{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ac82d980",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c9d89e5",
   "metadata": {},
   "source": [
    "# Lecture 4: Solving differential equations\n",
    "Attendance code: EY-XB-CJ"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9d31a2b",
   "metadata": {},
   "source": [
    "## The logistic equation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7661b0a3",
   "metadata": {},
   "source": [
    "A 1D differential equation:\n",
    "$$\n",
    "\\frac{dx}{dt} = x (1 - x) .\n",
    "$$\n",
    "For each initial value $x_0$, there is a solution $x(t)$. This is a function of time called an *integral curve* of the differential equation.\n",
    "\n",
    "This equation can be solved in closed form by separation of variables.\n",
    "\n",
    "Let's look at using <code>solve_ivp()</code> to obtain numerical solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "37ada893",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 100)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b226868620>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def dxdt(t, x):\n",
    "    return x*(1-x)\n",
    "\n",
    "x0 = 0.5  # initial value\n",
    "ts = np.linspace(0, 6, 100)\n",
    "sol = solve_ivp(dxdt, (ts[0], ts[-1]), [x0], t_eval=ts)\n",
    "print(sol.y.shape)\n",
    "plt.plot(sol.t, sol.y[0], '-' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "440e16ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0s = np.linspace(0, 2, 20)\n",
    "for x0 in x0s:\n",
    "    sol = solve_ivp(dxdt, (ts[0], ts[-1]), [x0], t_eval=ts)\n",
    "    plt.plot(sol.t, sol.y[0], '-' )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21cdbf47",
   "metadata": {},
   "source": [
    "## The van de Pol equation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45cd3740",
   "metadata": {},
   "source": [
    "This a **second-order** 1D autonomous non-linear ODE:\n",
    "$$\n",
    "\\ddot{x} - a (1 - x^2) \\dot{x} + x = 0\n",
    "$$\n",
    "with one parameter, $a \\ge 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "453a7810",
   "metadata": {},
   "source": [
    "Before we can use <code>solve_ivp()</code> we must reduce higher-order ODEs to a **set** of first-order equations, by introducing new variable(s).\n",
    "\n",
    "In this case, it is straightforward. We define a new variable $y = \\dot{x}$. Then\n",
    "\\begin{align}\n",
    " \\dot{x} &= y \\\\\n",
    " \\dot{y} = \\ddot{x} &= a(1-x^2) y - x\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "05ec5dc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Z = [x, y]\n",
    "def dZdt(t, Z, a=1):\n",
    "    x, y = Z\n",
    "    return [ y , a*(1 - x**2)*y - x ]\n",
    "\n",
    "ts = np.linspace(0,20, 1500)\n",
    "ic = [0.5, 0]\n",
    "sol = solve_ivp( dZdt, (ts[0],ts[-1]), ic, t_eval=ts, args=(4,) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4b9a8930",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 't')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts, sol.y[0], '-')\n",
    "plt.plot(ts, sol.y[1], '-')\n",
    "plt.xlabel('t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5104f8c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kezjDrKmxB66pIXIzV64AhQvr5127Ar/8oiwcIqcqWlTqLgFSrsCNd/e53ZoaIiIr585ZJzT/+x8TGvIs+/bpx88+qy4OF8KkhoiM5/BhIDRUPx89Ghg5Ul08RCoUKgSUKyfHBw4A166pjccFMKkhImPZtk0WAltMnw4MHKguHiKVtm7Vj2vXVheHi2BSQ0TGsWqV9R/uxYuBbt2UhUOknNkMVKkixydPAjduKA1HNSY1RGQMc+YAzZrp5+vWSW8nIk+3dq1+3KCBsjBcAZMaInJ9EycCHTvq53v2sFMxkYXZDJQtK8cHDnj0aA2TGiJybcOHA3366OcnT+rD7UQkNmzQj5s3VxeHYkxqiMh19ekDDBmin0dFAaVKqYuHyFUVKgSEhMjx9u1AbKzaeBRhUkNErqldO5l2srhxAwgOVhcPkavbvFk/7txZXRwKGab3ExF5kFq15NOmxe3bQK5c6uIhMoLixYGcOYHERGDJEiAhAfDxUR2VU3Gkhohch6YBQUHWCU1CAhMaIlvt368fe2D9JiY1ROQaNA3w8gIuXdKvS06WT55EZBtLhWEAGD8eSElRF4sCTGqISL3EREloLPLmlT/GXvwTRZRpmzbpx99+qy4OBfgXg4jUun3bet7/6adlUbDJpC4mIiN75hn9+KOP1MWhAJMaIlLn2jUgTx79/KWXgF271MVD5C5+/10/XrpUXRxOxqSGiNQ4exYoWFA/f+89YMECdfEQuZMOHfRjD2onwqSGiJzvwAGgRAn9/OuvgXHjVEVD5H5MJuCTT/Tz1Lui3BiTGiJyrg0bgEqV9PMZMzxu3p/IKT7/XD+uUUNdHE7EpIaInGfRIutGlCtWAF26qIuHyJ35+ACtWslxQgJw9araeJyASQ0ROceUKbIQ2GLrVqBFC3XxEHmCGTP0Yw9oncCkhogcb9gwoFcv/fzoUWmFQESOVaAA4O8vx3/9BSQlqY3HwZjUEJFj9ewJDB2qn1+4AJQtqywcIo+zZYt+PHq0ujicwKRpmqY6CGeJjY2F2WxGTEwMAgMDVYdD5P6eew5Yt04/v3kTMJtVRUPkuVIXszTg276t798cqSEi+9M0oEgR64Tm7l0mNESqpF5bs2GDujgcjEkNEdlXUpL0bLp8Wb8uORnw81MXE5GnS71IOPUORDfDpIaI7OfWLeuu2sHBbExJ5ApMJuDVV/XzK1fUxeJA/EtDRPYRFQUEBOjnLVrIdWxMSeQaJk3Sjzt1UheHAzGpIaLs278fKFZMPx84UArrEZHrMJuB3LnlOCLCLbd3M6khouz5+2+gcmX9fPJkt982SmRYqRfvT5miLg4HYVJDRFk3YQLQvLl+vmIF8Pbb6uIhovRVq6Yf9+2rLg4HYVJDRFnzzjvWfxT37mXbAyIjCA/Xj48dUxeHA7D4HhFlXpUqwL59+nlUlOx0IiLXl5gozS4BoEQJ4PRppeHYwtb37xxOjImIjC45GcjxwJ+N27eBXLnUxENEmZczJ1CpkizwP3NGOnhbkhyD4/QTEdkmJsY6ofHxkRo0TGiIjGfJEv14xAh1cdgZkxoiytiJE0DevPp506ZAfDxr0BAZVWiofjxsmLo47IxJDRGl7++/gTJl9PNPPwVWrVIXDxHZR+ot3Xv3KgvDnpjUENGjff219ZbtuXOBL75QFw8R2U/37vpx06bq4rAjLhQmorQ1bQr8849+vmeP7HoiIvfg7Q3UqQNs2QJcvSpTyr6+qqPKFo7UEJG1pCRZK5M6oblyhQkNkTuaM0c/doMFw0xqiEh3+bJ1l21AkpyCBdXEQ0SOFRKiHw8fri4OO2FSQ0Ri61agSBH9vFkzQNNkiJqI3NfEifrxkSPq4rADwyQ14eHhqFGjBgICAlC4cGG8+OKLOOZm5Z2JlBk3TubWLUaNAv76S1k4ROREb72lH7/wgro47MAwSc26devQp08fbN26FREREUhKSkJYWBhu376tOjQiY6tfHxgwQD9fswb44AN18RCRc3l7A2XLyvHJk1I53KAM2/vpypUrKFy4MNatW4f69evbdB/2fiJK5c4dIHdu6+suXgSCgtTEQ0TqHD0KPPmkHE+aBPTqpTaeB9j6/m2YkZoHxcTEAADy58//yNvEx8cjNjbW6kJEAA4dsk5ovL1lQTATGiLPVK6cfty7t7o4ssmQSY2maXj//fdRr149VKhQ4ZG3Cw8Ph9lsvn8JSb3Km8hT/fgjkPr3pnt3SWi4IJjIs330kX587Zq6OLLBkNNPffr0wfLly7Fx40YUL178kbeLj49HfHz8/fPY2FiEhIRw+ok8V4MGwPr1+vnChUDbturiISLXkXpK+pVXrGvYKGbr9JPhkpp+/frhzz//xPr161GyZMlM3Zdrashj3bgBPDhVe+aMdVM7IqLUTWpdKD1wuzU1mqahb9++WLhwIVavXp3phIbIY0VEWCc0vr4y3cSEhogetHChfrxnj7o4ssgwSU2fPn0wa9YszJ49GwEBAYiOjkZ0dDTu3r2rOjQi1/Xmm0BYmH7+0UfAvXtcP0NEaXvxRf24XTtlYWSVYaafTKmHxFKZPn06unXrZtNjcPqJPMbt20CePNbXbd0K1KqlJh4iMo6yZYHjx+U4JcV6SkoRW9+/DdOl2yC5F5F6f/0FtGhhfd2tWw/XpCEiSsu8eUDlynK8eLH16I2LM8z0ExFlQNOApk2tE5o33pDrmdAQka0qVdKPDbY7kkkNkTs4fx7w8gL++Ue/bvNm4Oef1cVERMbVurV+nJCgLo5MYlJDZHTffQekLizp5wfEx1s3qCQiyowpU/TjH35QF0cmMakhMqr4eJlW6t9fv270aODuXcDHR1lYROQGgoP1YwM1uGVSQ2REy5bJiMydO/p1Z88CAweqi4mI3Evqvyc3byoLIzOY1BAZSVISULKk9Xx3kyay7fKxx9TFRUTuZ+hQ/XjQIGVhZAaTGiKjWLUKyJlT2htYbNggFYNdoI4EEbmZ1LWuUq+xcWFMaohcXXIyUL480KyZfl3VqnJ9vXrq4iIi9zdpkn587py6OGzEpIbIlS1ZAuTIARw5ol+3ejWwe7ds4SYicqTu3fXjvn3VxWEjw1QUJvIosbGA2Wx9XdmywKFD7NtERM6TM6d+vHSpujhsxI96RK5m6NCHE5o1a4CjR5nQEJHzzZ6tH6de0+eCmNQQuYojR2TB77Bh+nXt2snOpueeUxYWEXm4Dh30YxefguL0E5Fq9+4BVaoAx45ZX3/mDBAaqiIiIiJd6vV7y5eri8MGHKkhUmnwYMDf3zqhGTNGmlAyoSEiVzFtmn4cFaUujgwwqSFSwVJbZuRI/brKlWXUZsAAdXEREaWlSxf92IX/RjGpIXKmo0clmQkLs77+5Elg717A11dJWERE6cqRarXK3Lnq4sgAkxoiZ7h8WXo1Pfmk9fVz5shUU6lSauIiIrJV6m7dly6piyMdTGqIHCkmRqoBFykiXbUt3n9fdjW98oq62IiIMqNnT/148GB1caSDSQ2RI1y/DpQuDeTNa10N+IUXpCnlt9+yXxMRGUvq6fHp09XFkQ4mNUT2dPkyUKwYUKAAcOqUfn2FCsCtW8DixSygR0TG9cUX+nFcnLo4HoFJDZE9nDgB5M4t00yptztWrSpTUAcOyPeJiIws9c6n0aPVxfEITGqIsmPpUplGKlMGuHNHv75uXRmZ2b0bCAxUFx8RkT2l/nA2fLi6OB6BSQ1RZiUnAx9/LMnMCy9Yf695c+DuXWDjRo7MEJF7St02ISVFXRxpYFJDZKujR4HgYKnXEB5u/b0hQ+SXe+VK2bpNROSuUv/9W7FCXRxpYFJDlJ6UFBliNZmkxkx0tPX3ly6VOjNDh3I3ExF5hpIl9eN33lEXRxrY0JIoLf/+C7RoASQmPvy9GjVkF1NwsPPjIiJyBaGhwNmzQGSk6kiscKSGyOLkSemWbTIBTZo8nNBMnSojN9u3M6EhIs82frx+nLp8hWJMasiznTgBNGggicwTTwD79ll/v0kT4OJFmWLq2ZNTTEREgIxkWwwdqiyMBzGpIc+zaRPw1FP6Vuz1662/HxwM7NghiUxEBBAUpCZOIiJXlbqI6KxZ6uJ4AJMacn/37gHffCNJjMkE1KsHHD5sfRtvb2DhQpleiooCqldXEysRkVH07q0fu8jWbiY15H40TXYlVawoSYy/P/C//z18u0KFgL/+ktsnJQFt23J6iYjIVoMG6cerV6uLIxUmNWR8SUnAH38AlSpJUuLlJUXxDh58+LaNG0uDSU2TPk3Nmjk/XiIid/DYY/rxJ5+oiyMVbukm4zlwAJgwAZgyJePb+vsDI0cCvXoBPj6Oj42IyBNt3646AgAcqSFXlpwMrFkD9Ogha14sa2IqVXp0QuPtLSvxr12T0Zg7d4B332VCQ0TkCCNG6Md376qL4/8xqSH1kpNlR9IHHwCPP64nLzlyAI0aAdOmPXoRWvnywE8/yS+TZW3MkCFA/vzOfQ5ERJ6oVy/9eO5cdXH8P5OmaZrqIJwlNjYWZrMZMTExCGTnZOdKTAS2bZPFZBER0vAxs0JDgTffBLp3B4oVs3+MRESUeZYNFkWLAhcuOORH2Pr+zTU1lH2aJuWyd+yQedUtW2TkJTvatgVeew1o1UrWxRARkWsqUgS4dEnKYSjGpIbSpmmyLuXwYeDQIbkcOADs3QvExtrnZ4SGAi1byqVRIyBXLvs8LhEROc9HHwEDB8pxUpIsHVCESY07S0oCrl8Hzp2TkZQHL2fOADdvOu7n+/sDdetKsbtGjYBatbhgl4jI3XTqpCc1W7fK33xFmNS4msRE4NYtudy+DVy5oicgZ88C58/rF0cmJBkpWVKaP1atCtSsKRV4CxRQFw8REalRpIh+PHmy0qSGC4Xt7fp1YPduSUCuXpXz27dla/Hdu/I1rcvt25LIPNgZ2hl8fYHSpeVSqpRcSpeWnUXFirHKLhERpS/1+4QD0gouFHa2qCigTx9g8WKHvKDpKlBAko+QEKBECanyGBoql8ceAwoW5LQPERE5TvXqwM6dqqMwXlIzceJEjBo1ChcvXsRTTz2FcePG4dlnn1UbVHw80KSJlN8HZJSjTBnpLZQ/P5A7tyyCfdTF319qsUyeLPdv1Qro0EF6F5UsCQQGcrSEiIhcV/v2TGoya86cOejfvz8mTpyIunXrYsqUKWjRogUOHz6Mx1L3oHC2efMkoSlcGPj3X6BChczdX9OANm3keOxYoH9/u4dIRETkMKkHF27eBPLmVRJGpisKd+vWDevXr3dELBkaM2YMunfvjh49euDJJ5/EuHHjEBISgkmTJimJ574NG+Rr166ZT2gAIDJSpq9y5LCuzkhEBEh5hago509tE9mqbFn92DJroUCmk5q4uDiEhYXhiSeewIgRI3DBQdUDH5SQkIBdu3YhLCzM6vqwsDBs3rw5zfvEx8cjNjbW6uIQ167J1xIlsnZ/S8GiYsUAPz+7hEREbmTaNPn70LWr6kiI0pYvn34cGaksjEwnNQsWLMCFCxfQt29fzJs3DyVKlECLFi0wf/58JDpw587Vq1eRnJyMIqm3jgEoUqQIoqOj07xPeHg4zGbz/UtISIhjgktKkq/e3lm7v6VQ0aP6GxGRZztxQr6GhqqNg+hRkpP1Y4WFVLPU0LJAgQJ47733sGfPHmzfvh2lS5dG586dUbRoUQwYMAAnLL+ADmB6YMGspmkPXWcxePBgxMTE3L9EOip7tGSolhGbzMqTR77evMnhZSKylpAALF0qx7VqqY2F6FEOHtSPS5dWFka2unRfvHgRq1atwqpVq+Dt7Y2WLVvi0KFDKF++PMaOHWuvGAEABQsWhLe390OjMpcvX35o9MbC19cXgYGBVheHsHx6OnMma/cvWVJ2N8XFAZcv2y0sInIDEyZIX53gYKBZM9XRED3sxAkpxGqRen2Nk2V691NiYiKWLFmC6dOnY9WqVahUqRIGDBiATp06ISAgAADwxx9/oHfv3hgwYIDdAvXx8UG1atUQERGBtm3b3r8+IiICbSw7h1SxrKU5ezZr9/f1lcc4fRo4dsy6OiMRea7Tp4EhQ+R4+HAgZ0618ZD7SEmR4rCXL0vSbLlcufLw5epV22cievdWWoIk00lNcHAwUlJS8Oqrr2L79u2oUqXKQ7dp1qwZ8jpgO9f777+Pzp07o3r16qhTpw6mTp2Kc+fOoZfqHUOWobbDh7P+GOXKyR+wffuA+vXtExcRGVdiIvD66zKCW68e8MYbqiMi1eLjpUVO6h5+qXv7RUbKdKUq77wjI4sKZTqpGTt2LNq3bw+/dHbp5MuXD6dPn85WYGnp0KEDrl27huHDh+PixYuoUKECVqxYgVDVi+eqVAG8vOQ/28WLMkycWXXrAitXyvbwfv3sHiIRGYimyd+BzZul+ObMmVnfiECuJz5epmyOHHn4ojIpsVXevEDRovJhvHJl4KWXslbOxAHY+8leKlaUhVKLFwMvvJD5+2/YICM0RYpIYsQKwkSe6/vvgffek78DS5YAzz+vOiLKiKbJqMnOncCOHfJ1504gJkZNPMHBUhC2SBHry4PXFSxoiGlN9n5ytpo1JanZvj1rSU2NGrK25tIlyeDLlLF/jETk+ubM0auKf/01ExpXce8esGULsGYNsHatXnTVEYKCpLHwg738QkOlx59lxyw9hEmNvdSsCfz8s2ToWeHnJ9s1168H1q1jUkPkiVaskHU0mibVxT/4QHVEniU+XpKWP/+UUfdH1EDLtDJlZJqmQgXgySeB8uVlLaavr30en+5jUmMvNWrI1+3bZVW5VxZ2yzdqJEnNihVAz572jY+IXNv69UC7dlLM87XXZMElp6EdIyFB1jD++iuwcGHWHycwUNZD1qkjH2yrVZPpHFKGa2rsJSlJOnLHxQG7dgFPP535x9izR+6XK5dsofP3t2+MROSaNm0CWrSQvx/PPy9vtAZY52AIN2/KQuupU60LxNmqSRMgLEw+dFapwgXbinBNjbPlyAE0aAAsWwasXp21pKZKFaB4cdlFtXo10KqV3cMkIhezYYMkNLdvyxvn3LlMaLIqJQVYtQr47jvgr79sv19oqOzgadNGRl5y8K3RqLJVUZge0KiRfF29Omv3N5n0RcZLltgnJiJyXevW6QlNkybSDoEjtLZLSgJ++UUW05pMMorSokX6CU27dvL3NSFB1i5pmlSDHzNGPpgyoTE0JjX2ZElq1q+XwllZYUlqli5lg0sid7ZmDdCypSQ0YWHyRquwEaAhaJos4C1bVpKYnDmlKOGj+vq99JIkjikpegIzfz7QujVHw9wUkxp7qlgRKFBA/kht3561x3juOdmud/GirM0hIvezapVML9+5AzRvLm/UHKFJ2/XrQN++ksR4eQEvvggcP/7w7QoXBsaNk3VJlgRmwQKp/8UF1x6DSY09eXkBjRvL8d9/Z+0xfH3ljxyQvVX5ROSaFi2SkYK7d2WkZtEiKelAuiNHpMSFySQfFNMqvR8QAIwdK4mhpkmNr/feYw0XD8ekxt4sCcnKlVl/jJdflq9z5sgvKxG5h5kzgfbtZT3Hyy8zoUnt2DE9kSlfPu3R7rfflgaMmgbExkqRQo5wUSpMauzNktTs3CmfHLKidWsgd25pcLltm/1iIyJ1Jk0CunQBkpOBbt2A338HfHxUR6XWxYtAw4aSyJQr93Ai4+8viaBlTczkyUChQmpiJUNgUmNvwcFA1apynNUpqFy5ZN4YAGbPtktYRKTQN99IB2NAGlVOm+a5u2ySk4GhQyWRKVpUWg6kFhgou5c0TaaWXn+da2LIZkxqHKFlS/manSmoV1+Vr3PnyrZFIjIeTQM+/RT43//k/OOPpYZKViqOG9327bLjKEcOYNgw6+/5+gLLl8u/V0wM0KyZmhjJ8DzwN8sJWrSQr3//nfWEpGlTqVB86dLDn2SIyPWlpMiaj6++kvORI+XYk0YdUlKAzz6T51yr1sN/D7/9Vm5z757+YZAoG5jUOEKtWkDevMCNG1nf2u3jIwsKAWDWLLuFRkROkJwM9OgBfP+9nE+YoI/WeIKoKOCpp6QY3pdfWn+vRQtpA6NpwPvve1aSRw7HpMYRcuTQh0+XLs3643TpIl/nzZPaC0Tk+hISZPp4+nSZZpoxQ19P4+6io2VXV7FiwOHD1t/74w9JZFaskG3aRA7ApMZR2rSRr3/+mfXHqFNHKmfeuSNra4jItd25I4v8582T9SPz5ukfTtzZ8eOy3bpECSl4Z1G6NHDunCQzHTooC488B5MaR2nZUv6oHT0ql6wwmYA335Tjn3+2X2xEZH8xMVLSYeVK2Yq8bJmU6Xdne/ZIL6Vy5aQLdnw8ULs2MHGirJ85cQIICVEdJXkQJjWOYjbrvaCyM1rTubPMS2/enPXkiIgc6+pV+X3fsEG2JEdESD8nd7V/vyRsTz8tlc81DXj+eXn+mzcDvXvL3y0iJ2NS40ht28rXRYuy/hjBwfqugOnTsx8TEdnXhQvSX2j3bikMt3YtULeu6qgc49Ah4JVXgMqV5e+ayQS89hpw8KCsH6xXjwt/SSkmNY7Upo38gm/fLn/4ssoyBTVjRta7fxOR/Z06JW/kR44AxYsD69frxTfdyYkTkrxUrCjrhABZI3PwIPDbb7LTicgFMKlxpKAgmV8GpAtvVrVqJR1oL12SnQNEpN7Bg8CzzwJnzsiC2I0bZW2JO7l6VZpEli8vbR00TdbQ7N8vu5nKl1cdIZEVJjWOZo8pqJw5ga5d5Xjy5OzHRETZs3070KCB9C6qWFHWkoSGqo7Kfu7dA0aNkmTt++9l0W+LFrIweP58ec5ELohJjaNZejitXSvF+LKqVy+ZyvrrL+DkSXtERkRZsXYt0LgxcP26jMSuXSujsu5A06R8RLlywEcfyY6uypVl4fOKFUCVKqojJEoXkxpHe+IJmW9OSpItnln1+ON6+4VJk+wTGxFlzrJlsm371i3Z7RQRIe1M3MGRI9KepUMH4OxZKaD3yy/Arl1AkyaqoyOyCZMaZ7DUqshuAT1LVdKff5YiX0TkPL//LtPJ8fGyCWD5ciBPHtVRZd+tW9LCoVIl4N9/pbnkkCFSUK9rV27NJkNhUuMMHTvK17//liHrrGreHChZErh5U/7AEpFzTJ0KdOokI66vvy47gPz8VEeVPamnmr75Rp5b69bS3mDoUCBXLtUREmUakxpnKF9eFtYlJmZvwbC3txS1AqRBnqbZJz4ierTRo6UFgKbJaOmMGbJ438giIyWB6dBByk08/rjUmVmyRI6JDIpJjbNYRmv++CN7j/Pmm/IJcc8eYOvW7MdFRGnTNJmG+fBDOR88GBg/XppUGlVKirQweOopmT7z8ZHneOiQVAQmMjgD/3YajKWZ2+rVUm8mqwoU0BOkCROyHxcRPUzTgIEDgeHD5Tw8HBgxwtjVco8dk23offoAcXHAM88Ae/fKVJPRp9KI/h+TGmcpVQqoWVM+Kc2fn73H6tNHvs6bl70EiYgelpws001jx8r5Dz8AgwapjSk7EhMlKatcWQoE5s4tz2nDBuDJJ1VHR2RXTGqcyV5TUNWrS32MhASO1hDZU2Ii0KUL8OOPMs00fTrQt6/qqLLu2DHpQ/Xxx7Jrq3lzmWrq29fY02hEj8D/1c70yisyfL1xoyzUy46BA+XrhAnA7dvZj43I08XHA+3bA7NnAzlyyIePbt1UR5U1miZ/G6pWBXbsAPLmBX79VQrouVPlY6IHMKlxpmLFpFcMkP2aNW3byi6F69elQBYRZd2dO8ALL0iPNl9f4M8/JcExogsXZESmb1/g7l0pqHfgANC5s7HXBBHZgEmNs1mmoLJbZ8bbG3j/fTkeM0bWARBR5sXEAM2aAatWyXqTFSukiawRzZkj5SNWrZLFv99/L61VihdXHRmRUzCpcbZ27SQh2bULOHEie4/VrZuUaP/vv+zVvyHyVNeuSR+njRsBs1naHjRqpDqqzIuJkeKAHTtKj7lq1aTsQ79+XDtDHoX/252tcGH5IwrIp6rsyJ1bb50wahSL8RFlRnQ08Nxz8gGjYEFgzRqgTh3VUWXetm3SaHL2bPnA9PnnwJYtUimYyMMwqVHBMgU1a1b2E5G+fWUNwPbtwKZN2Y+NyBOcOyfr2w4eBIoWBdavl0W1RpKSIu0N6tUDzpyRFiobNwLDhhm/4jFRFjGpUaFdO8DfX7Zbbt+evccqUkS2oAIyWkNE6TtxQhKakyeBEiWMWa/l0iWgRQtpRJmUJDsr9+yRUg9EHoxJjQqBgZLYAPbZuWRZMLxkiSRKRJS2gweB+vVlpKZsWUlojNbraM0amW5atUo+HP34o2w/N5tVR0akHJMaVSz1L37/Hbh3L3uPVa6cbEcFZCcUET1s505pExAdLdV116831q6glBRg5EigSRN5Dk89JTVoevTgVm2i/8ekRpWGDYGQENm1sHhx9h/vgw/k64wZwMWL2X88IneycaPsarp+HahVS0Y7ChdWHZXtbt6U2lSDB0ty07WrTF0/9ZTqyIhciiGSmjNnzqB79+4oWbIk/P39UapUKQwZMgQJCQmqQ8s6Ly99LcyMGdl/vHr1pEFdfDzX1hClFhEBhIVJE8fnnpPzfPlUR2W7ffukNcqSJdJVe+pUad+QK5fqyIhcjiGSmqNHjyIlJQVTpkzBoUOHMHbsWEyePBkff/yx6tCyp2tX+fr330BUVPYey2QCPvtMjidPBi5fzt7jEbmDxYuB55+XyrotWkhhvYAA1VHZbsYMWfx76pS0N9i0CejZk9NNRI9giKSmefPmmD59OsLCwvD444/jhRdewAcffICFCxeqDi17nnhCms2lpMj27uxq1gyoUUP+gH/7bfYfj8jIZs+WBfkJCcDLL0vrA39/1VHZJjEReO89WXt3754kZLt3y4gNET2SIZKatMTExCB//vzp3iY+Ph6xsbFWF5djWTD8yy/Zr1mTerRmwgTg6tXsPR6RUf34I/D669I+pGtXWZDv46M6Kttcuya9m77/Xs6HDAGWLZPq4USULkMmNadOncIPP/yAXr16pXu78PBwmM3m+5eQkBAnRZgJ7dvLp8cjR2QnQ3Y9/7xs97x9Gxg3LvuPR2Q048YBb70lHxLeeQf4+Wfpum0EBw7IaOvq1UCePNL+ZOhQtjogspHS35ShQ4fCZDKle9m5c6fVfaKiotC8eXO0b98ePXr0SPfxBw8ejJiYmPuXyMhIRz6drDGbZVcDYJ8FwyaTlEkH5JPetWvZf0wiI9A04IsvgAED5Pyjj4Dx442TECxYIG0aTp+W2jlbtgAvvqg6KiJDMWmauoZBV69exdUMpkhKlCgBPz8/AJLQNGzYELVq1cIvv/wCr0z+sYqNjYXZbEZMTAwCAwOzHLfdWXZn5MsnC4b///lmWUqKNLTbuxf48EMppU7kzjRNqutadv59+SXw8cfGWFCbkiKtDYYPl/MmTaQvHKebiO6z9f1baVKTGRcuXEDDhg1RrVo1zJo1C97e3pl+DJdNapKTpVz7+fPA3LkyJZVdy5fLVJS/v+ycCA7O/mMSuaKUFOmBNmmSnI8dC/TvrzQkm929K+vq5s6V8wED5EOIUabLiJzE1vdvQ4zLRkVF4bnnnkNISAhGjx6NK1euIDo6GtHR0apDsw9vb71mjT3aJgBAy5YylH33LvDVV/Z5TCJXk5QEvPGGJDQmkywQNkpCc+mSFOGcO1caUE6fLhXBmdAQZZkhRmp++eUXvPHGG2l+LzPhu+xIDQAcPy69aLy8ZMTGHiMra9fKH82cOeXxS5TI/mMSuYqEBOC112Qtirc3MHMm8OqrqqOyzcGDMpJ69qxMMy1cKC0ciChNbjVS061bN2ialubFbZQpIyMr9qpZA0j11CZNpObFsGH2eUwiV3D3riyiXbBAtmovWGCchOavv6T699mzUqtq61YmNER2YoikxmNYRqN++in7NWssLFNPv/4KHD5sn8ckUikuTorRrVwprQKWLQPatFEdlW0mTABatZLn0KCBJDRPPKE6KiK3waTGlXTsKLUpjh8H1q2zz2PWrCmfaFNSZIsrkZHduAE0bSq/H4GB0mKkaVPVUWUsOVnW+vTtK7+L3boBq1ZxhxORnTGpcSUBAbJGAJCmdfby9dey+HD5cuDff+33uETOdOmSTKlu2ybJwOrV0sjV1d29C7zyCvDdd3IeHi4FAY1S4ZjIQJjUuJq33pKvCxbYr81BmTJA795yPHCgfGokMpLz54H69YH9+4GgIBmpqVZNdVQZu3ZN1rUtXChJzO+/A4MGGaN+DpEBMalxNdWqySUhQdbB2Mvnn0v14n37ZJcIkVGcOgU8+6xMyz72GLBhA1ChguqoMnb6tCwI3rwZyJtXpps6dlQdFZFbY1LjiiyjNVOn2m/BcMGCwCefyPEnnwB37tjncYkc6cgRGaE5c0YW1G7YAJQurTqqjO3cCdSuLYlYSAiwcSN3OBE5AZMaV/Tqq0Du3MCxY8D69fZ73H79gNBQacXw7bf2e1wiR9i1SxKaqCgZmVm/XkZqXN2KFbL25/JloHJl2eH01FOqoyLyCExqXJGjFgz7+QEjR8rxyJHAuXP2e2wie/rnH0kMrl4FqleXQpJBQaqjythPPwEvvADcvi1radavB4oWVR0VkcdgUuOq3n5bvs6fb78FwwDQoYPsGLlzRxYNE7mauXOlzcetW0DjxrLLqUAB1VGlT9OkiWbPnrIQv0sX2W3oapXLidwckxpXVa0a8PTTsmB42jT7Pa7JJAXAvL0lYYqIsN9jE2XXhAmymDYxUbZBL18uI5euLCUFeO894LPP5Pzjj6WHG7dsEzkdkxpX1revfJ04URr32UulSkCfPnLcr58kTkQqaZrs0OvbV4779AFmzwZ8fVVHlr6EBOD114EffpDz776TKt7csk2kBJMaV9axowy7nzsHLF1q38ceNgwoUkQWI48da9/HJsqM5GSgVy/giy/kfPhwSRK8vdXGlZFbt4DWraX2TI4cwG+/Ae++qzoqIo/GpMaV+fvLHD2gfxK0l7x5gW++kePhw4HISPs+PpEt7t2TaaapU6VD/eTJMo3j6iMdlqJ6q1ZJ/6mlS/XF/USkDJMaV9e7t/yxX7MGOHjQvo/duTNQt64sGh4wwL6PTZSRmBigeXO92u68efoCeVcWGSnFAFO3a2jeXHVURAQmNa7vsceAtm3lePx4+z526kXDCxYAixbZ9/GJHiU6WorRpW5M+dJLqqPK2JEjUiX4yBGgeHEpBlirluqoiOj/Makxgn795OvMmdKl2J4qV9a7d7/zjv0fn+hBJ0/KCOG+fbKua906qUnj6rZtk3II588DZcsCmzYB5curjoqIUmFSYwT16wMVK8o00c8/2//xP/9c/khHRwMffGD/xyey2L1bEpr//gNKlZLEoEoV1VFl7O+/gUaNgOvXgRo1pO2BEaobE3kYJjVGYDLpozUTJti/y7afn9TCMZkkafrnH/s+PhEA/Puv3j6galVJaEqVUh1Vxn7/XXY53bkDNG0qa2gKFlQdFRGlgUmNUXTqBOTLJ51/ly+3/+PXravXrunZU8q8E9nLjBmymDYuDmjYUNoeFCmiOqqM/fCD/O4lJko17mXLgDx5VEdFRI/ApMYocuXSt3ePHu2YnzFihAypnzkDfPqpY34GeRZNA4YOBbp1kwKSr74KrFzp+u0DNA0YMkTqzmiaFAWcPZtVgolcHJMaI3n3XSBnTtlxsXWr/R8/IEBvoPndd7KAkyirEhKAN96QQo8AMHgwMGuW61cJTkkB+veX+k2AxP/991JagYhcGn9LjaRYMSnJDgCjRjnmZzRrBnTvLp9OO3cGbt50zM8h93bzJtCihUw7eXsDU6bISKCrJwZJSfL///vv5Xz8eFlI7+rFAIkIAJMa47HsTlq0CDh+3DE/Y9w4oHRpKTLWq5ckOES2OndOtj6vXi3rT5YuBd56S3VUGYuPl3Uzv/wiidivv+rrzIjIEJjUGE358rITQ9OAb791zM/Ik0f62Hh7A3PmyJQBkS1275ZidIcOAUWLylRpixaqo8rY7dvACy/o1Y3nz5eRSiIyFCY1RvThh/J1xgypLeMINWvqayH69JG6IkTpWb5caipFR0tdpa1bjVGD5uZNICxM+jjlzi3P48UXVUdFRFnApMaI6tUDateW4XJ7N7pMbdAg+VlxcbKWJynJcT+LjG3SJBnpuH1barls2ACEhKiOKmOXL8sW882bpclrRIQ0qiQiQ2JSY0Qmk97aYOJESTocwdtbpp4CA4EtW4Avv3TMzyHjSkqS7c7vvCO7ht54Q0Y6zGbVkWXM0phy716gcGGpnVOnjuqoiCgbmNQY1QsvAGXKyND5tGmO+zmhofIpHJAtrn//7bifRcZy4wbQsqVUuQZkd9O0aVJ2wNWdOCGjkMePS22mjRulDxoRGRqTGqPy9tZ3Qo0ZIxVPHeW112T3iqZJ8bTTpx33s8gYTpyQKdCICCkMuXCh1KExwtbn/ftlhObcOflgsGED8MQTqqMiIjtgUmNknTtLqfnISNl+6kjffy+Lh2/cAF56SfrgkGf691/Z4XT8uKyb2bQJaNtWdVS22bIFaNAAuHRJFjFv2MDGlERuhEmNkfn56WtrvvxSKrg6iq+vbHMtVEjWILB+jefRNBkVDAuT5LZ2bWD7dmPscAKkUWvTpjJl+8wzwJo1spaGiNwGkxqj69VLRmvOnHH8aE1IiNSt8fYGZs6URcrkGe7ckZHBgQNlQXCXLpIUBAWpjsw2f/4JtGql785atUp2OxGRW2FSY3S5cgH/+58cO3q0BpDtr19/Lcf9+8vUA7m3M2eki7ulIOP330vVXT8/1ZHZZuZM4OWX5XfjpZekwnHu3KqjIiIHYFLjDnr1kk/MZ8/Km42jvf8+8Morsp23XTsuHHZnq1cD1avLlGOhQrKepl8/YywIBmQ0sUsXIDlZOoXPmeP6DTWJKMuY1LgDf38plAcAX33l+NEak0m27laqJAsumzcHrl517M8k50pJAcLDZarm2jWgWjVg505ZZGsU4eF676Z335X/szlyqI2JiByKSY27eOstIDhYtqlOn+74n5cnD7BypewcOX5c+lFxR5R7uHZNXs+PP5bkpls3Y+0S0jTZXv7xx3L+2WfSpNXVO4QTUbbxt9xdPDhaEx/v+J9ZtCjw119AvnzS56djR7ZSMLrt24GnnwZWrJA1M9OmSZLs7686MtukpEiF45Ej5fybb6RopFGmy4goW5jUuJOePWW0JjLSOaM1APDkk7Lw0s9Pvr7zDrd6G5GmSWXgevVktK90aUlU33xTdWS2S0qSUaWJEyWJmTxZb/5KRB6BSY078feXYXfAeaM1gOyMmT1b3kh+/JE9oozm+nXZHdS3r1SmbtdO1s8YqW1AfLwsXp85U3Zo/fYb8PbbqqMiIidjUuNuevaUaaHz5yXBcJa2bfWO4Z9/Ltt+yfWtXSsLvhculJ5NY8cC8+YZoyGlxe3bsgZo0SLZ2bRwobTzICKPw6TG3fj5AZ9+KsfDhgExMc772X36AJ98IsfvvQeMHu28n02Zk5go/08aNQIuXJAeSFu3Su0hI60/uXlTKhxHREjtmeXLpdkrEXkkJjXuqEcPoGxZ2WZtKZTnLF98oSdVH37IqShX9N9/0tDxq69kLU337sCuXbJA2EiuXJFikJs3S3Xgf/4BGjdWHRURKWS4pCY+Ph5VqlSByWTC3r17VYfjmnLmlF0fgEwnnDvnvJ9tMkli88UXcv7ZZ3Lh4mH1NE2mJCtXBrZtkymmOXOAn36SLfpGcv48UL++FAUsXFim0WrXVh0VESlmuKTmo48+QtGiRVWH4fpat5ZCaffu6SMnzvTpp8CoUXL85ZfSyoGJjTqRkVIk8a23gFu3ZJfTvn2yuNZoTp2S+I8elX5kGzYYa1EzETmMoZKalStXYtWqVRjNtRoZM5n0NS0zZwK7dzs/hg8+0BcMjxol62xSUpwfhyfTNKk1U6GCNHH08wO+/VZGNkJDVUeXeYcOydTZ2bOy7XzjRlkPREQEAyU1ly5dQs+ePTFz5kzkypXLpvvEx8cjNjbW6uJRqlcHOnWS44ED1YyU9OsHTJkiSdYPP8guqbg458fhic6fB1q2lDVWsbEyPbN3r/Tu8vZWHV3m7dwpU04XLwIVKxqryjEROYUhkhpN09CtWzf06tUL1atXt/l+4eHhMJvN9y8hISEOjNJFffWVbHNdu1Z2hqjw1ltSN8TXF1iyBHjmGTbBdKTkZEkgn3pKKj77+spI2caNsoDciNavl51a168DNWvK/+egINVREZGLUZrUDB06FCaTKd3Lzp078cMPPyA2NhaDLYXlbDR48GDExMTcv0RGRjrombiw0FDZpgvIbiRVbQxefRVYt04qHh88CNSoIW9MZF87dsib/rvvyuhMrVrAnj0yFWjE0RlAeow1ayYjfM89J7uc8udXHRURuSCTpqlbvXn16lVczaC7c4kSJdCxY0csXboUplT1M5KTk+Ht7Y1OnTphxowZNv282NhYmM1mxMTEIDAwMFuxG0pMDFCqlDQqnDQJ6NVLXSwXLgAvvihTCTlyyJqb3r3VxeMubt6UGkGTJsk0Y9680qW6Z0/jJjOAFALs1Enq6rRqJedG6UNFRHZj6/u30qTGVufOnbNaDxMVFYVmzZph/vz5qFWrFooXL27T43hsUgMA48fL+pbChYGTJ4GAAHWx3L0rtVF+/13Oe/cGxoyRRayUOZomLSoGDgQuXZLrXn9dFokXKaI2tuyaNk2mLlNSgA4dZMF7zpyqoyIiBWx9/zbEmprHHnsMFSpUuH8p8/+7HUqVKmVzQuPx3n4beOIJ4PJlqTSskr+/rLEZMUIWEE+aJIuad+1SG5fRrF8v00uvvy4JTdmywL//ypu/kRMaTZMu2z16SELTo4f8f2FCQ0QZMERSQ3aQMycwbpwcjxsnNUpUMpmk+ebSpTJ6dOiQ7M4ZOlSmGujRjh4F2rSROkQ7dkh7gK++kte0USPV0WVPSoqMOlnWzw0aBEydauwpNCJyGkMmNSVKlICmaahSpYrqUIylZUvpxpycLOtqXKFmTKtWsnD45ZdlEfOwYZLcHDyoOjLXc+mSTNVVqCC7yLy95XU8dQr4+GPZ5WRkiYlA165SBRuQejrh4cbqRUVEShkyqaFsGDdO1tNs3ercLt7pKVQImDtX1tjkyyeFAqtVk1YPycmqo1Pv8mVJWkqXBiZPln+TF14ADhyQqTsjTzVZ3L4to0+zZkmy9uuvUk+HiCgTmNR4mmLF9CaTgwbpi0tVM5mAjh1lGqpVKyAhQVorVK4sU1Suv57d/s6flyrMJUrIiMWtW/pW+MWLgSefVB2hfVy/DjRtKlu3/f3luXXurDoqIjIgJjWeqE8f6ch886asX3AlwcGSxEybJqM2hw7JqET9+tKN2ROcPClbsR9/XLa8370rycyff8oIW4MGqiO0n/Pnpe3Bli16p+1WrVRHRUQGxaTGE3l7S+sCLy/ZVfLPP6ojsmYyAW++Cfz3n4wm+flJNdy6daXNwpEjqiO0P00D1qyRrctly0rn7MRESWBWrZKu2m3ayGvmLo4dk9f08GGgaFFpe/DMM6qjIiIDc6O/kJQp1avLiA0AvPOOdPN2NZYCcidOyLZeLy8ZrahQAejWzT22gF++LC0MypaVnUtz58oC7pYtJZFbu1amZtxtseyOHdJp+9w5aUi5ebO8rkRE2cCkxpN98YVM95w4IXVBXFXx4rKo+eBBqUackgLMmCGJWfXq8r1bt1RHabuUFKkn06GDPLePPpLXICBAdjPt3St9uurWVR2pY0REAA0bAlevyoLwjRuN2TGciFyOISoK24tHVxR+lHnzgFdeAXx8gP37jdHwcOtWadg4f74sKAYkIejUSYoMuuJW/3v3gNWrZaRp6VIgOlr/Xo0aEneHDkCePMpCdIq5c6VYYGIi0LgxsGiR2urWRGQIbtUmwV6Y1KRB02Rh5sqV0izw33+Ns27j6lUZsZk6FTh+XL/+qaeAsDCZtqlfX4rTqXD9uoy4LF4s3bJv39a/FxgoSVjPnkDVqmric7aJE4G+feX/3Msvy/Zto9fWISKnYFKTBiY1j/Dff0DFisCdO9KDacAA1RFljqbJ2pMpU4CFC60rEvv4yDSOJcmpVMkx5fbj42Wka8cOuezcKQtgUxc4LFZMdnK1aSMJpKe8oWsaMGSITHcCMsU2fjyrBBORzZjUpIFJTTqmTpUpEB8feVOuVEl1RFlz/bqMNq1aJZdz56y/7+0NlCwpfbBSX0qXBsxmef45c8rX1G+68fFS0yc62vpy/rwUC9y/P+32DhUrShLTpo2sH3G3Bb8ZSUiQ0ahff5Xzzz+XVhie9u9ARNnCpCYNTGrSoWnyxrt0qexC2bHD+F2zNU0W4EZESIKzZg0QF2f7/b289OQm9dTRoxQoIOtjqleXrzVqyEJsTxUTI9NM//wj/4aTJkmCQ0SUSUxq0sCkJgOXL8vIwuXLMgU1ZozqiOxL04CoKEl0HrycOpXxtnYfHyAo6OFLhQqSyJQowREIi/PnZa3W/v2ypmnuXNmmTkSUBUxq0sCkxgbLlwPPPy/HERFAkyZq43GmlBSZQkpIsL4kJgL580uFYyYtGTtwAGjRArhwQZK+5culgjURURbZ+v5tkG0u5DStWkknaEA6Jl+/rjYeZ/LyksW7AQEylRQcLPVTSpeWpIYJTcb+/VeK6l24IL2ptmxhQkNETsOkhh42erTUq4mKksXDnjOYR9kxYwbQvDkQGyvtHTZtkik5IiInYVJDD8uVS2qI5MghBe5mzlQdEbmylBRg8GBpXZGUJN3W//5bpuuIiJyISQ2lrXp1YNgwOe7bFzh9Wm085Jpu35YdTpY2G599Jk1SPaUGDxG5FCY19Gj/+58UrouLk9L2lpYERIDscHr2WWl14OMjo3vDhxunIjURuR3+9aFH8/aWqafAQOmi/O67qiMiV7FjB1CzJrBnD1C4sFR07tRJdVRE5OGY1FD6SpYEZs+WnT9TpkgBNfJs8+ZJT62LF6VGz7ZtQJ06qqMiImJSQzZo1QoID5fjd9+VT+XkeTQN+PJL6ep+7578v+AOJyJyIUxqyDYffQS89prsbnn5ZS4c9jSxsUC7drIQGJCK04sXy9QkEZGLYFJDtjGZgJ9+kqaM165Jn6hbt1RHRc5w7BhQq5a+IPjHH6WFBrtsE5GLYVJDtvP3B/78EyhSRErhd+kiNUrIfS1eLI05jx4FihUD1q8HevRQHRURUZqY1FDmFC+uf2JftEi28JL7SUkBPv8cePFF2dL/7LPArl0yYkNE5KKY1FDm1akjO6EAKdC3YIHaeMi+bt4EWrcGvvhCzt99V3o6FSmiNCwioowwqaGs6dYN6N9fjrt0AfbuVRgM2c3BgzLdtGIF4OcH/Por8N13QM6cqiMjIsoQkxrKulGjgKZNgTt3gLAw4PBh1RFRVmmaLACuUQM4eVK6k2/aBHTurDoyIiKbMamhrMuRA5g7F3j6aeDKFaBRI1lQSsYSEyNNKN96S+rPNGsG7NwprysRkYEwqaHsyZsXiIgAqlQBLl0CGjaULcBkDNu3A1WrSnKaIwfwzTcy9VSwoOrIiIgyjUkNZV/+/JLYVKwIREfLiM2JE6qjovSkpADffisNS0+flqrAGzYAH37IhpREZFj860X2UbCg7JCpUAGIipIRm1OnVEdFablyRXY3ffCBXiF6zx6gdm3VkRERZQuTGrKfQoUksSlfHrhwQRIbtlNwLatXy1ThihWAr680KJ07V6YRiYgMjkkN2VfhwpLYlCsHREZKYnPmjOqo6NYtoE8foHFjGUkrV07W0/TqJS0wiIjcAJMasr+gIBkRKFMGOHtWEptz51RH5bnWrAEqVQImTpTzt96S3U2VKqmNi4jIzpjUkGMEB0tiU7q0jNTUqQNs26Y6Ks9iGZ1p1EimAR97TBZ0T5kC5M6tOjoiIrtjUkOOU6yYjBKULy9THvXrA7/8ojoqz5DW6MyBA0CTJmrjIiJyICY15FjFiwNbt0pjxIQE4I03gPfeAxITVUfmntIbnQkMVB0dEZFDMakhxwsIkKaXQ4bI+fffS9Xaq1fVxuVONA3480+pFWQZnXn7benlxNEZIvIQTGrIOby8gKFDgYULZT3HmjXSZ2j/ftWRGd/hw5Iktm0r65csozOTJ0tCSUTkIZjUkHO1bSvTUY8/ri8gnjdPdVTGdPOmdEqvVEmSGB8fYPBg4NAhjs4QkUdiUkPOV6ECsGOH3uH7lVeATz6R6raUseRk6aj9xBPAd9/JeZs2MmIzYgSQJ4/qCImIlDBUUrN8+XLUqlUL/v7+KFiwIF566SXVIVFW5c8vVW0HDpTzESOAatWAzZvVxuXqNm2Sabu33pI1SU8+CaxaJetpSpVSHR0RkVKGSWoWLFiAzp0744033sC+ffuwadMmvPbaa6rDouzIkQMYPRqYPVuSnP37pcFiz57AtWuqo3Mt+/fLiFa9etKnyWwGxo0D9u2TES8iIoJJ0zRNdRAZSUpKQokSJTBs2DB07949y48TGxsLs9mMmJgYBHJ7q2u5cgUYNAj4+Wc5L1AA+OYboFs3z+4avWMH8NVXwOLFcm4yAT16yHWFCqmNjYjISWx9/zbEu8Xu3btx4cIFeHl5oWrVqggODkaLFi1w6NChdO8XHx+P2NhYqwu5qEKFgGnTgA0bZM3NtWtA9+5SsO/AAdXROd/69bKjqWZNSWhMJqBDB2DvXmDqVCY0RERpMERS899//wEAhg4dik8//RTLli1Dvnz50KBBA1y/fv2R9wsPD4fZbL5/CQkJcVbIlFX16gG7dwOjRsnW702bgKpVgQ8/lMJy7kzTZH1M/fpAgwZy7O0NdO0KHDkC/PEH+zUREaVDaVIzdOhQmEymdC87d+5ESkoKAOCTTz5Bu3btUK1aNUyfPh0mkwnz0tkOPHjwYMTExNy/REZGOuupUXbkzAl88IG8kb/0kuzuGT1aGmR+9RVw+bLqCO3r3j1g7lygVi0ZndmwQbZn9+oFnDghrSXKllUdJRGRy8uh8of37dsXHTt2TPc2JUqUQFxcHACgfPny96/39fXF448/jnPpdH/29fWFr6+vfYIl5wsJkUrEK1YAfftK2f9PPwWGD5epmL59ZXrGiDRNRqF+/VUSmpgYud7fXyoBf/CB9M4iIiKbKU1qChYsiIIFC2Z4u2rVqsHX1xfHjh1DvXr1AACJiYk4c+YMQkNDHR0mqdaypYzazJ0L/PCDLJ6dOVMuNWtKcvPKK4AREthTp/TY/39aFYAkcF27Av36AYULq4uPiMjADLH7CQD69++P+fPn4+eff0ZoaChGjRqFpUuX4ujRo8iXL59Nj8HdT25i+3Zg/HhgzhxpkgnIwtmePWXKxtXWTl2/LlWTf/3Vug5PnjzAyy8DXbrIGhpP3uVFRJQOW9+/DZPUJCYmYvDgwZg5cybu3r2LWrVqYdy4cXjqqadsfgwmNW7m8mXgp5+ASZOA8+f16ytWlMW2lktQkPNi0jTg3Dlg40a5bNokTSUtv2ZeXlJXpnNn6VyeO7fzYiMiMii3S2rsgUmNm0pKApYskamptWsf/n6ZMtZJjj2nLJOTZcu5JYHZuNE6wbKoWFFGZF57DSha1H4/n4jIAzCpSQOTGg9w+bLsHlq/Xi779umjJBYhIdJSIH9+KfKX1tf8+aXi8eXLwKVL8jX1seVrVJT0r0otRw7Zhl6vnlzq1gWKFHHevwERkZthUpMGJjUe6OZNGUGxJDk7d9q/cWZAgHQbtyQxNWtyWomIyI5sff9WuvuJyOHy5gVatZILANy+LYnNxYuygPfaNfma+tjyNTFRRlgKF5ZLWsdFisioj7e30qdJRERMasjT5M4tO42IiMjtcA8pERERuQUmNUREROQWmNQQERGRW2BSQ0RERG6BSQ0RERG5BSY1RERE5BaY1BAREZFbYFJDREREboFJDREREbkFJjVERETkFpjUEBERkVtgUkNERERugUkNERERuQUmNUREROQWcqgOwJk0TQMAxMbGKo6EiIiIbGV537a8jz+KRyU1cXFxAICQkBDFkRAREVFmxcXFwWw2P/L7Ji2jtMeNpKSkICoqCgEBATCZTA75GbGxsQgJCUFkZCQCAwMd8jNUcufn587PDeDzMzp3fn7u/NwAPj970DQNcXFxKFq0KLy8Hr1yxqNGary8vFC8eHGn/KzAwEC3/M9r4c7Pz52fG8DnZ3Tu/Pzc+bkBfH7Zld4IjQUXChMREZFbYFJDREREboFJjZ35+vpiyJAh8PX1VR2KQ7jz83Pn5wbw+RmdOz8/d35uAJ+fM3nUQmEiIiJyXxypISIiIrfApIaIiIjcApMaIiIicgtMaoiIiMgtMKnJhjNnzqB79+4oWbIk/P39UapUKQwZMgQJCQnp3k/TNAwdOhRFixaFv78/nnvuORw6dMhJUWfOV199hWeeeQa5cuVC3rx5bbpPt27dYDKZrC61a9d2bKBZlJXnZ6TX78aNG+jcuTPMZjPMZjM6d+6MmzdvpnsfV379Jk6ciJIlS8LPzw/VqlXDhg0b0r39unXrUK1aNfj5+eHxxx/H5MmTnRRp5mXmua1du/ah18hkMuHo0aNOjNh269evR+vWrVG0aFGYTCb8+eefGd7HSK9dZp+fkV6/8PBw1KhRAwEBAShcuDBefPFFHDt2LMP7qXr9mNRkw9GjR5GSkoIpU6bg0KFDGDt2LCZPnoyPP/443ft98803GDNmDMaPH48dO3YgKCgITZs2vd+bypUkJCSgffv26N27d6bu17x5c1y8ePH+ZcWKFQ6KMHuy8vyM9Pq99tpr2Lt3L/766y/89ddf2Lt3Lzp37pzh/Vzx9ZszZw769++PTz75BHv27MGzzz6LFi1a4Ny5c2ne/vTp02jZsiWeffZZ7NmzBx9//DHeffddLFiwwMmRZyyzz83i2LFjVq/TE0884aSIM+f27duoXLkyxo8fb9PtjfTaAZl/fhZGeP3WrVuHPn36YOvWrYiIiEBSUhLCwsJw+/btR95H6eunkV198803WsmSJR/5/ZSUFC0oKEgbOXLk/evu3bunmc1mbfLkyc4IMUumT5+umc1mm27btWtXrU2bNg6Nx95sfX5Gev0OHz6sAdC2bt16/7otW7ZoALSjR48+8n6u+vrVrFlT69Wrl9V15cqV0wYNGpTm7T/66COtXLlyVte9/fbbWu3atR0WY1Zl9rmtWbNGA6DduHHDCdHZFwBt0aJF6d7GSK/dg2x5fkZ+/S5fvqwB0NatW/fI26h8/ThSY2cxMTHInz//I79/+vRpREdHIyws7P51vr6+aNCgATZv3uyMEJ1i7dq1KFy4MMqUKYOePXvi8uXLqkOyCyO9flu2bIHZbEatWrXuX1e7dm2YzeYMY3W11y8hIQG7du2y+ncHgLCwsEc+ly1btjx0+2bNmmHnzp1ITEx0WKyZlZXnZlG1alUEBwejcePGWLNmjSPDdCqjvHbZZcTXLyYmBgDSfZ9T+foxqbGjU6dO4YcffkCvXr0eeZvo6GgAQJEiRayuL1KkyP3vGV2LFi3w22+/YfXq1fj222+xY8cONGrUCPHx8apDyzYjvX7R0dEoXLjwQ9cXLlw43Vhd8fW7evUqkpOTM/XvHh0dnebtk5KScPXqVYfFmllZeW7BwcGYOnUqFixYgIULF6Js2bJo3Lgx1q9f74yQHc4or11WGfX10zQN77//PurVq4cKFSo88nYqXz8mNWkYOnRomou4Ul927txpdZ+oqCg0b94c7du3R48ePTL8GSaTyepc07SHrnOUrDy/zOjQoQNatWqFChUqoHXr1li5ciWOHz+O5cuX2/FZPJqjnx9gnNcvrZgyilX165eezP67p3X7tK53BZl5bmXLlkXPnj3x9NNPo06dOpg4cSJatWqF0aNHOyNUpzDSa5dZRn39+vbti/379+P333/P8LaqXr8cDn10g+rbty86duyY7m1KlChx/zgqKgoNGzZEnTp1MHXq1HTvFxQUBEAy2eDg4PvXX758+aHM1lEy+/yyKzg4GKGhoThx4oTdHjM9jnx+Rnr99u/fj0uXLj30vStXrmQqVme/fmkpWLAgvL29Hxq5SO/fPSgoKM3b58iRAwUKFHBYrJmVleeWltq1a2PWrFn2Dk8Jo7x29uTqr1+/fv2wZMkSrF+/HsWLF0/3tipfPyY1aShYsCAKFixo020vXLiAhg0bolq1apg+fTq8vNIf/CpZsiSCgoIQERGBqlWrApA59XXr1uHrr7/Oduy2yMzzs4dr164hMjLSKglwJEc+PyO9fnXq1EFMTAy2b9+OmjVrAgC2bduGmJgYPPPMMzb/PGe/fmnx8fFBtWrVEBERgbZt296/PiIiAm3atEnzPnXq1MHSpUutrlu1ahWqV6+OnDlzOjTezMjKc0vLnj17lL5G9mSU186eXPX10zQN/fr1w6JFi7B27VqULFkyw/soff0cvhTZjV24cEErXbq01qhRI+38+fPaxYsX719SK1u2rLZw4cL75yNHjtTMZrO2cOFC7cCBA9qrr76qBQcHa7Gxsc5+Chk6e/astmfPHm3YsGFanjx5tD179mh79uzR4uLi7t8m9fOLi4vTBg4cqG3evFk7ffq0tmbNGq1OnTpasWLF3OL5aZqxXr/mzZtrlSpV0rZs2aJt2bJFq1ixovb8889b3cYor98ff/yh5cyZU5s2bZp2+PBhrX///lru3Lm1M2fOaJqmaYMGDdI6d+58//b//feflitXLm3AgAHa4cOHtWnTpmk5c+bU5s+fr+opPFJmn9vYsWO1RYsWacePH9cOHjyoDRo0SAOgLViwQNVTSFdcXNz93y0A2pgxY7Q9e/ZoZ8+e1TTN2K+dpmX++Rnp9evdu7dmNpu1tWvXWr3H3blz5/5tXOn1Y1KTDdOnT9cApHlJDYA2ffr0++cpKSnakCFDtKCgIM3X11erX7++duDAASdHb5uuXbum+fzWrFlz/zapn9+dO3e0sLAwrVChQlrOnDm1xx57TOvatat27tw5NU8gA5l9fppmrNfv2rVrWqdOnbSAgAAtICBA69Sp00PbSI30+k2YMEELDQ3VfHx8tKefftpqW2nXrl21Bg0aWN1+7dq1WtWqVTUfHx+tRIkS2qRJk5wcse0y89y+/vprrVSpUpqfn5+WL18+rV69etry5csVRG0byxbmBy9du3bVNM34r11mn5+RXr9Hvcel/pvoSq+f6f+DJiIiIjI07n4iIiIit8CkhoiIiNwCkxoiIiJyC0xqiIiIyC0wqSEiIiK3wKSGiIiI3AKTGiIiInILTGqIiIjILTCpISIiIrfApIaIiIjcApMaIiIicgtMaojIsK5cuYKgoCCMGDHi/nXbtm2Dj48PVq1apTAyIlKBDS2JyNBWrFiBF198EZs3b0a5cuVQtWpVtGrVCuPGjVMdGhE5GZMaIjK8Pn364J9//kGNGjWwb98+7NixA35+fqrDIiInY1JDRIZ39+5dVKhQAZGRkdi5cycqVaqkOiQiUoBraojI8P777z9ERUUhJSUFZ8+eVR0OESnCkRoiMrSEhATUrFkTVapUQbly5TBmzBgcOHAARYoUUR0aETkZkxoiMrQPP/wQ8+fPx759+5AnTx40bNgQAQEBWLZsmerQiMjJOP1ERIa1du1ajBs3DjNnzkRgYCC8vLwwc+ZMbNy4EZMmTVIdHhE5GUdqiIiIyC1wpIaIiIjcApMaIiIicgtMaoiIiMgtMKkhIiIit8CkhoiIiNwCkxoiIiJyC0xqiIiIyC0wqSEiIiK3wKSGiIiI3AKTGiIiInILTGqIiIjILfwfPnZjp+KLdQIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sol.y[0], sol.y[1], 'r-')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a034bad4",
   "metadata": {},
   "source": [
    "This is an example of a **limit cycle**."
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## The predator-prey equations"
   ]
  },
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   "metadata": {},
   "source": [
    "- $x$ = population of rabbits (prey)\n",
    "- $y$ = population of foxes (predators)\n",
    "- Rabbits eat grass and reproduce. Foxes eat rabbits.\n",
    "- Without foxes, the rabbit population grows.\n",
    "- Without rabbits, the fox population declines."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed8c669",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    " \\dot{x} &= a x - \\ldots  \\\\\n",
    " \\dot{y} &= -c y + \\ldots\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "398f6e7e",
   "metadata": {},
   "source": [
    "The two variables $x$ and $y$ can be packaged into a vector $\\mathbf{Z} = [x, y]$, which we can represent in Python with a list or array with two elements."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de50ec2d",
   "metadata": {},
   "source": []
  }
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