si valeurs propres de $\\mathbf{A}$ sont réelles et ayant signe discorde."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Système non simple\n",
    "\n",
    "Considérons le cas où $\\det(A) = \\lambda_1\\lambda_2 = 0$ et la valeur propre $\\lambda_2 \\neq 0$.\n",
    "\n",
    "Tous les états qui appartiennent à la droite $a_{11}x_1 + a_{12}x_2 = 0$ sont des états d’équilibre. \n",
    "Aussi, toutes les trajectoires sont des droites parallèles à la droite $v_2$. \n",
    "\n",
    "Deux configurations sont possibles:\n",
    "- $0 = \\lambda_1 > \\lambda_2$ : ceci implique que tous les états d’équilibre sont stables.\n",
    "- $ 0 = \\lambda_1 < \\lambda_2$: ceci implique que tous les états d’équilibre sont instables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas 2 - Racines réelles et multiples - $\\lambda=\\lambda_1=\\lambda_2$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\lambda t} \\mathbf{v_1} $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\lambda t} (\\mathbf{v_2} + t\\mathbf{v_1}) $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}3 & -4\\\\\n",
    "1 & -1\\end{bmatrix}\\mathbf{x}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Stabilité - Racines réelles et multiples - $\\lambda=\\lambda_1=\\lambda_2$\n",
    "\n",
    "### Systéme simple - $\\lambda_1 = \\lambda_2 = \\lambda \\neq 0$\n",
    "    \n",
    "- A diagonalisable - : Tous les vecteurs sont vecteurs propres. Chaque droite qui passe par l’origine est une\n",
    "trajectoire. Si $\\lambda < 0(> 0)$ nous avons la (in)stabilité asymptotique. L’origine est dénommée **noeud singulier**.\n",
    "- A non diagonalisable: il existe un seul vecteur propre et donc seul une droite qui contient une trajectoire. L’origine est dénommée **noeud dégénéré**.\n",
    "    \n",
    "### Systéme non simple - $\\lambda_1 = \\lambda_2 = \\lambda = 0$\n",
    "\n",
    "- Il y a une infinité de points d’équilibres instables (multiplicité plus grande que 1) et toutes les trajectoires se trouvent sur des droites parallèles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Cas 3 - Racines complexes et conjuguées - $\\lambda_{1,2} = \\alpha \\pm i\\beta$\n",
    "\n",
    "### Solution générale - Théoreme 5.11\n",
    "$\\mathbf{X}(t) = C_1 \\mathbf{X}^{(1)}(t) + C_2 \\mathbf{X}^{(2)}(t) $\n",
    "\n",
    "### Solution particulières - $\\mathbf{v_{1,2}} = \\mathbf{u} + i \\mathbf{v}$\n",
    "$\\mathbf{X}^{(1)}(t) = e^{\\alpha t} (\\cos(\\beta t)\\mathbf{u} - \\sin(\\beta t)\\mathbf{v} ) $\n",
    "\n",
    "$\\mathbf{X}^{(2)}(t) = e^{\\alpha t} (\\sin(\\beta t)\\mathbf{u} + \\cos(\\beta t)\\mathbf{v}) $\n",
    "\n",
    "### Exemple\n",
    "$\\mathbf{\\dot{x}}=\\begin{bmatrix}0 & 4\\\\\n",
    "-1 & 0\\end{bmatrix}\\mathbf{x}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Stabilité - Racines complexes et conjuguées - $\\lambda_{1,2} = \\alpha \\pm i\\beta$\n",
    "\n",
    "### Centre\n",
    "- $\\alpha = 0$: \n",
    "Les trajectoires sont des ellipses fermées avec période $T = \\frac{2\\pi}{b}$. L’origine est dit un **centre**.\n",
    "\n",
    "### Foyer stable\n",
    "- $\\alpha < 0$: Le système est asymptotiquement stable et les trajectoires convergent vers l’origine en suivant des spirales.\n",
    "\n",
    "### Foyer instable\n",
    "- $\\alpha > 0$: Le système est instable et les trajectoires s’éloignent de l’origine en suivant des spirales. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Plan Trace-Determinant\n",
    "\n",
    "### $tr(A)= \\sum_i \\lambda_i$\n",
    "\n",
    "### $det(A)= \\prod_i \\lambda_i$\n",
    "\n",
    "### $det(A) = \\frac{1}{4} tr(A)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = -10:0.1:10;\n",
    "plot (x, 1/4*x.^2);\n",
    "hold on;\n",
    "A_vec = [[-2 1; 1 -2];[2 1; 2 3];[5 9; 6 2];[0 1; 0 1];[0 -1; 1 0];[1/3 -2; 3 -1]]; #cbind like\n",
    "i = 0;\n",
    "while i<(rows(A_vec)/2)# Column-wise iteration\n",
    "    A = A_vec(2*i+1:2*(i+1),1:2); # Get the proper submatrix\n",
    "    plot(trace(A),det(A),sprintf(\";[%d %d];o\",trace(A),det(A)))\n",
    "    i++;\n",
    "endwhile\n",
    "set(gca, \"xaxislocation\", \"origin\");\n",
    "set(gca, \"yaxislocation\", \"origin\");\n",
    "h = legend; legend(h,\"location\",\"southwest\");\n",
    "xlabel(\"tr(A)\");\n",
    "ylabel(\"det(A)\");\n",
    "box off;\n",
    "hold off;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercice 1\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} 2 & 1 \\\\ 1 & 2 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer les valeurs propres et vecteurs propres et en déduire le type du système\n",
    "2. Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "3. Associer les signes des portions du plan délimitées par les isoclines.\n",
    "4. Tracer des trajectoires qualitativement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   2   1\n",
      "   1   2\n",
      "\n",
      "V =\n",
      "\n",
      "  -0.70711   0.70711\n",
      "   0.70711   0.70711\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   1   0\n",
      "   0   3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. Calcul valeur propres et vecteurs propres\n",
    "A = [2 1; 1 2]\n",
    "[V,L] = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tr(A) = 4\n",
      "det(A) = 3\n",
      "Tr(A) > 4*det(A)? = 0\n"
     ]
    }
   ],
   "source": [
    "printf(\"Tr(A) = %d\\n\",trace(A));\n",
    "printf(\"det(A) = %d\\n\",det(A));\n",
    "printf(\"Tr(A) > 4*det(A)? = %d\\n\",(trace(A) > 4*det(A)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "line_range = -1.5:.1:1.5;\n",
    "eigenvector_1 = (V(2,1)/V(1,1)) * line_range;\n",
    "eigenvector_2 = (V(2,2)/V(1,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,eigenvector_1,\"linewidth\",10);\n",
    "plot(line_range,eigenvector_2,\"linewidth\",10);\n",
    "quiver([0;0],[0;0],V(1,:),V(2,:),\"linewidth\",10,\"color\",\"k\");\n",
    "legend(\"v_1\",\"v_2\",\"location\",\"south\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2.Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "line_range = -1.5:.1:1.5;\n",
    "isocline_1 = -(A(1,1)/A(1,2)) * line_range;\n",
    "isocline_2 = -(A(2,1)/A(2,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,isocline_1,\"linewidth\",10);\n",
    "plot(line_range,isocline_2,\"linewidth\",10);\n",
    "legend(\"isocline_1\",\"isocline_2\",\"location\",\"southwest\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "point_sequence = [line_range;isocline_1];\n",
    "point_sequence = horzcat(point_sequence,[line_range;isocline_2]);\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec;\n",
    "    velocity_sequence = [velocity_sequence,velocity_vec];\n",
    "endfor\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "hold on;\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\")\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-1.5:.1:1.5;\n",
    "x2range=-1.5:.1:1.5;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Eigenvectors plot\n",
    "plot(line_range,eigenvector_1,\"linewidth\",10);\n",
    "plot(line_range,eigenvector_2,\"linewidth\",10);\n",
    "# Isoclines plot\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\");\n",
    "grid on;\n",
    "axis tight;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symbolic pkg v2.7.1: Python communication link active, SymPy v1.3.\n",
      "ode_sys = (sym 2×1 matrix)\n",
      "\n",
      "  ⎡d                          ⎤\n",
      "  ⎢──(x₁(t)) = 2⋅x₁(t) + x₂(t)⎥\n",
      "  ⎢dt                         ⎥\n",
      "  ⎢                           ⎥\n",
      "  ⎢d                          ⎥\n",
      "  ⎢──(x₂(t)) = x₁(t) + 2⋅x₂(t)⎥\n",
      "  ⎣dt                         ⎦\n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "              3⋅t       t\n",
      "  x₁(t) = C₁⋅ℯ    + C₂⋅ℯ \n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "              3⋅t       t\n",
      "  x₂(t) = C₁⋅ℯ    - C₂⋅ℯ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "pkg load symbolic\n",
    "syms x1(t) x2(t);\n",
    "ode_sys = [diff(x1(t),t) == A(1,1)*x1(t) + A(1,2)*x2(t);  diff(x2(t),t) == A(2,1)*x1(t) + A(2,2)*x2(t)]\n",
    "solutions = dsolve(ode_sys);\n",
    "solutions{1}\n",
    "solutions{2}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercice 2\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} -1 & -1 \\\\ 1 & -1 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer les valeurs propres et vecteurs propres et en déduire le type du système\n",
    "2. Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "3. Associer les signes des portions du plan délimitées par les isoclines.\n",
    "4. Tracer des trajectoires qualitativement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "  -1  -1\n",
      "   1  -1\n",
      "\n",
      "V =\n",
      "\n",
      "   0.70711 + 0.00000i   0.70711 - 0.00000i\n",
      "   0.00000 - 0.70711i   0.00000 + 0.70711i\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "  -1 + 1i        0\n",
      "        0  -1 - 1i\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. - Calcul valeur propres et vecteurs propres\n",
    "A = [-1 -1; 1 -1]\n",
    "[V,L] = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tr(A) = -2\n",
      "det(A) = 2\n",
      "Tr(A) > 4*det(A)? = 0\n"
     ]
    }
   ],
   "source": [
    "printf(\"Tr(A) = %d\\n\",trace(A));\n",
    "printf(\"det(A) = %d\\n\",det(A));\n",
    "printf(\"Tr(A) > 4*det(A)? = %d\\n\",(trace(A) > 4*det(A)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAAsTAAALEwEAmpwYAAAAHXRFWHRTb2Z0d2FyZQBHUEwgR2hvc3RzY3JpcHQgOS4xNnO9PXQAABuqSURBVHic7d2/a1xnuy7gV4fUNmqDxQEVO4XUCQwKpDEOSHWQ3OzCKuxwiuBCgbhy4coBC9JKKtycysJuThGD50s5Ax9MZxdxIdhInNbY/4B2sbInK7I0Gs2sNev9cV3FxpY12jOez7rz3M+rtRbOzs4CAHTtf3X9BAAgBIEEQCQEEgBREEgAREEgARCFr2Z8/Js3b96/f7+7u1v/4O3bt1dWVkIIq6ur5/4IAC40UyDt7Oz0+/2HDx/WP3h6erqysvLixYvZnhgAZZmpsnvx4sW5NAohnJyc3Lx588mTJ3t7e58/f57l6wNQjuZ3SJ8+fVpaWtrc3Lxx48bOzs6Fn7Pw8x+N//8FIAYftr6e7oHNB9LGxsbu7u76+vqDBw8u/ISFn//4j//3fxZ+/mPhfzT+HADoRJVG02VS84F0eHg4GAzGfMLZ8zt//Wr3X2H3X65dBJCBD1tfj3LoP47+/xRfYdZTdnWDweD+/fuvX79+9OjR5ubmu3fv7t27d+WjFn7+4++IAiBBM0ZRZaGlAWUwGCwtLd26devCP/3mm2/+/PPPUFsmySSARDWSRqG9QBpvFEhBJgGkrKk0CjEEUvjnoTuxBJCE+smF2dMoRBJIfz0VoxJAIhocjEYiupbdKIf8lBJAzNpIoxDVhFRR3wFEq/Gari6iCalSDyGjEkA86oNR42kUIgykEMLZ8zvqO4CotFTT1cUYSBWZBBCJOaRRiHCHdI6VEkCHWl0anRN7IFWcCAeYv/kMRiPxVnZ16juAOZtzGoVUJqSK+g5gDuZZ09WlFEgV9R1Ae+Y/GI2kUdnVqe8AWtJhGoUUAynIJICmzX57vdklGUjhn5kklgBm0dXS6Jz0dkjnWCkBzKLzwWgk1QlpRH0HMLV40ihkMCFVnAgHuJZIarq6TAKpor4DmERUg9FI8pVdnfoO4EpxplHIbEKqqO8ALhRhTVeX1YRUcYs/gC9FnkYhywlpxEoJoBJtTVeX4YQ0YqUEEBJJo5D3hFSxUgKKFX9NV5d/IFXUd0BpUhmMRnKu7OrUd0BRkkujUM6EVFHfAdlLq6arK2VCqjgRDuStPhillUahtEAKIZw9v6O+A7KUYk1XV1wgVWQSkJnU0yiUtkM6x0oJyEC6S6Nzig6kihPhQLoyGIxGCq3s6tR3QKJySqNgQhpR3wEJyaamqzMh/cWJcCAVSZ/tHkMg/c2JcCB+mdV0dQLpPJkERCvjNAp2SJexUgKikuXS6ByBNI4T4UAM8h6MRlR246jvgM4VkkbBhDQJ9R3QiRJqujoT0tWcCAfmL9ez3WMIpIk4EQ7MUzk1XZ1AugaZBLTtw9bXZaZREEjXVc8ksQQ0q7Sl0TkONUzJiXCgWcUORiMmpCmp74AGSaNgQpqRE+HAjAqv6eoEUgPUd8B0DEZ1KrsGqO+AKUijcwRSM2QSMLmSz3aPIZAa40Q4MAlLo8vYITXPSgm4jMFoDBNS89R3wIWk0XgmpLY4EQ6MqOkm0daE9ObNm729vZa+eBJcjxWoFHjd7um0Ekg7OzuPHj1q4ysnRyZB4dR0k2ursqvGo93d3Qv/tITKrk59BwVS012XQw3z4BZ/UBppNIXOAmmhpqvnME9WSlAOS6PpdBZIZzVdPYf5k0mQPUujqans5s0FHSBXLgg0Iz+H1BkXdICciKLZmZA6o76DbEijRpiQOuZEOCTNaboGmZA65kQ4pEsaNcuEFAsrJUiLmq5xJqRYWClBQqRRG0xIcbFSgsip6dojkGKkvoM4GYxapbKLkfoOIiSN2mZCipf6DiKhppsPE1K8nAiHGLhS6twIpKi5Rjh0S003TwIpATIJ5s+VUudPIKXBNcJhniyNOuFQQ2KcCIe2GYy6YkJKjPoOWiWNOmRCSpIT4dA4NV3nBFLC1HfQFINRDFR2CVPfQSOkUSQEUtpkEszC2e6oCKTkOREO07E0io0dUj6slGByBqMImZDyob6DCUmjOJmQcuNEOIyhpouZQMqT+g6+ZDCKnMouT+o7OEcaxU8gZUsmQcXZ7lQIpJw5EQ6WRgmxQyqClRJlMhilxYRUBPUdBZJGyTEhFcSJcAqhpkuUQCqO+o68GYzSpbIrjvqOjEmjpJmQCqW+IzNqugyYkApVDyGjEqmTRnkwIZXOSonUqemyYUIqnZUSSZNGOTEhEYKVEglS0+VHIPE39R2pMBhlSWXH39R3JEEa5cqExHnqO6KlpsubCYnznAgnTtIoeyYkLmWlRDzUdCUwIXEpKyUiIY0KYULiClZKdEhNVxSBxETUd8yfwag0Kjsmor5jzqRRgUxIXIP6jjlQ0xXLhMQ1OBFO2+qDkTQqjUDies6e31Hf0RI1XeEEEtOQSTTrw9bX0giBxJTqmSSWmIWlERWHGpiVE+HMwmDEiAmJWanvmJo0os6ERDOcCOda1HR8SSDRJPUdkzAYcSGVHU1S33ElacRlBBINk0lcxtluxpupstvb2+v3+yGEp0+frqysjD5++/bt6rerq6u7u7tfPlBllz0rJc6xNOJKX039yMFgcHJy8urVq8FgcHh4+Ntvv1UfPz09XVlZefHiRUPPkCRVIVTF0sLPf8ikwhmMmMT0lV2/36/GoPX19WpOqpycnNy8efPJkyd7e3ufP39u4DmSLPUdQRoxsZl2SKurq9Uv6n3dp0+flpaWNjc3b9y4sbOzM9OzI30u6FAySyOuZfrKLoRwcnKyvr4eQnj//v3ogxsbGxsbGyGE9fX1N2/eXPbYhYWF0a87OXrO3KjvyiSKuK7pJ6SVlZWTk5MQwunp6dLS0ujjh4eHg8Hgyoef1Uz9HEiI+q4o0ogpTD8hbWxsHB4ehhD6/f6DBw9CCIPB4P79+69fv3706NHm5ua7d+/u3bvX2DMlfWfP74zmpOD0XaacpmNqs16pYTAYLC0t3bp1a8KPVxz7LpkT4RmTRszCpYPohosM5UdNx4xcqYFuWCllRhoxOxMSXVLfZUBNR1MEEt1T36XLYESDVHZ0T32XKGlEs0xIxEJ9lxA1HW0wIRGLeggZlWImjWiJCYnoWCnFTE1He0xIRMdKKVrSiFaZkIiUlVJU1HTMgUAiauq7GBiMmA+VHVFT33VOGjE3JiQSoL7rhJqOOTMhkQAnwuevPhhJI+ZDIJGGs+d31Hdzo6ajEwKJlMikOZBGdMUOifRYKbXE0ohuCSRS5UR4swxGdE5lR6rUdw2SRsTAhETa1HczUtMRDxMSaXMifBbOdhMVgUTynAifjpqO2AgkMiGTJvdh62tpRIQEEvmoZ5JYuoylEdFyqIEMORF+GYMRMTMhkSH13YWkEZEzIZEtJ8JH1HQkQSCROfWdwYhUqOzIXOH1nTQiIQKJ/JWZSc52kxyBRBFKOxFuaUSK7JAoSwkrJYMRiTIhUZbs6ztpRLpMSJQoyxPhajpSJ5AoV071ncGIDKjsKFc29Z00Ig8mJEqXdH2npiMnJiRKl+4t/qQRmTEhwV/SWimp6ciPCQn+ktBKSRqRJRMS/EPkKyU1HRkTSHCBOOs7gxF5U9nBBSKs76QR2TMhwaUiqe/UdBTChASXiuFEuDSiHCYkuFpXKyU1HUUxIcHVOlkpSSNKY0KCSc1tpaSmo0wCCa6n7frOYESxVHZwPa3Wd9KIkpmQYBqN13dqOjAhwTSaPRFeH4ykEcUSSDCls+d3Gqnv1HRQEUgwkxkzSRrBiB0SNGCKlZKlEZwjkKAxk58INxjBl1R20JgJ6ztpBBdqZULa29vr9/shhKdPn66srHz5CSYkMjamvlPTwRjNT0iDweDk5OTVq1c///zz4eFh418fInfZ6Ttnu2G85gOp3+9XU9H6+no1J0GBzmWSmg6u1MoOaXV1tfrFhX0dFKLKpD//6z+lEUyilUA6OTmpfvH+/fvLPmehpo3nADH487/+c/Trb/73/+3wmUD8mg+klZWVKpBOT0+XlpYu+7SzmsafA8SgPhhVadTVbWchCa2csvvhhx++/fbbfr//4MGDjY2NLz/BKTuy92VN19VtZyEVbf1g7GAwWFpaunXr1oV/KpDI2Jiz3XO7xR+kyJUaoEmTnF8wKsGFXKkBGjPhabpWb/EH6TIhQQOmuASD+g7OMSHBrKa7IFCzt/iDDJiQYCaz/9CrlRJUTEgwvUYuwWClBBUTEkyj8et2WymBQIJra+/adOo7Sqayg+tp9Uqp6jtKZkKCSc3t9nrqO8pkQoKJzPP2ek6EUyaBBFeb/w2NLrvtLGRMIME4H7a+7vD2ejKJoggkuNTclkZj1DNJLJE3hxrgYrHdd9yJcLJnQoILxJZGQX1HAUxI8A8x1HRjOBFOxgQS/C3CwehC6juypLKDv6SSRkF9R6YEEnR8tns6Mon8CCRKF/nSaAwnwsmMHRJFS24wupCVEnkwIVGuPNIoqO/IhQmJEqVb043hRDipE0gUJ5vB6ELqO9KlsqMseadRUN+RMoFEKVI82z0dmUSiBBJFyHJpNIYT4aTIDon8FTIYXchKiYSYkMhcyWkU1HckxYREtkqr6cZwIpwkCCTyVPhgdCH1HZFT2ZEhaXQh9R2RMyGRFTXdldR3RMuERD6k0STqIWRUIiomJDKhprsuKyViY0IiB9JoClZKxMaERNrUdDOyUiIeAomEGYyaor4jBio7UiWNGqS+IwYmJNKjpmuJ+o5umZBITH0wkkbNciKcbgkkUqKma9vZ8zvqO7oikEiGNJobmUQn7JBIgKVRJ6yUmDOBROwMRt1yIpy5UdkRNWnUOfUdc2NCIlJquqio75gDgUSMDEZxUt/RKpUd0ZFG0VLf0SqBREQ+bH0tjSInk2iPQCIWlkapqGeSWKJBdkhEwWCUIislmmVConvSKFHqO5plQqJLaroMOBFOUwQSnTEY5UR9x+xUdnRDGmVGfcfsZpqQ9vb2+v1+COHp06crKyujj9++fbv67erq6u7u7pcPNCGVTE2XMXMSs/hq6kcOBoOTk5NXr14NBoPDw8Pffvut+vjp6enKysqLFy8aeoZkRRrl7ez5nSqTqv8rlriW6Su7fr9fjUHr6+vVnFQ5OTm5efPmkydP9vb2Pn/+3MBzJBdu9loCt/hjajPtkFZXV6tf1Pu6T58+LS0tbW5u3rhxY2dnZ6ZnR0YsjYoik5jCpDukly9f/v7776Pfbm5unpycLC0tbW9vhxBu377973//+8tH/fDDD69evfry4998882HDx9Gv+3kpB9zo6YrlhPhXMukO6Tt7e0qe0bevHnz/v37EMLp6enS0tLo44eHh6urq+vr6+O/oBAqhMGoZFUIjbZKMonxpj/UsLGxcXh4GELo9/sPHjwIIQwGg/v3779+/frRo0ebm5vv3r27d+9eY8+UBEkjwj9POsgkxpj1B2MHg8HS0tKtW7cm/HjFse/sqek4R33HlVypgeZJIy4kkxhPINEwNR3j+eFZLuPSQTRJGnElJ8K5jAmJZqjpuBb1HV8SSDTAYMR01HfUqeyYlTRiauo76kxITE9NRyPUd1RMSExJGtGUeggZlUpmQmIaajraYKVUOBMS1yaNaImVUuFMSFyDmo45sFIqlkBiUgYj5kl9VyCVHRORRsyZ+q5AJiSuoKajQ+q7opiQGKc+GEkj5s+J8KIIJC6lpiMGZ8/vqO8KIZC4mDQiKjKpBHZInGdpRLSslPImkPgHgxHxcyI8Vyo7/iaNSIL6LlcmJEJQ05Eg9V1+BBIGIxKmvsuJyq500oikqe9yIpDK9WHra2lEBmRSNgRSoSyNyEk9k8RSuuyQSmQwIldWSkkzIRVHGpEx9V3STEgFUdNRCCfCEyWQSmEwojTqu+So7IogjSiQ+i45AilzznZTMpmUFoGUM0sjcCI8IXZI2TIYQZ2VUvxMSHmSRnCO+i5+JqTcqOlgDCfCYyaQsmIwgkmo7+KkssuHNIIJqe/iZELKgZoOpqC+i40JKXnSCKZTDyGjUgxMSGlT08HsrJQiYUJKmDSCRlgpRcKElCQ1HTTOSqlzAik9BiNoj/quQyq7xEgjaJX6rkMmpGSo6WBu1HedMCGlQRrBPDkR3gkTUgLUdNAVK6V5MiHFThpBh6yU5smEFC81HUTCSmk+BFKkDEYQG/Vd21R2MZJGECH1XdtMSHFR00Hk1HftMSFFpD4YSSOIkxPh7RFIsVDTQSrOnt9R37VBIEVBGkFyZFLj7JA6ZmkESbNSapBA6pLBCPLgRHgj2qrs3rx5s7e319IXz4M0gmyo7xrRSiDt7Ow8evSoja+chw9bX0sjyEw9k8TSdNqq7KrxaHd398I/LbmyE0WQN/Xd1JyymytpBNlT303tq9m/xMuXL3///ffRbzc3N7e3t6981MLCwujXnRysmD9pBIU4e36nSqOFn/8wJ02ugUDa3t6eJIHOKSSEKs52Q2nqmRTUd5NR2bXOBYGgTC7ocF1+DqldajrAMYcJCaS2qOmAERd0mIRAaoXBCPiSUWk8O6TmSSPgQlZK45mQmqSmA66kvruMCakx0giYhFv8XcaE1Aw1HXBdVkrnmJAaII2AKVgpnWNCmomaDpiRldKIQJqewQhoivouqOymJo2ABqnvgglpCmo6oCWF13cmpOuRRkB7Cj8RbkK6BjUdMB9lrpRMSJOSRsDclLlSMiFdTU0HdKK0lZJAuoLBCOhWOfWdym4caQR0rpz6zoR0MTVdrhYWFrp+CvPTyb9uWlJCfWdCuoA0yttZGbr+a6ZhJZwINyGdp6bL28JCN/+bn79yXmlpMl4pmZD+QRoBkct4pWRC+ouarhDlzA3lvNIyZblSEkghGIxKUs636XJeackyq+9UdtKItvR6vePj4+t+/nUfRckyq++KDqQPW19LI9qzvLy8uLg4+edXUXTdR1G4eialHktfdf0EOiOKaFuv11tbWwshHBwchBDW1ta2trYeP34cQlhcXHz27NnHjx8fP35cxc+zZ8/qjxoOhyGE4+Pj4+Pj/f39xcXFx48ff/z4sfpMiUXd2fM7oyha+PmPdOu7QickacQcHB8ff/z48ejoaGtra39///j4+ODgYHl5eX9/P4RwcHBwcHCwtrZWRdGopqsedXx8PBwOnz17dvfu3YODg19//XVxcXF/f395ebmKN6g7e34ng/quxAlJGjHS7D/dC//LtJqKDg4Otra2Dg4OqjS6e/dur9cbDodv374NtfGorhqDlpeXe73ex48fh8Nh9Yu7d++GEI6OjqrEavD5k7rRqJTonFRWIDnbzTlz+Ec7HA5fvnwZQvj++++/++674XC4vLxclW/Ly8vD4XBtba0alcZ8kcXFxV9++WVra6sq8aoRqu1nTorqmRRSO31XUCAZjOjE4uLijz/+WB1V+Omnn7a3t4fD4dHR0du3b6sdUrUx2traGvNFHj58WD1wOBxWK6W1tbVerze3V0FCqhBKcVQq5eeQpBGVTn46p5ppRjNQr9erarcQQtXFjX47Xv2BvV6v1+uNqez8HBLJ/ZRS/oGkpqMum2/TAolJpHVBh8wDyWDEOeV8my7nlTJeQpmU87FvaQSQ0InwbANJGgGMJJFJGVZ2lkaMUU6RVc4rZXKR13e5BZLBiPHK+TZdzivluqI9fZdVZSeNAK4UbX2XyYSkpmNC5cwN5bxSphNhfZdDIBmMmFw536bLeaXMIqr6LvnKThoBTC2q+i7hQHJ7PYDZxZNJqQaSpRFAUyK57WySgVQfjKQR0apuSX7dz7/uo6ARMVzQIb1AUtORiuqWE5N/fhVF130UNKjbTErpfkhqOtLS6/WqW05UNx1fW1ur7h4bQlhcXHz27Fl1P6QqfkbX7a4eNRwOQwjV7fiqGyA9fvy4uq3fs2fPJBbt6fAWf8lMSGo6klPdBuno6Ghra2t/f//4+Pjg4GB5ebm6i/nBwUF1o9gqikY13eiGsNUdyu/evXtwcPDrr78uLi7u7+8vLy9X8Qbt6aq+S2NCUtPRkvrYPbsL//dZTUUHBwdbW1sHBwdVGt29e7fX6w2Hw7dv34baeFRXjUHLy8u9Xq+6j1/1iwnv5gczqo9K85mTYg8kNR2tmsP/qIbD4cuXL0MI33///XfffTccDpeXl6vybXl5eTgcrq2tVaPSmC+yuLj4yy+/bG1tVSXe0dHR0dFRCGFra2v8vc9hFnOu76IOJGlEBhYXF3/88cfqqMJPP/20vb09HA6Pjo7evn1b7ZCqjdH4XHn48GH1wOFwuL+/f3R0VIXc9va2QKJVo0wK7Y9K8V46SE1HGzq5oE61FhrNQL1eb1S7VV3chC1c/YHHx8e//vrrw4cPLxutXDqIZs3hIkORBpI0oiV5fJvu9Xq9Xu+XX34Zc9wuj1dKVNrOpOgCSU1Hq/L4Nr29vV1toUaH9L6UxyslNq1eIzyuQDIY0bZyvk2X80qZv5ZGpYh+DkkaASShpZ9SimJCUtMxN+XMDeW8UrrSeH3X/YRU1CUYFhYWun4KnfHay+S1Z6weQvVwmvqFz/rfUG/evHn//v3u7m79g7dv315ZWQkhrK6unvujymhCKq2mK/k/WiN57dl/j6iL5C88hqfRiXJe+7mV0tQvfKYfjN3Z2en3+w8fPqx/8PT0dGVl5cWLF1c+vLQ0IgadfIMo5xsTZWrqIkMzVXYvXrw4l0YhhJOTk5s3bz558mRvb+/z58+XPVYaAWTjH8ccdv813Rdpfof06dOnpaWlzc3NGzdu7OzsfPkJRS2NAAox+zXCJ20SXr58+fvvv49+u7m5ub29HULY29sLIVy4KAoh/PDDD69evfry4998880UzxWAJFx5cbgLTbpD2t7erhLoSoeHh6urq+vr62M+Z7rnCkDGmrza92AwuH///uvXrx89erS5ufnu3bt79+41+PUByFhbh38Gg8HS0tKtW7fa+OIA5MdpVACi0P2VGgAgzP+OsdNd2SE/F/495Gpvb6/f74cQnj59Wr3RlULe98tefpbGvNhC3u6Rov6Nh4a+t881kGa8skM2Lvx7yNVgMDg5OXn16tVgMDg8PPztt9+qjxfyvl/28rM05sUW8naPFPVvPDT3vX2uld0sV3bIyYV/D7nq9/vVfyKtr69X/+1cKeR9v+zlZ2nMiy3k7R4p6t94aO57e/c7pCuv7EDqVldXq1/UO5xy3vcLX36uLnux5bzdjEzxprdV2V12ZYcvbWxsbGxshBDW19ffvHnT0vPpyuR/D3n48vWGEE5OTqoflH7//v3oj/J+3+sufPm5uuzFlvN2MzLFm95WIDV7ZYd0Tf73kIcvX2+16gwhnJ6eLi0tjT6e9/s+srKycuHLz9KYF1vI203dFG/6vE/Z1bmyQwk2NjYODw9DCP1+/8GDB9Wb/ueff3777bclvO/nXn7XT6ddX77Y0t5uKlN/b4/lB2Nd2SFvl72/hbzvhbzMypgXW9TfA5VrvemxBBIAhev+lB0ABIEEQCQEEgBREEgAREEgARCF/wbh1Jki5MMl8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2.Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "line_range = -1.5:.1:1.5;\n",
    "isocline_1 = -(A(1,1)/A(1,2)) * line_range;\n",
    "isocline_2 = -(A(2,1)/A(2,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,isocline_1,\"linewidth\",5);\n",
    "plot(line_range,isocline_2,\"linewidth\",5);\n",
    "legend(\"isocline_1\",\"isocline_2\",\"location\",\"south\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "point_sequence = [line_range;isocline_1];\n",
    "point_sequence = horzcat(point_sequence,[line_range;isocline_2]);\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec;\n",
    "    velocity_sequence = [velocity_sequence,velocity_vec];\n",
    "endfor\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\");\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\");\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-3:.1:3;\n",
    "x2range=-3:.1:3;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Trajectory plot\n",
    "sys_str = sprintf('[%d*x(1)+%d*x(2);%d*x(1)+%d*x(2)]',A(1,1),A(1,2),A(2,1),A(2,2));\n",
    "sys_ode = inline(sys_str,'t','x');\n",
    "for x_0=0:0.1:1\n",
    " [ts,ys] = ode45(sys_ode,[0,10],[0;x_0]);\n",
    " plot(ys(:,1),ys(:,2))\n",
    "end\n",
    "# Isoclines plot\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\",\"linewidth\",5);\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\",\"linewidth\",5);\n",
    "grid on;\n",
    "axis tight;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ode_sys = (sym 2×1 matrix)\n",
      "\n",
      "  ⎡d                         ⎤\n",
      "  ⎢──(x₁(t)) = -x₁(t) - x₂(t)⎥\n",
      "  ⎢dt                        ⎥\n",
      "  ⎢                          ⎥\n",
      "  ⎢d                         ⎥\n",
      "  ⎢──(x₂(t)) = x₁(t) - x₂(t) ⎥\n",
      "  ⎣dt                        ⎦\n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "                                    -t\n",
      "  x₁(t) = (-C₁⋅cos(t) - C₂⋅sin(t))⋅ℯ  \n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "                                    -t\n",
      "  x₂(t) = (-C₁⋅sin(t) + C₂⋅cos(t))⋅ℯ  \n",
      "\n"
     ]
    }
   ],
   "source": [
    "pkg load symbolic\n",
    "syms x1(t) x2(t);\n",
    "ode_sys = [diff(x1(t),t) == A(1,1)*x1(t) + A(1,2)*x2(t);  diff(x2(t),t) == A(2,1)*x1(t) + A(2,2)*x2(t)]\n",
    "solutions = dsolve(ode_sys);\n",
    "solutions{1}\n",
    "solutions{2}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercice 3\n",
    "\n",
    "$ \\mathbf{A} = \\begin{bmatrix} -2 & 0 \\\\ -4 & -2 \\end{bmatrix} $ \n",
    "\n",
    "1. Calculer les valeurs propres et vecteurs propres et en déduire le type du système\n",
    "2. Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "3. Associer les signes des portions du plan délimitées par les isoclines.\n",
    "4. Tracer des trajectoires qualitativement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "  -2   0\n",
      "  -4  -2\n",
      "\n",
      "V =\n",
      "\n",
      "   0.00000   0.00000\n",
      "   1.00000   1.00000\n",
      "\n",
      "L =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "  -2   0\n",
      "   0  -2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 1. - Calcul valeur propres et vecteurs propres\n",
    "A = [-2 0; -4 -2]\n",
    "[V,L] = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tr(A) = -4\n",
      "det(A) = 4\n",
      "Tr(A) > 4*det(A)? = 0\n"
     ]
    }
   ],
   "source": [
    "printf(\"Tr(A) = %d\\n\",trace(A));\n",
    "printf(\"det(A) = %d\\n\",det(A));\n",
    "printf(\"Tr(A) > 4*det(A)? = %d\\n\",(trace(A) > 4*det(A)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dessiner les droites correspondants aux vecteurs propres et le sense des trajectoires associés\n",
    "line_range = -1.5:.1:1.5;\n",
    "eigenvector_1 = (V(2,1)/(V(1,1)+1e-170)) * line_range;\n",
    "eigenvector_2 = (V(2,2)/(V(1,2)+1e-170)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,eigenvector_1,\"linewidth\",10);\n",
    "plot(line_range,eigenvector_2,\"linewidth\",10);\n",
    "quiver([0;0],[0;0],V(1,:),V(2,:),\"linewidth\",10,\"color\",\"k\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2.Calculer les isoclines et dessiner des vecteurs vitesse sur ces isoclines\n",
    "line_range = -1.5:.1:1.5;\n",
    "isocline_1 = -(A(1,1)/(A(1,2)+1e-170)) * line_range;\n",
    "isocline_2 = -(A(2,1)/A(2,2)) * line_range;\n",
    "hold on;\n",
    "plot(line_range,isocline_1,\"linewidth\",10);\n",
    "plot(line_range,isocline_2,\"linewidth\",10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "point_sequence = [line_range;isocline_1];\n",
    "point_sequence = horzcat(point_sequence,[line_range;isocline_2]);\n",
    "velocity_sequence = [];\n",
    "for point_vec = point_sequence # Column-wise iteration\n",
    "    velocity_vec = A*point_vec;\n",
    "    velocity_sequence = [velocity_sequence,velocity_vec];\n",
    "endfor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hold on;\n",
    "quiver(point_sequence(1,:),point_sequence(2,:),velocity_sequence(1,:),velocity_sequence(2,:),0.2,\"linewidth\",5,\"color\",\"k\");\n",
    "plot(point_sequence(1,:),point_sequence(2,:),\"ok\");\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Define grid for plotting\n",
    "x1range=-1.5:.1:1.5;\n",
    "x2range=-1.5:.1:1.5;\n",
    "[x1,x2] = meshgrid(x1range, x2range);\n",
    "\n",
    "# Define the system to plot (based on matrix A)\n",
    "x1p = A(1,1)*x1+A(1,2)*x2;\n",
    "x2p = A(2,1)*x1+A(2,2)*x2;\n",
    "\n",
    "#Normalize values for plotting\n",
    "arrow=sqrt(x1p.^2+x2p.^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vector field plot\n",
    "hold on;\n",
    "quiver(x1,x2,x1p./arrow,x2p./arrow,0.5);\n",
    "# Eigenvectors plot\n",
    "plot(line_range,eigenvector_1,\"linewidth\",10);\n",
    "plot(line_range,eigenvector_2,\"linewidth\",10);\n",
    "# Isoclines plot\n",
    "plot(line_range,isocline_1,\"linestyle\",\":\",\"color\",\"k\");\n",
    "plot(line_range,isocline_2,\"linestyle\",\":\",\"color\",\"k\");\n",
    "grid on;\n",
    "axis tight;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ode_sys = (sym 2×1 matrix)\n",
      "\n",
      "  ⎡     d                       ⎤\n",
      "  ⎢     ──(x₁(t)) = 2⋅x₁(t)     ⎥\n",
      "  ⎢     dt                      ⎥\n",
      "  ⎢                             ⎥\n",
      "  ⎢d                            ⎥\n",
      "  ⎢──(x₂(t)) = 4⋅x₁(t) + 2⋅x₂(t)⎥\n",
      "  ⎣dt                           ⎦\n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "              2⋅t\n",
      "  x₁(t) = C₂⋅ℯ   \n",
      "\n",
      "ans = (sym)\n",
      "\n",
      "                           2⋅t\n",
      "  x₂(t) = (4⋅C₁ + 4⋅C₂⋅t)⋅ℯ   \n",
      "\n"
     ]
    }
   ],
   "source": [
    "pkg load symbolic\n",
    "syms x1(t) x2(t);\n",
    "ode_sys = [diff(x1(t),t) == A(1,1)*x1(t) + A(1,2)*x2(t);  diff(x2(t),t) == A(2,1)*x1(t) + A(2,2)*x2(t)]\n",
    "solutions = dsolve(ode_sys);\n",
    "solutions{1}\n",
    "solutions{2}\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "4.4.1"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}