{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def circle_map(K, y):\n",
    "    return K/(2*np.pi) * np.cos(2*np.pi*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "N_SIM = 10\n",
    "for y0 in [0.74, 0.8 ]:\n",
    "    pass\n",
    "    # berechnen und plotten Sie HIER die Zeitdynamik"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAD4CAYAAADhNOGaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy89olMNAAAACXBIWXMAAAsTAAALEwEAmpwYAAAOn0lEQVR4nO3cf4zkdX3H8eerrBINDT9PpHdcl8i19oi1tlOw0aZUEA4TPdrSBGz0Ymjuj0qjtU2kNREL/gFNFWP80VyA3Gka0VBarrGWniC1qYLMUSqeFG8LVQ5RTo7Qoqnkyrt/7Jdm2e7dzd7M7dzM5/lINjff7/ezO+9v9jLPmfnubqoKSVK7fmLcA0iSxssQSFLjDIEkNc4QSFLjDIEkNW5m3AMcjlNOOaVmZ2fHPYYkTZSdO3f+oKpWLd4/kSGYnZ2l3++PewxJmihJvr3Uft8akqTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGGQJJapwhkKTGjSQESTYkeSjJXJIrlzh+bJLPdsfvSTK76PjaJM8k+aNRzCNJGtzQIUhyDPBx4CJgPXBZkvWLll0OPFVVZwLXA9ctOv5h4AvDziJJWr5RvCI4G5irqoer6lngZmDjojUbgW3d7VuA85IEIMnFwCPArhHMIklaplGEYDXw6ILtPd2+JddU1X7gaeDkJMcB7wX+9FB3kmRzkn6S/t69e0cwtiQJxn+x+APA9VX1zKEWVtWWqupVVW/VqlVHfjJJasTMCL7GY8DpC7bXdPuWWrMnyQxwPPAkcA5wSZI/A04Ankvy31X1sRHMJUkawChCcC+wLskZzD/gXwq8ddGa7cAm4KvAJcCdVVXArz6/IMkHgGeMgCStrKFDUFX7k1wB3A4cA9xUVbuSXA30q2o7cCPw6SRzwD7mYyFJOgpk/on5ZOn1etXv98c9hiRNlCQ7q6q3eP+4LxZLksbMEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS4wyBJDXOEEhS40YSgiQbkjyUZC7JlUscPzbJZ7vj9ySZ7fa/McnOJA90/75hFPNIkgY3dAiSHAN8HLgIWA9clmT9omWXA09V1ZnA9cB13f4fAG+uqlcBm4BPDzuPJGl5RvGK4GxgrqoerqpngZuBjYvWbAS2dbdvAc5Lkqr6l6r6brd/F/CSJMeOYCZJ0oBGEYLVwKMLtvd0+5ZcU1X7gaeBkxet+S3gvqr68QhmkiQNaGbcAwAkOYv5t4suOMiazcBmgLVr167QZJI0/UbxiuAx4PQF22u6fUuuSTIDHA882W2vAf4aeHtV/fuB7qSqtlRVr6p6q1atGsHYkiQYTQjuBdYlOSPJi4FLge2L1mxn/mIwwCXAnVVVSU4APg9cWVX/PIJZJEnLNHQIuvf8rwBuBx4EPldVu5JcneQt3bIbgZOTzAHvAZ7/EdMrgDOB9ye5v/t42bAzSZIGl6oa9wzL1uv1qt/vj3sMSZooSXZWVW/xfn+zWJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaZwgkqXGGQJIaN5IQJNmQ5KEkc0muXOL4sUk+2x2/J8nsgmN/3O1/KMmFo5hHkjS4oUOQ5Bjg48BFwHrgsiTrFy27HHiqqs4Ergeu6z53PXApcBawAfhE9/UkSStkFK8IzgbmqurhqnoWuBnYuGjNRmBbd/sW4Lwk6fbfXFU/rqpHgLnu6x0x83d75G6vxH20MuvRMsc0zHq0zDENsx5Nc4zKKEKwGnh0wfaebt+Sa6pqP/A0cPKAnwtAks1J+kn6e/fuPexhq+qI3l6J+2hl1qNljmmY9WiZYxpmPZrmGJWJuVhcVVuqqldVvVWrVo17HEmaGqMIwWPA6Qu213T7llyTZAY4HnhywM+VJB1BowjBvcC6JGckeTHzF3+3L1qzHdjU3b4EuLPmX+NsBy7tfqroDGAd8LURzCRJGtDMsF+gqvYnuQK4HTgGuKmqdiW5GuhX1XbgRuDTSeaAfczHgm7d54BvAvuBd1bV/ww7kyRpcDlSFx+OpF6vV/1+f9xjSNJESbKzqnqL90/MxWJJ0pFhCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcYZAkhpnCCSpcUOFIMlJSXYk2d39e+IB1m3q1uxOsqnb99Ikn0/yb0l2Jbl2mFkkSYdn2FcEVwJ3VNU64I5u+wWSnARcBZwDnA1ctSAYf15VrwReA7wuyUVDziNJWqZhQ7AR2Nbd3gZcvMSaC4EdVbWvqp4CdgAbqupHVfUlgKp6FrgPWDPkPJKkZRo2BKdW1ePd7e8Bpy6xZjXw6ILtPd2+/5PkBODNzL+qkCStoJlDLUjyReDlSxx638KNqqoktdwBkswAnwE+WlUPH2TdZmAzwNq1a5d7N5KkAzhkCKrq/AMdS/L9JKdV1eNJTgOeWGLZY8C5C7bXAHct2N4C7K6qjxxiji3dWnq93rKDI0la2rBvDW0HNnW3NwG3LbHmduCCJCd2F4kv6PaR5IPA8cC7h5xDknSYhg3BtcAbk+wGzu+2SdJLcgNAVe0DrgHu7T6urqp9SdYw//bSeuC+JPcn+d0h55EkLVOqJu9dll6vV/1+f9xjSNJESbKzqnqL9/ubxZLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUOEMgSY0zBJLUuKFCkOSkJDuS7O7+PfEA6zZ1a3Yn2bTE8e1JvjHMLJKkwzPsK4IrgTuqah1wR7f9AklOAq4CzgHOBq5aGIwkvwk8M+QckqTDNGwINgLbutvbgIuXWHMhsKOq9lXVU8AOYANAkuOA9wAfHHIOSdJhGjYEp1bV493t7wGnLrFmNfDogu093T6Aa4APAT861B0l2Zykn6S/d+/eIUaWJC00c6gFSb4IvHyJQ+9buFFVlaQGveMkvwC8oqr+IMnsodZX1RZgC0Cv1xv4fiRJB3fIEFTV+Qc6luT7SU6rqseTnAY8scSyx4BzF2yvAe4CfgXoJfmPbo6XJbmrqs5FkrRihn1raDvw/E8BbQJuW2LN7cAFSU7sLhJfANxeVZ+sqp+qqlng9cC3jIAkrbxhQ3At8MYku4Hzu22S9JLcAFBV+5i/FnBv93F1t0+SdBRI1eS93d7r9arf7497DEmaKEl2VlVv8X5/s1iSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxhkCSGmcIJKlxqapxz7BsSfYC3z7MTz8F+MEIxzmaTPO5wXSfn+c2uSbp/H66qlYt3jmRIRhGkn5V9cY9x5EwzecG031+ntvkmobz860hSWqcIZCkxrUYgi3jHuAImuZzg+k+P89tck38+TV3jUCS9EItviKQJC1gCCSpcVMZgiQ3JXkiyTcOcDxJPppkLsnXk/ziSs94uAY4t9/pzumBJF9J8uqVnnEYhzq/Bet+Ocn+JJes1GzDGuTckpyb5P4ku5L840rON4wB/l8en+Rvk/xrd27vWOkZD1eS05N8Kck3u9nftcSaiX1MgSkNAbAV2HCQ4xcB67qPzcAnV2CmUdnKwc/tEeDXqupVwDVM3oWsrRz8/EhyDHAd8A8rMdAIbeUg55bkBOATwFuq6izgt1dmrJHYysG/b+8EvllVrwbOBT6U5MUrMNco7Af+sKrWA68F3plk/aI1k/yYMp0hqKovA/sOsmQj8KmadzdwQpLTVma64Rzq3KrqK1X1VLd5N7BmRQYbkQG+dwC/D/wV8MSRn2h0Bji3twK3VtV3uvUTc34DnFsBP5kkwHHd2v0rMduwqurxqrqvu/1fwIPA6kXLJvYxBaY0BANYDTy6YHsP//8bOw0uB74w7iFGKclq4DeYsGdcA/oZ4MQkdyXZmeTt4x5ohD4G/BzwXeAB4F1V9dx4R1q+JLPAa4B7Fh2a6MeUmXEPoCMjya8zH4LXj3uWEfsI8N6qem7+yeVUmQF+CTgPeAnw1SR3V9W3xjvWSFwI3A+8AXgFsCPJP1XVf451qmVIchzzr0TfPUlzD6LVEDwGnL5ge023byok+XngBuCiqnpy3POMWA+4uYvAKcCbkuyvqr8Z61SjsQd4sqp+CPwwyZeBVwPTEIJ3ANfW/C8uzSV5BHgl8LXxjjWYJC9iPgJ/WVW3LrFkoh9TWn1raDvw9u5K/2uBp6vq8XEPNQpJ1gK3Am+bkmeSL1BVZ1TVbFXNArcAvzclEQC4DXh9kpkkLwXOYf796GnwHeZf6ZDkVOBngYfHOtGAuusaNwIPVtWHD7Bsoh9TpvIVQZLPMP+TCack2QNcBbwIoKr+Avg74E3AHPAj5p+tTIQBzu39wMnAJ7pnzfsn6S8jDnB+E+tQ51ZVDyb5e+DrwHPADVV10B+jPVoM8H27Btia5AEgzL+9Nyl/uvl1wNuAB5Lc3+37E2AtTP5jCvgnJiSpea2+NSRJ6hgCSWqcIZCkxhkCSWqcIZCkxhkCSWqcIZCkxv0viq72IN1ZObAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1)\n",
    "\n",
    "# anzahl der simulierten kontrollparameter\n",
    "K = np.linspace(1, 2.1, 100)\n",
    "N_K = K.size\n",
    "\n",
    "# für jeden kontrollparameter wollen wir die \"fixpunkte\" von y, beginnend bei y0 = 0.1\n",
    "y = np.ones(N_K)*0.1\n",
    "\n",
    "# anzahl der simulationen pro K\n",
    "N_SIM = 10000\n",
    "\n",
    "for t in range( N_SIM ):\n",
    "    # berechnen Sie HIER die Zeitdynamik\n",
    "    y = np.zeros_like(K)\n",
    "    \n",
    "    # wir warten, bis das System seine \"Fixpunkte\" erreicht, bevor wir diese plotten\n",
    "    if t > 0.9*N_SIM: \n",
    "        ax.plot(K, y, ',k', alpha=.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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