{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "empty-fleece",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "driving-system",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import root"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cardiac-sitting",
   "metadata": {},
   "source": [
    "## Equilibrium solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "alternate-allowance",
   "metadata": {},
   "source": [
    "The 'equilibrium' solutions are given by the roots (zeros) of the following function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "accredited-accuracy",
   "metadata": {},
   "outputs": [],
   "source": [
    "def equilibrium(a, F, zeta, sigma, gamma ):\n",
    "    '''\n",
    "    a : oscillation amplitude\n",
    "    F : forcing amplitude\n",
    "    zeta : damping amplitude\n",
    "    sigma : detuning parameter\n",
    "    gamma : non-linearity amplitude\n",
    "    '''\n",
    "    return 4*a**2*(zeta**2 + (sigma - 3/8*gamma*a**2)**2) - F**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "aboriginal-success",
   "metadata": {},
   "outputs": [],
   "source": [
    "F= 0.3\n",
    "zeta = 0.1\n",
    "epsilon = 0.2\n",
    "gammas = np.array([-3, -1, 0, 1, 5])\n",
    "omegas = np.array([0.5, 2])\n",
    "\n",
    "def func_sigma(omega, epsilon=epsilon):\n",
    "    return (omega - 1)/epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "altered-limit",
   "metadata": {},
   "source": [
    "We first look at how the function varies to see how many solutions there might be. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "changing-container",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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20RWvahLyVmNwBNyPDFyIYIc6SHneTaTvFfUuBMGALGIKITASIv4WSts7zkvh9gQvlzGSbfsnZhm4Ow9zZZxaNQn5Zvw7EQJYLemPBw7B9kOREmWhuCgBD4LAFzFLfe/C9DASWvwz8IQOqRHyjkPJaHWaWUEcM/B2L/B2Bl5JQb5eHggBb9o+LWJCwFN5nIG0UN797nczNTXVdwfC1SgBD4JOBh7AIqZjQ7PsSwYOroDHPgMHtxa8ZbFsWK6FYrYz8NgJeNtCKXkZuGC4Uoh9HxRwrTSVgQfHO9/5Tu655x5fj6kEPAiCzMCbrjD4KeDNuJcRgrsb02pQTQqwbXTpri/ErQ7catoYyQRO2RWvahLyrfpAZODuIqZPwpgK2gPvLc6oRqoB3HTTTYyN+Xsij3dd06DS2UofQAbuUx8Uj6Q+OBn4UOVIZzu9aFSB+HngraaDmdaxi+7fqZKCfNUZHAH3MwPfaCrPV38XTj3a27GtqivgXo8Zj+1XwS13bvjUKEeqBYES8CDQEiASwWTgPgt41IuYLdvh8HyFPWMZUsYGJWyZCfILj3ZaylKtktC12HngVsMmO5zsZOC1pGDIkZsK+Hy5QbVhs2c8E0aYa2LZA7KI2SdRjVQLAiXgQZEwg6lC6Qi4f4uYUQn484Ua7/jU/Tw1W2ZqKMmn3vkSrtw1vPaDsxPkawWqSbcixSmX0GPYkbDjgS+XcDSBmU5v2kr2Mz9+lj/68s+xbMlbXjzN//3LV5Pod7BwDzRtB0P3S8A3sVA2yZQ3ZPYg6CkY29/T06MeqeYnfQm4EOK3gX+D29/xUeBdUsq6H4ENPLoZTDOrTi9wHz3wCKpQpJS87/MPc3K5zv/1S5fxqe8f4b1//RPued+rGEqtMUc0O0HealJLusLmbeaJWwbeqUIplWimdfLeekh27T4oP3l2kT/40mPcdNEkF07luPv7R7hwKse/nbkgxKjdv4fvi5hWxV1013zYHLQa2V8VShQj1YKi57+WEGIX8O+B66WUVwIJ4Da/Aht4EslgBLzus4Dr0Sxifu3np7n/6CJ/8IbL+DevOsCf/eqLOVGo8ZffO7L2EzIT5B1nVU/w9lCHmGXgXh24XS7RSCfIi/bJaI0qFCkl//ErB5kaSvKJX3sxf/CGy3nN5dv4s289RaEa7rxPbzeuLxt5INjt9H1WoUQxUg3gbW97Gy972cs4dOgQ09PT3H333X0fs9/odSAthNCBDPB83xGdL+jJwVjETGhYEWTg/+MHR9gzluEtL3YXj67bO8prLt/GX/3oKHVrDVHOningXgYepyoUKSWthmuhOMWSW0KI5q6HJM+1hn50eIFHjhX47ZsvJpt0L4Z/++aLqTZtPv/AsVBj92w00zcLJciOhP3vxAx7pBrA5z73OU6ePIllWRw/fpz3vOc9fR+z53dBSnkC+BjwHHASWJZSfv3sxwkhbhdCPCiEeHBubq73SAeNhDkYi5h6+IuYxxar3HdkkV+5brrTUAvgX79sL4Wqxdd+fu6CEJlxUlLSTLmX4067pWycuhHaloOUYKTcDLyahLyUbva9Rqb3+fuPkU/p/Itrd3V+dvnOPNftHeV/PXQizNCxWm4G7quFAsFl4H1YKGqkGiCEGAXeBOwHdgJZIcTbz36clPIvpJTXSymvn5yc7D3SQUNPBryIObgbeb70sCtOb37xrjN+/ooLJtg9lubvfrJGTW52EgEYGTcFtzsZeHwE3IvFSOo4xRIl0yZv251eLqsp1S3ueewU//LF0+dU37zh6h08carE07PlUOIGdwETBkjA+7BQ1Eg1l5uBI1LKOSmlBXwReLk/YZ0HJIJaxCyBmfNtYchIaDRCtlC+fWiOq6eHmR49s2RO0wS3XrWDHx9eoFg/qxFYexEwlzCxkgmcopuBx0nAm3U3FjOVwC6VWDZaDFvNNRcwv3Nojqbt8Iard5zzu1uv2oEQcM9jJwOP2cMTcP/qwINsKTuYW+mDoJ+/1nPAjUKIjHCvRX4ROOhPWOcBgWXg/gxz8DBDzsCXqxYPPbfEqy9e+2rstZdvw7Il3zl0lt1mpMHIkkej3hZII6nFykJZycAT2KUi5aQk36ytKeDfePw041mTa/ecO+RhWz7F5TvyfP/p+cBj9vDWQQy/dmIG5YGreZhn0I8Hfh/wd8BPcUsINeAvfIpr8AkyA/dTwHUt1Ik8P3hmHkeyroC/aPcoEzmTbx08fe4vs+PkHUktpeGUim4VSowy8M5AY1NDVqquB94onzNKzXYk3zk0yy9cOrVuvfcrLpzgp88WqIV0guosYiZ8KvlLBZSBSy/ZUF1AoM93QUr5YSnlpVLKK6WUvy6lDKj93gAS5EYeHwU87J2YDxxdJGVoXLN7ZM3fJzTBjQfG+fHhRaQ868SSmSBv25RTErtYQk/Gq4zQarQASDhNkJJqSjBcL0H2zJPVwZNFivUWr7xo/RmZL7tgnKbt8JNnlwKN2WPFA/c5A6+rDDxI1GksKPSA6sB9F/BwLZSHnitw9a6RDRfLbjwwzqlinWcXqmf+IjtJvtWklHSwi0W3aVRL4sSkl0snA2/VgHYjK8c5x0L58eEFAF66f/3dmTfsG0MTcP+RhYCiPRPvKsy3nZiGN5XHbw/cE3AlXaAEPDgGxEIJcydmo2Xz+PNFrt07suHjbjzgCpsndB2yEww36ywbrY6AA1jNmAh4exFTs9zNyBsJ+P6JLNuHU+seK5vUuXjbEA8fXw4u4FVYfi9ialow/VA8C0Vl4IAS8OAIsozQpz4o4HrgzZAy2J8/X6RpO1y7e+Pp7BdMZpnIJc8V8Mw4I40ylRTYxWLshjp4GXii4Zb/VVJtAV/lgduO5L4ji9x4YPO2otdMj/DIscK5VlIAeCdx38oIISAB994LJeCgBDw4BiYDF6EtYj70XAGAa/eMbPg4IQQvPTDGA0fP8n+zEwy3GlRSIMtldMP9EsdlIdOLQ6tXgPYwB9s5wwN/8nSJUr3FDfs3F/AX7RlhuWZx9GwrKQB898Ch3dDKbw/cy8CVdIES8OAIIgOXMoAywgS2I7FDmEz/yLECO4ZTbMuvbx14vGh6hBOFGnOlVe9hdpJh26GSEiDlqqEO8RFwIUDU3Ay8kRRkpDzDQvnZ8QLgVttsxtXTw2c8J0i8MkLfttJDQC1l4+OB33PPPVxyySVceOGF3HlnH90V+yD6d+F8JYhmVs0KIP3NwNt1v2EsZD5xqsjlO7Zm/3hVKmeIV2aCYceh0tZ/zXLFPS6VKM16y11Ybbcj1dImQmidocwAPzu+zFBKZ+/Y5n2/L5oaQtcET5wKvq+2dxXmmwcOwczFjIkHbts2d9xxB1/96ld5/PHH+dznPsfjjz8eehxKwINCD6CM0Odt9LDyhQ1awJsth8NzFS7ZvrXYr9yVRxPwyOpFvOw4I7ZDpd3QKtFyrYU4eeCrx6mZqYS7jX7VrtlHTyxz1a5htC30+zZ1jQOTWQ6FIuAvDA/cr5Fq999/PxdeeCEHDhzANE1uu+02vvSlL/UUUz+ogQ5BkUiCY4HjrNnIqCd8HuYAK1/YoCtRnpkr03LklgU8Y+pcNDV0TgY+4jhUvQy84ZbreVvYo8Zq2Bgpd5yaZWhkNXGG/91o2Rw8WeTdr9z6IIJLtuf5aQi14J1FzJAslD+5/094YvGJ7o/ptKBVByNzjo1y6dilfOCGD2z4dL9Gqp04cYLdu3d37k9PT58x2ScslIAHRaLdB9pugra557slAsjAjU4GHqwH7mWRl27f+snn6ulh7j14Giml2zkuO0HOcahk3OxLa5aBRGcDTdR0MvBSiXpKY8ixIbu98/tDp0pYtuSa6ZEtH/PS7UN8+ZHnKdYt8msNuvCJQBYxU8OxHKvmx0i1tSqDouhuqAQ8KPRVk+kNvwTc32EOsLJoFbSF8sSpEkZCcGAyu/mD21w9Pcz/95PjPL9cZ9dIGswsCSODltIBm0StBIzEJwOvuwJuz7qtZIdbFuRXNuv8rG0HXbXe2Lg1uGSb+7d+8lSJ6/f5O9F8Nd7fP+nXVnpwP6fN8ppTeTbLlNelugiFZ2Hq8pXvWJf4MVJtenqaY8dWerYfP36cnTt39hRPPygBDwpvlJZtbfy4bggkA3ezhqBrwQ+dKnLBZK4rj/XS9oLnoVNFV8ABMhMYaR1ooFWLwEhnA03UWA2bzLCJUypRTkpGmrUzLJRHjy8zmjGYHk1vcJQz8SynJ0IScN+aWcGZLWXTI/4cs9MLJdqRai95yUt46qmnOHLkCLt27eLzn/88f/M3f9NzTL2iFjGDQjfdWz8XMgd4EfOp2TIXb+subk+8Dp5clRFlx0kaIAWIShFNF7GyUMxkglaxSMl02gK+UkL4xKkil+/Md3WpPT2aJmsmeOp0sFZEZyu934uY4K+NIvsvI/RjpJqu69x111287nWv47LLLuOtb30rV1xxRc8x9YrKwIMiscpC8YuOhTJYi5h1y+ZEodYZn7ZV8imDXSPpM6swMhMMN4tuS9nlImZSp1mLSQbeLiNsFZYoD8GIvbKN3nEkT54uc9sNuzc5ypkIITgwmePwfCWIkDt4PeH1LVTHbJlAhjr4U0box0i1W2+9lVtvvbWvY/SLysCDopOB+1gLHoSFEoIHfmyxipR05X97XLp9iCdOraolzk4w3GpSTQnsUhEjlaAZkwy82bAxkjp2sUglBSOrttEfW6pSs2wu3WIVzmr2T2Q5uhCsgFu2g5nQ/F2ICzQDVyPVQAl4cASRgdeXQU+vVLj4QMcDbwVXheJlj/vGexDwHUMcnqvQaLWz7OwEI80a5aSDUyxhphKx8MCllFgNGz2pIUslyinO2EbvXUV0ayMB7JvIcnyptvIeBIDVcvytQIGVQc6+Cnj/HrgaqabYHG+F3NcMvLjSKN8nkiFk4Ec9AZ/oJQPP03Ikz8y2M9CMm4GXkpJWcRkjqceiCqVlOSBBFzbCkZTTghHH7lgonoBf1IOAH5jIIiU8F2BPFMt2/N1GD8FM5ZES0CLfiRkXlIAHRaJtofiagRd99b9hdR14gAK+UGEsazKc7v7K4bIdXhVGWwSyE+1+KGAtF9oZePQWincVoDvuCbtjoXgZ+OkSu8fS5JLdLzvtb5/4gvTBm7b0dwETAhqr1t9E+vMNJeBBkQiiCsX/DDwMAT8yX2Hf+Oa9P9Zi33gWU9dWFjLbuzErSbelrJGKx1g1rxJGa7m9wF0BF5AaAdwuhJf0kH3DypXL0QAF3LKdAAXcZwtFCXgHJeBB4S1i+tnQKsAMPMjJ9Efnqz3ZJwB6QuPARJanZ90Of2RXGlrJchkjFQ8LZWUajyvg9ZRGOj0GmtbpA9OL/w0wnDaYyJkcCTIDbwVgoZg5fJ/KI2UsOhHGBfVOBIXe3n3pZwZeX/Y9AzcD3kpfbbY4Vayzv4cFTI8LpnI8M7dKwG2bSkogag1MU8TKQtGark+dSGmItv99ZL7SVR+Ytdg/kQ3UQnEzcJ8z2yCm8kgHNcxhBSXgQRGEgDf8z8CD3kp/dN4VtF4zcIALJrI8t1h1qzBWWSjgLho2G3YoU2s2YmWYg3uiSSRFZwHTO/lcMJnr+fi7xzIcXxywRUzwv6WsysDPQL0TQdER8Jp/x6wX3QZBPuJlXYEJeLt+eX8/Aj6Vw5G4Q47NLMPC7HQk1KUFMvqhDp6No9XbrWRNu1MD7lkf/bwH06MZThbrgW24CmQREwJoKas88NUoAQ8KvzNw23JPBn574HqwOzGPtbPGPT0uYsJK5np4rgxCkE2PU0u5X+KE0x7qELGAd+ZhVpZpJQQ5aZ2RgW/Pp8j2UIHisXs0jZRwctnHhGAVbh14QAJeVxl4UKh3Iii8DoTtRa2+8b4EAXngQTWzOlGokU/pfbVC9TLXZ+bcTFZkJxApN+5E+wQZ9WYeT8BFeZlKWjDSqndKCA/PVXrahbqa6VH3BHhsMRgBb7Z3YvrOeeyBv/vd72Zqaoorr7wyshiUgAeFtxPT8knAG+3JNEHVgQe0E/P4Uo1do71n3wDZpM7O4RTPrKpE8Taj6pab4TcjXsj0yghFaZFS0mlvox9HSsnhuXLfAr57zO1geHwpGB88kEVMCEDA41MH/s53vpN77rkn0hiUgAdFQgdNj30GntAECU0E5oGfWKp11T51Pc6sRJnEML2qDzcrjzoDb9ZtNE3QKsyfsY1+odKkWG9xYKL3BUyA7fkUCU1wLCABD6SMENqT6f30wPuzUPwaqQZw0003MTYWXIvfraC6EQaJnvbPAw+gE6GHkQhGwKWUHF+q8vILxzd/8CZcMJnj735y3J3Ok53ESDQBHa1WBEZpRr2IWWthpnVaJwquheK4nQgPt22ffjNwPaGxYzjF8aWAPPAgNvLAugJ+6o//mMbBHkaqWRUQiZU1ptUvddmlbP+939vw6X6NVIsLSsCDRE/6V4USUAYOro0ShAdeqFpUmvbKMIY+uGAyS7nRYrbUYFtuirxo0TANchX3fYm6FrxZb2GmE9jLy5QnYI9tQ3aSI0fcq4Z+M3CA3aOZzqKw31i2DM4Db5bcqTx+IOnbQvFjpFpcUAIeJHpqIDJwM6EFUoVyouCevKb79MABDrQrUZ6ZLbMtO8WI7VBOwVDJHfgb9W7MZs3GTOvIYonKNAy3PfDDc6cxdY1dPthI06NpvvvknA/RnkszyCoUcEerrWKzTHldTv4M0qMw0l1f9dX4MVItLigBDxIjFYAH7m8dOLgZeBAWirfg5osH7gn4XJmXT00y7DgU05IdRVfQol7EbNZamMkEWrVOOaUxIjVIj/LM3GH2jWdI+DAoYfdYhtlSg7plkzJ8nF1J20Lxc5yah+/9UPovI/RjpFpc6OudEEKMCCH+TgjxhBDioBDiZX4Fdl6gp3ysQgnQA9dFIFvpPb/WDwHflk+SMjSOLlQhO8WIY1NOCVpLp4E4LGK2MAz3PaykYCQ1BkJweL7si30CK++jd2XjJ82gPHDP8vNLwH1oZuXHSDWAt73tbbzsZS/j0KFDTE9Pc/fdd/cVVy/0m4F/HLhHSvnLQggT6P9a+XxCT/qYgbeHOXhNsnwkKAvl+FKNXFLvqY3s2Qgh2DeedXdj5vYwajs8mwa7UMDYHv1Qh2atxUje/TpV0jCUncSyHZ5bqPL6K7b78hq7x7xa8Gpf2/LXwgqyDhzaAt7nJCkf5mF6+DFS7XOf+1zfcfRLz++EECIP3ATcDSClbEopCz7FdX7gdxVKAAuYAKaeCKQb4YlCjV0jad9GV+0dz/DsQgUy44w5knIa5HI8xqo1aza6cGOQSYGW28axxSotR/a1hX41O4bdyotTyz4lBW2klDRaTme4h694V4x+9EPxpvH0+XlSI9VcDgBzwP8QQjwkhPhLIcQ5n1QhxO1CiAeFEA/OzQWzABNb/K5CCcA+AXcqTxDjuo77VAPusW88y7OLVRw0Rs1hSmkQxQpmMtoMXErpWijSbR2smRKyU50eKAd8ypa35VMIAc/7LOAtRyIlJH321YGVDNyP7fSdhmX9Ca8aqeaiAy8G/ruU8lqgAvzu2Q+SUv6FlPJ6KeX1k5OTfbzcAOJ3FUpAGXhSD8ZCeb5QY6cPJYQee8YzNFsOp4p1RtMTlFMC4TgYpoi0CsW2HBxbkmhPX9KNFuSmeK5d8tfrMIuzMRIak7kkp3zuh+JdfQVrofjRD8XLwNX+Q49+3onjwHEppVdE+Xe4gq7w8LsKJagM3PDfQqk1bZZrFjtGzt1w0SveUOSjCxWGMpNUvI6ECdnZyh4F3snD29ZvrhLwrJlgLOvfusWO4RQnfc7AvZN30ghiEbNdNeVnBn4eWB9+0fNfTEp5CjgmhLik/aNfBB73JarzBb+rUALMwP0W8FNF99+9Pe+fgO9tZ7LPLlTRhrZB+9CGsGnWIhTw9msnLNcySRnuNvpji1V2j2V89Vq3D6d898A9+yyQDNzMuRmzrx64ysA9+q1C+U3gs+0KlMPAu/oP6TzC1yqU4DJwMwAP3Gt7un3YPwHfMZzGTGhuj/HsJMJ0v9CG1qJRiy4r82rQE/UyDQPywoHcNp5brHauGvxix3CaHzy94OsxG1aAGbgQ7ue2vtz/sXzywM8n+hJwKeXDwPX+hHIe4nsViv+beKCdgVs+Z+DtLHHHsH8eeEIT7B5L8+x8FQ5swzRbgI7uNGnWosvKGl72X16kmIYx20ZmJ3lu8QivusjfdZ8dwynKjRalusVQHy16V+O1UUjqASxigvu59UPA8a+M8HxBvRNB4lcVim2BVQ2wCsV/D9zzaf20UMD1wY8uVCA3RdJoe892jWa9hXSiGatm1dw4nOIcpTSM2g7zDFO3HPaM+bs1YnsApYTeyTsQCwXaAh6fMsLzCSXgQaKnwGmB3ac/6+1iC9QD99dCOV2sM5w2SJv+ZnV725t5ZHaSjOF+oXWrCpLIOhJ2MvDCHKW0YEwKnqu6C5d+C7hX1eNnKaH3tw/EQgH/MnDlgZ+DeieCxJvKY/dpo9SDGebgkTT8LyM8uVzvbDzxk30TGWqWzZIYYQSHahISDbdRUqNq+f56W8HzwEVhjlIGxpLDHFtyBXa33xl43svA/SslbAZZRghKwANENbMKEq9nsVUHs4/FLG8FP7AM3LVQpJS+VUycWq77uoDpsbe9KPhsI8eobVNOgVFdAC6gWYsmA/eqUPTCPKVtMJoa69SA+7mRCdzNPICvpYSNThlhgB54jHZi+sW+ffsYGhoikUig6zoPPvhg6DEoAQ8SvT1Wrd9KFM8/DHAnJriLWX4tZJ1crnPFTv/j9TbFPFM2GXUcSmkYKy+CAc1aRBl4rYVuahjlKqW0xljGrUDZnk/53jXQ1DUmckl/PXBPwIPYSg/+V6HEKAP/9re/zcTERGSvH5934nxEb2df/Qp44Bm4+zHwayGz2XJYqDQCycB3jaTRNcGRpQZjes7djVl0y+oaUWXgdRvTdN/DWlqSbpcQ+u1/e+wcSQXigQcyUg1WMnDZ5yKzDxaKnyPV4oDKwINkwDLwhuV0Nsf0w2ypjpQE4oHrCY2dI2mOLdYYTY1RTpfQSgswDs2oPPBaC6O92VKmJCK3jWMHq7z8gmAys+35lFuJ4xOBZ+Cd8tcVAf/e3z7J/LHy2o9fD7vp/mc+wlq14BO7c7zqrRdveAg/R6oJIXjta1+LEIL3vve93H777d39e3xACXiQeB64bxl4UHXg7mW+X5Uo3uX9dh9rwFezeyzNc4tVRnMTlNMl9FNRZ+AtDM0VQZG0sdITnCrWO5Pk/WbHcIofHfZvM09nETNoAZf9XuH5s5HHr5FqP/jBD9i5cyezs7O85jWv4dJLL+Wmm27qK7ZuUQIeJF4VSr+beYLOwNvlY35VogRVA+6xZyzDNx4/zci2HZTSR0gut8eqRemBa+5CpmE6LIgRpPS/hNBjx0iaUr1FudEil+z/K7ySgQe1iNn+3K4S8M0y5TVZPgHVedhxTV/h+DVSbefOnQBMTU3x5je/mfvvv18J+HlFpwqlz5KvxrJ7rACGOYD/Hvhprw9KABYKuDM258tNZGaSVhISjo1uiEg98Kx0Tx4p0+ZkyxWsoAR8pZSwzoVT/beqbYZlofSbgUsHP7bR+zFSrVKp4DgOQ0NDVCoVvv71r/OhD32o79i6RQl4kHQ8cB8y8ICyb1htofiXgWfMBPlUMB8vTxgLYgSS7pfaTGqReuDDwj1ppU2H5xpZoBaYgE/l3c/VbMkfAQ+0mRWsEnAfFjF9qEDxY6Ta6dOnefOb3wxAq9XiV3/1V3n961/fd2zdogQ8SDpVKP1m4MF1IoQV77Nh+eeBb8+nApt44m2OOS3zaEkHSGDoMroMvNZCGBXqBowIm6erGZJ6g8mhZCCvNzXkZuCzRX/67DRa7jg1zYfBy2uSPNdC6QmfBBz6H6l24MABHnnkEV9i6QdVRhgkA5OB+2uhnCrWOxtOgsDLbE9YeRLJdkfChBOJBy4d6W7hrxfdPihS48nlBHt8biO7mtUZuB80W05wC5jgo4XS/0R6UCPVFFvFzyqUADNwvy2U2VK9IzJBMJoxyJoJjtQzmF5LWaxIMvBmvQUSRLVAKQPjRo7nluqB2ScAQ0mdtJHwMQO3g/O/wecMvH/RVSPVFFvDWLWVvh+CzsB9rEKRUjJXajAVkH0Abv3t7rEMT5XTZJLtbexOPZKhDo1quxd4dYliWjCSGu0McggKIQRT+SSnS/4IeDOogcYeCd0d7NB3GaF/Fsr5gno3gsSvDLy+HHAG7lko/WewpUaLuuV0fNqg2D2W4fHlJMOaQ0MH0SxH0syqI+DlRcppGDLHKTdagQo4wLahFLNFfyyURtAWCrg2SkwWMc8n1LsRJAm/PPBlSI30Hc56+GmheJf1QVoo4PrgR5cajOgZlrOgNYqRNLOqt08aRnGJUhoMfaITX5BM5pPM+ZSBNyz/euCsS2oYpI3sR8R98sDjTLfvz/n9bkSNprki3h522xOthlvFEqCA+1mF4i2sTeaCFfDdo2lqls2IOUwxDVSXsVsOLZ8qabZKo+Jm4KnyMtU0VDR3Ak/QAj41lOzU2/dL0w4hA0/mSVVPsrCw0LuIn+cZuJSShYUFUqmtX72qMsKgMdL9WSheF7f0iC/hrIWfVSheVhh4Bt7uSpjRx3guU2G8ugQmNGs2elBtUdfAs230VhUnJTlluxUXQW2j99iWT1Fp2r7sxgx8ERMgNcz0U3/F8d03MDc319sxlk+636dMHwlRzEmlUp2+LFtBCXjQmNn+MnBPwAPqgwL+CrhnoUwG7YGPugKe0CYoZY4xVS7AiCuomXwwO1bXwvPADauKSDocbeaZyCXJmMF+tbxF4tlindxkf5t5mi0nuGk8HqlhjPlD7N+/v/dj/PFr4Nq3wy13+hfXgHP+Xo/EBSMNzT4EvFZwbwO0UPSERkITvixizpUbJHUtsF2YHtNtAW/ISUoZMEsFgNB98Ea1haaB5jTRTIenazn2BJx9w8pgh1kffHBvI0+gpPL9z8Vs1dzvk6KDEvCgMdL99UIJIQMHNwv3o4xwtujWgAe9SSJtJpgcSnKyNYKVkpi19li1kDfzNKoWpiERQCpp8/NiJnD/G1Zl4H4IeFiLmPXl3itRbMudL6sE/AyUgAeNkQWrj97N9YJ7G6AHDt5gYx8EvNQIfAHTY89YhmfqQ8iUg95uV+BZGmHRqLYwNDfrzxo2jxWTIQm4t52+/4XMUBYx21UoNHv8LnhJkB6sNTdoKAEPmr4z8IJ7G6CFAu25mJY/Ah50DbjH7tE0T1YzJJIORssVhvAF3ELHzYJz2SRNqQdeAw6QT+skdc2nDDyERUxvI1qvszG9QgCVgZ+BEvCgMTL9CXjHAw/WQjF1zRcP3LNQwmDPWIafFzOYSQejvVBcL4dtobTQWhXKKciZrkiFIeCd3Zg+ZOA1y/Z9duc5eJ/fXmdjet8hJeBnoAQ8aMxM75eN4GbgemplW35A+GGh1C2bYr0V6Db61UyPZTgtR0gnbTTZQk9I6pVwBbxebaFZJYoZSItg+4Cfjbsbs/8MvG45pM2YC7iXgSsL5QyUgAeNH4uYAWff4PZD6VfAOzXgIVkoe8YyWOik027ZoKG1aIQs4I2qhVYvUsiClOOYCS3QToyrmcon++5IKKWk3rJJBe6Bj7i3vVaieKW4KgM/AyXgQeOHhRKw/w2uB95vFYrnx06GZKF4VkU6maWZAJ16qBm4dCTNagu9ukwxI6i0xpgeTZMIqq/2WUz5kIE3bQcpIRm4hdL2wHu2UJQHvhZKwIPGyPRZhbIceAUKeBZKfx74XEjb6D2251MYCYHBMMUMJOwK9Up4i5jNho2UYFYKlDOSU42RUPxvj6l8klKjRbXZ+7+53nRP2uF54IXenu8NRdGVgK9GCXjQGBm3ftXuMTOsF8KxUHzwwGdD2kbvkdAEu0bS2M4wxSwkmuVQM3DPrklWyrTS8FRlKDT/G/yZzFNvn7TTQQt4v1UonQxceeCrUQIeNN4lX6/b6QPuROhh6lrfZYSzxQaagPFsOAIOro1SaYxSTAsS9eVQW8p2ttG3qjgph6ONcAV8W77/zTz1dvOvVNBb6Y2UuwDpVVV1i/f9URn4GfT9VxNCJIQQDwkhvuJHQOcdZvsL3et2+lohpAw84YOF0mAilwzNAwZXwE/WRillwKgWqFda/bUs7QKvlaxuVUikbE7L0XAtFC8D72Mhs26FZKGAm4j0bKEoD3wt/Djt/hZw0IfjnJ8Y7S90Lxm444Tqgdf7zcADHqW2FrtHMxxt5GmmJGal6C4shjSZx6s5N6wKZtJhnuHAuxCuZqWhVe8ZeC2sDBwgPQq1pd6eq+rA16Svv5oQYhr4JeAv/QnnPKRjofRQidIsATKUDDxtJjp+aK+EuQvTY89Yhlk5ipN2SNVLAKEtZHoCblplzLSORTi7MD1GMgZGQvhkoYSQgadH+7BQ1Fb6tej3tPunwO8A66ZuQojbhRAPCiEe7LkP8CBjZN3bXjLwEDoReqSNBLVm/wIeVgWKhyvgI8j0ynb6sBYyvdfRWxW0dIrRjEE+ZYTy2uDuxpzM9VcLHq6Aj/TvgZtZv6I5L+hZwIUQbwBmpZQ/2ehxUsq/kFJeL6W8fnJysteXG1z6WcQMYZiDR8pI0Gg5OE5v/rHtSBbKjdAtlD1jGeYYIZFyMNrlmmFt5qmXLXRhYWsOJMJdwPSYzKf6Gq3W8cCD7kYI/VkozYqbfWvhDesYBPrJwF8BvFEIcRT4PPALQojP+BLV+UQ/FkqnkVU4Fgr0PtRhodLAkYS2jd5jOGOQSqVJZBLorXY/lJAEvFa2SMg6yxlotPKh2iceU0PJ/soIw/TAUyP9CbgR/vsbd3r+q0kpPyilnJZS7gNuA74lpXy7b5GdL3iXfL30Q+n0Ah/xLZz18OqAaz3OlAxrEs9a7BnPoKWSnQw8NA+8YqHbFZazUKgNR5KBTw0lmSv3L+CB90IBNwO3KtBqdv9cqwpmf5OHzkdUHXjQ9JOBh9SJEPoX8LBmYa7FnrEMlp5DCzkDr5ct9EaR5YygaE1GJOApFivNntsgdDLwUCyUkfaLFrp/brOyUpKr6OCLgEspvyOlfIMfxzrv6JQR9mKhhOiBtzOwXhcyvYW0sC0UcGvBa9YwxaxDgmaoAm7Ui9QyktPOVDQC3j5hzveYhddbIdaBp0fd215sFGWhrInKwIOmI+C9WCgFEBqYQ76GtBZeBl7v00KZCLkKBdwMvNKYoJAF3amGt4hZsUhWizTTklNyLDIPHHrfjemdsAMf6AAriUgvlShWVVWgrIES8KDx6lZ7tVCSedCC/zP17YGXGgynjXAyubPYM5ahaE9RyAkSViWUDLxl2VgNm2SzjMw4zIpxdgyH7/9PrppO3wv1lo2pa2hh7J7tNwNXAn4OSsCDRtPc/g29lhGGYJ/AShVCrxbKXKkRiX0CroCfdqaoZiRGoxjKIma93O6DYlXQ0pLM8BR60JPd12BlO31vGXjDcoJvZOXR6Qle6P65VlVZKGugBDwMzExvvVBC6kQIKx5o7xl4+NvoPXaOpDnNGK2MJFkvUy/3UOXQJV6Wb1hlSBvsGY8mO5zImQjRu4DXLTucEkLwIQNXAn42SsDDoNehDrWllQ99wHhlZD174BFso/cwEhoivwuZdkg2StSKIQh4+yRhtCpYZoo949GIi57QGM+anV7s3RLKPEyP1DAgehRwVUa4FkrAw8BI97aIWVuC9Jj/8axBP4uYUkrmSo2OHxsFk+PjiBQYVgmr6WD12RZgM2rllQy8auQjqUDxmOxjMk/dssMpIQR3F2Uq3/0ippTu90dZKOegBDwMes3Aq4uQCVfAe/HAi/UWjZYTmQcOrg/uJE3MptvQKugs3Kt0sUSFqhxjb4QC3s9mnrrldEpIQ6GX7fR20x2KoiyUc1ACHgZGDx6447geeMgWSq2HlrLeJp4oM/DdYxkaZhrTagt4KdhKFC8DL6cqVFpTkVko0N92ejcDD1EGetlO7+1iVhbKOSgBDwMzC81yd8+pF0A6oVkoXh1wL4uY3iaeKAV873iGmjG8koGXgs3Aq8UmCbvKcsamYG2P1EKZyieZLzd6akRWD9MDBzch6bYKpTORXmXgZ6MEPAySue4F3MtSQrJQhBCkjURPHnhnG33EFkqZcRxcAa8GLOC1YhPDKlHNQjW1g6EQ28iezdRQipYjWax2/2+uNm0ycbdQOhm4qgM/GyXgYWDmoNGjgIeUgYNro/TigXcslFx0zfb3jGUot7ZRNsLLwJONIq2MgzG6O9DX2ozJPibzuAKu+x3S+qRHlID7iBLwMEgOdZ+BVxfd25AycGgPdegxAzd1jXw6RCE4i+G0QU3bRSljoTkNasVgPfDqcp1ko4hMS0bGtwf6Wpuxsp2++1LCarMVQQZecCtLtoqyUNZFCXgYmG0LxeligbDWFvCQFjHB3Y3Zq4UymUsiRHjDjM9GCIE2vIda1i0lDNxCKTUxmyVa6QR7J6LNDPvZjVlt2mSSIQu4tKFR2vpzVAa+LkrAwyDZXj3vZjt9NQoB780Dny2FP4lnLdLju2lmHcxGMdAywpZl02xIt+Y8aUbSxGo13nvf7WQe25E0Wg4ZI8QrJ287fTc2iifgKgM/ByXgYeCVP3Vjo9SW3E6EIQxz8OjHQgl7FuZabJ8Yx8pAslmiutz7nMjN8EoUzWaRejIXaQ04uCfeoZTedUOratPt55INOwOH7ipRVAa+LkrAwyDZbgfbzUJmbdEV7xA6EXqkzQTVHhYxo+yDsprdYxla6QRms0StjzFjm+EtkJrNEsvGBHsj6oOymqmhZNcWirdgHco0Ho9e+qF4dksq7388A44S8DDoZOBd+H4h7sL06GUyfbPlsFS1Iq1A8dgzlqGZTrsCXrV7HtC8GdW2PWNToqTtiLR80mNqqPvhxpX23zobdhUK9CbgIfTFHzSUgIeB54F3m4GH6H8D5JI6lWZ3rVi9STBxyMD3jGWoJIcxrBIgAhvs4Al4JVkikT4QTi/tTZjKd5+BexZKqBl4Zrz94otbf06z5LZkTkRX5RRXlICHQWewcZceeIg14ACZZIJqo7sMfKUGPHoB3zmSpqBvbwt4cJt5PAulki6RHLkokNfolslcktlSHdlFeV41kgy8/ZmuLmz9OY3Sig2pOAMl4GFg9uCBV5dCt1Cypk650V0GPhvhMOOzMXUNzH00EsE2tKoVLTS7QSPTIDu5N5DX6JapfJK65VDq4u9XjcID101IDisB9wkl4GGQ7KUKZTH0DDyb1Gm0HFr21uvV49DIajXG0MVUzWAz8Eqhhtks0szCrslwba716NSCd7F4W21EUIUCbmJSmd/64xulle+Q4gyUgIdBt2WErab72Ey44uDtyKt0sZDp7f6LYpjxWqQn99NIFgCoLgck4PNlks0izbTB3gi7EK6ml92YXgYeah04QHaiywy87M6GVZyDEvAwMLtcxIxgFya4i5iwsri1FeZKDcayJkYE8yDXYnLbLqxMDc1uUikEU0pYWqqTbBRopNORdiFcTS+beby/c6g7McFdyKx2m4ErC2Ut4vGtO9/RNDC6aCkbQSMrgExbwCtdLGTORjjMeC32TeSw0hrJ5jLl+R6mIG2ClJJaxSHZWKaYGmV6NB4CPtmLheJl4GF64ACZie6qUBpFJeDroAQ8LJK5rfd/iKCRFUCunYlVulgIi3qU2tkcmMxSzyRJNgqU5rtsILYFmnUb29FINgvUc7vD7aW9AfmUTlLXurJQKk0bIQhvpJqH54FvtWKmUVLDHNZBCXhYmF30BPcuLzMTwcWzBl5b0W5qweMm4HvGMlSTQ5iNZUpL/m+n92wZWxZIDV/s+/F7RQjBVD7ZlYVSa7ZIG4nw69izE2A3VrbIb4ayUNZFCXhYpPJbz8Arc+5tdjK4eNbAqwfeqoUSh2HGZ5MyEtRz290MuSq7qoveCp6A1/VlRsYv8/XY/TI1lOpqM08l7F7gHp3NPFvwwVsNcCwl4OugBDwsUsNQX97aYyvtFfqw68DbFspWFzGXaxZN2+mUsMUFZ/JijOYyjkzQqHZX174ZlWVXIJvJAqM7L/T12P3ibubpJgMPeRqPh3dluZVKFC/pUVUoa6IEPCy6EvA5twIlEe6Yrmx7EXOrm3niVgPuMTJ2BZZWAFYE1y+8DLyVLLBn27ivx+6XqXyyq46ElUbIwxw8sm0Br2xFwIvuraoDXxMl4GHRrYCHbJ/AioBvdTv9bAxmYa7F2M7LqJnue+13KWF5roxuVWlkJQcm4iUqU0NJivXWlnu6V5qtzt88VDJdbKfvZODKQlmLngVcCLFbCPFtIcRBIcTPhRC/5Wdg5x3J/NYFvLoQ+gImuN0IYeuLmHHNwHdt304j6ZZi+i3gyycLboliLs2u0bSvx+4Xz8ra6kJmqd5iKBWFgHsWyhY8cG/vhBLwNeknA28B/0FKeRlwI3CHEOJyf8I6D0mNuBN5WlvYHViZW7nMDJGE5k6m32oZoVeyFrcMfP/kEM2MW+FQXqj5euziQgmzUaAxNEEiBl0IVzOZ7243ZrneYigVrk0HuGKsGVvLwL2kRwn4mvQs4FLKk1LKn7b/vwQcBHb5Fdh5R2rYvfU8vY2IyEIB10bZ6lb62WKDlKF1dnDGhenRNI2shm6VWT7RxY6/LVAt2yQbBeRkPLoQrmaqy+n0xXormr+dEG6CspV+KN7knpB3JQ8KvnjgQoh9wLXAfWv87nYhxINCiAfn5ub8eLnBxBPwzWwUx3Y38kSQgYNbibLVDPxUsc72fCrSYcZrYSQ06kNjpOpLLJ4s+HZc23awWikSrSWGd17n23H9otvhxqW6RT4KCwXa2+m3kIHXCu5tiKMFB4m+BVwIkQP+J/A+KeU56aWU8i+klNdLKa+fnIwmq4wFHQEvbPy46iIgo8vATX3LAn66WGdbPl4lhB72+H5SjUXKBf8281SWGiA0molFJnde49tx/WI8a5LQxJY88GbLodFyovHAYesC7n1fvO+P4gz6EnAhhIEr3p+VUn7Rn5DOU7aagXubeDLRlKgNpXRK9S4y8OF4Cnhq14sxG4s0GknfNvOUFtyTgWUsMr1z2pdj+ommCSZy5pY8cK9UNDL7KzO+NQulVnC/O1o8WhbEjX6qUARwN3BQSvlf/QvpPGWrAu6tzEeUgefTBsUtCLiUktPFBttjmoHv2P0SbBZxMH3bzFOcrwLQSi2xfypeJYQek1scblyqu+PmIlnEBMhtW0lWNqK2pOyTDegnA38F8OvALwghHm7/d6tPcZ1/dAR8k0XMiLbRe+RTBsXa5rMkC1WLZsuJrYWyd/d+LN1tCuZlzv1SOOZe8tfS1ViMkFuLqaHUlhYxvausyCyU3JS7oN+sbvy4emFlELLiHHr+60kpvw/Ea/UqzmzZQvEy8GgWMfNpnWJ9cwE/1d7xF1cL5aJtQxwyVwR8ck//ZWhzz57CbJSpjw/HbuHWY2ooyc+Ob77fwBPwXFQCPrTdvS2fgrED6z+uVlAZ+AaonZhhYWZBJDYX8PKs+7iIyqbyKYNSvYXtbOwbewK+LQazMNdiNGtSa9eCF04s+XLM5bkSqfoiYnK/L8cLgqmhJAuVxqZj8TwLJR+ZhTLl3pZnN35cvaBKCDdACXhYCNHeTl/Y+HGlU64/GNGiTT7tfqHLm/jgp5c9AY9nBg7QGE2h2Q1mDx/z5Xi1ikaqvkj+wA2+HC8IJvMppISFysYbxqK3UNoZeOnUxo+rFZSFsgFKwMMkM7Z56VTp5MrlZQR4dcGb2SheBh63ToSrETsOkKovsuTDZh7pSCwni5SL7LvkJh+iC4atbuaJxSImQPn0+o+R0k14lIWyLkrAwySzhWGupVMwtCOceNbAy8CXN1nIPF2sM5EzMfX4foTGLrqRVH2RSrH/MsLKcgOEjqUvcuGePT5EFwxbHW4cizJCTd9YwK0a2E2VgW9AfL995yOZ8c1baEaegbsCvmkGvhzfTTweBy56JThzNO1837XghVm3WqJpLrAjpgu3AFP5re3GLNVbJHUtuhOwpkF2CkobCHhnNqzywNdDCXiYZDfZfdZquBPpI83A2xZKbRMPPMY14B4X7NmLnZhDaimqxS00EduA2SdPANDKVWJbgQLuUAch3BPsRhSjamS1mtyUW4WyHp1dmCNhRDOQKAEPE2/78HrZoLegM7QtvJjOYqsZ+OlinW0xzkQBJnImlun634XTm9Qbb8KJg0+hORbOZNaP0ALD1DWmhpKcKGzchbFYszon68gY2r6xhRJxSe0goAQ8TDLj7ny/9ToSeh/mCDPw4UxbwDfwwBstm4VKM/YZuBCCVs4V7tOHnuvrWIvPl0jX5slccK0foQXKrpE0z28i4IuVJmMZM6SI1iG3iYXS2dQ2FU48A4gS8DDZbBZg6aR7G6EHnjN1hNhYwE+2G0TF2Qv2kJNDCMfm+OOH+jpOvZokWZ9l39Wv8ymy4Ni5BQFfqjYZzUYt4NtdkbbXses6Aq4y8PVQAh4mXoOq9RYyOxZKdBm4pgmGkvqG/VC8y/O4TaRZi+FLbiBdn2fx+VLPx5COxBajSDnHRRde6WN0weBm4HWcDTZjLVVjkIEPbQMkVNbZzFOedStV1CLmuigBD5NsW8A3ysA1A9LhTqM/m+GMQaG6/qLfiSVXwKdHMmGF1DMX3/AmzMYszWrvJ5vSUh0pDFr6XOx9f3BPrE3bYb6ydiWKlJKlisVINuJFzOHd7u3yibV/X5l1ewLFeNE4apSAh0lmMwE/5donWrR/lrFscsOdfMcLNYSIbx+U1Vy2fx8Oc7TEKHKT9gDrMf+M69M2s8VYV6B47Bx2T1bPr9MLvdK0adpO9Bn4cLsl7/I6O2Ur85E1dRsUlICHSUfA19kZuHw8UvvEYyJrslDeOAPfNpSK9SYej5SRoKXPIrUkxcXe5mM+fd8D7v9si1jwtsjOEVfAvSuls1lqn5wj98A9AS+uk4GXZ5WAb0L8v4HnE2YOjMz6DXwKz8FI9Lv8xnMmC+tcfgOcKFQHwv/2cPKu//3cQ0/29PyTT89hWGVGr47fGLW18P426y1kLrXtsdGoM/DUMCTzbuKyFioD3xQl4GEiBOR3rp1x2C3357EQ8CQL5ea6uxdPFGrsGhkcATd3u618n7rvpz09v1HJkKo+zzWv+BU/wwqMfEonl9TXrQVfbGfgY1F74OBm4WsJuGwvbuaUgG+EEvCwye+E4vPn/rx0EpwWjO4NP6azGM+atBy55m5M25GcLNQHKgOfvvGXSNUXKDzfvYUiHUlL24aQz3Ng184AovMfIQQ7R1LrCnih6paIjkSdgUNbwNfwwJtlaNVVBr4JSsDDJr9rbQEvtDeaxCADn2hPm1mrimG2VKflyIHKwK996Wsw689jNUa6fu7yXAWpJXGM02ha/BcwPTbazNPJwGMj4Gtk4F5JbS66PRGDgBLwsMnvbGfb9pk/7wh4DDLwnPvFXmsh01sYG6QMfCSbwtFO0tKnsFsbDzo4m0Pf+xEA9ujmY8rixM6R9LoZ+FK16bp56RhYKCN73Kqsxll1+p6oewudijVRAh42+Z2uVXL2QFdPwGPwgR3Puhn4Qvlc0Xp2wd2avmcs/jXgq2lll0AkOPH4M1097/ADjwKQu+qCIMIKjL3jGQpVa816/rlSg/FskkQcrijGL3RvF876u3QEfFe48QwYSsDDJt/+QJ69kLl01C0h1KMfUTbhZeBr1IIfXaigCdg9OlgCru924334H7/Z1fMq8wap2iwvvfWdAUQVHPsncgAcma+c87vTxXp8RuGNtU+MC0+f+fPiCUDA0GCsO0SFEvCw8eq8z/bB5w/BxMXhx7MGXn3w/BoZ+JH5CtOjmYGoAV/NZa99HXqryvzRcwVtPaSUtMQ0Cesoe3ftDjA6/znQ7pp4eG4tAY9RK+Cx/YBYIwM/5m5q02Pg08eYwfoWng9424cLq7rjSQlzh2Dy0mhiOgsjoTGeNTm9xliuowsV9k3Eu6XqWlz3kteSrD1Lq7n1znZLJxex9WGkuc5GkxizezRDQhNrZuCzpXpn8EPkGGn3O3F2Bl54LhZ2YtxRAh42mTF3A8PqjKN4wi2bmrwkurjOYq2OdlJKjs5X2T8+WPYJQCKhgXgOy9hBY4M+L6v58Rf/NwD6tu4WPuOAqWvsGcucI+CW7TBfbsbHQgEYv+BcAZ9/esUfV6yLEvCwEQLGL4KFp1Z+NveEexuTDBxg50jqHAGfLzcpN1oDmYEDyPEKCI0HvvTlLT3+9GOn0ByLC17/+oAjC4b9E1memSuf8TNv1FqsxuFNXATzT4LTPlE2ylB6Xgn4FlACHgXjF7oZhsdcu1d1rATczcBX78Z8atYt9TowmYsqrL7Y9errATj8w8e39Hi7PkWyfowbX/2GIMMKjP0TWY4uVM5oK3ts0a0imo5TGej2q90r0KUj7v3F9tWpEvBNUQIeBZMXuxlGreDef/5hd8OC1242BuwaSVNp2mfsxjx40hXwy3YMRRVWX/yzN76dVO04zdLmu/uKsws0kntAOzxQG3hWc2AyS91yOFlc6Ur4XLsMdO9YjK6idlzj3p582L2d9a5I42MpxhUl4FGw88Xu7fPt3hzH7oPdN0QXzxp4Gdqziyse6hMni0zkTKaGYnT53QWGrqPJJ2maB6gsrzPWrs03//qzIBKY0xsPd44zl2xzT7RPnFz5tz67WCGhuVvtY8PkpZBIwvGfuPdPPOg2fotJVVacUQIeBbteDAg4/qBbTlh4Fna/NOqozuDCKdcmeXp2xUM9eKrIZTvyUYXkC8aOOlLT+canPr3h4xYPltDsJi+97a3hBBYAl+/Mown42fHlzs+eXaiyaySNnojRV183Yc9L4ch33fvHH4Cd14KWiDauASBGf8UXEKlh2H4lPPUNOPgV92cX3hxtTGexdzyLromOgLdshydPlwdewF/+rneg2U0WH10/A3ccB9u5BLPxJBddeX2I0flLxtS5aGqInx0vdH72zFyF/XFchD7wz+D0Y/D8Q3DyZ7DnZVFHNBAoAY+KK38Zjt8P3/5PMHU5TMVnARPcWvC94xmeagv4wZMlmi2HK3cNRxxZfxy49CrMxhNY4nKs5tqDm7/12c9imWNow/1Nso8DV00P8+iJZaSU1C2bp06XuGJnDE/CV/5LEBr8j1tB2nDlW6KOaCBQAh4VL/o1d0JPfRle/TtRR7MmV+wc5pFjBaSU/PiwOwbuxv3Rzuv0A3PiBC1jhH/4sz9b8/fPfecIwmlx3dt+KeTI/Oea6WHmy02eXajy5OkSLUfG8yQ8ug+u+VWwqnDR62KX0MSVvgRcCPF6IcQhIcTTQojf9SuoFwS5Sfh3P4Z/+yO44s1RR7MmN+wfY7bU4NmFKv/01BwHJrLx2cHXBzO/+X+QaNVY+Nm5G3SW5k7TFNeSrD/K1S//ZxFE5y83XexW3Hz70CwPHF0C4Ko4CjjAP/84vOde+Fd/HXUkA0PPAi6ESAB/DtwCXA68TQhxuV+BvSDITcG2+L5lL7vALWv87H3P8oOn57nlqvOjN/Pu/ReTbN1PPfUi7vvH/3XG7770kf8HW8+Sv3TrPVPizN7xLBdO5fjSw8/ztcdOcen2IXbHtZNkQofdL4lFQ7dBoZ8M/AbgaSnlYSllE/g88KaNnnDo0CE+/elPA2BZFjMzM3zmM58BoFqtMjMzwxe+8AUAlpeXmZmZ4Ytf/CIA8/PzzMzM8OUvu7voTp06xczMDPfccw8Ax44dY2ZmhnvvvReAw4cPMzMzw3e/+93Oa8/MzPDDH/4QgMcee4yZmRkeeMAdWPvwww8zMzPDww8/DMADDzzAzMwMjz32GAA//OEPmZmZ4dAhd9PNd7/7XWZmZjh8+DAA9957LzMzMxw75k4Xueeee5iZmeHUKbcx/Ze//GVmZmaYn3cHGn/xi19kZmaG5WW3QuALX/gCMzMzVKtune5nPvMZZmZmsCzXp/30pz/NzMxM57385Cc/yc03ryx8fuITn+CWW27p3P/4xz/OG9/4xs79j33sY7zlLSu+4p133sltt93Wuf+Rj3yEt7/97Z37H/rQh/hPv/ObvOzAOJ/83hGWvvtX/PSzf9L5/fvf/37uuOOOzv33ve99vO997+vcv+OOO3j/+9/fuX/77bfzwQ9+sHP/Xe96Fx/60Ic699/+9rfzkY98pHP/tttu48477+zcf8tb3sLHPvaxzv03vvGNfPzjH+/cv+WWW/jEJz7RuX/zzTfzyU9+snN/ZmbmjM/eXQ/9PQ88+XUe+8JhyqUSMzMz3PXfPkajcgP28qPc9bVvnjefvWucp7nnT/5PfvT4Ef75NTsH4rP3rne9q3P/gx/8ILfffnvn/qB/9nrRvfXoR8B3AatnIR1v/+wMhBC3CyEeFEI86H0gFIPDH77xCl510QSvvniSoVQMBgD4xNDoGKY8SD39Ij77239Es17j0b9/lJaeZdt1NYQYzM07a/HKCyfYlk/xhqt28O5X7I86HIWPiPUG1276RCF+BXidlPLftO//OnCDlPI313vO9ddfLx988MGeXk+h8JtyqcQXfuNT1NNXuT+QDlnzW7zzz/442sAUirMQQvxESnlOTWs/GfhxYHWT5GlgjWGPCkU8yQ0N8bZPvId87pukW99h1+WPKvFWDBR6H899ALhICLEfOAHcBvyqL1EpFCGRyeb49Y99NOowFIqe6FnApZQtIcRvAF8DEsCnpJQ/9y0yhUKhUGxIPxk4Usp/BP7Rp1gUCoVC0QVqJ6ZCoVAMKErAFQqFYkBRAq5QKBQDihJwhUKhGFCUgCsUCsWAogRcoVAoBhQl4AqFQjGgKAFXKBSKAUUJuEKhUAwoSsAVCoViQFECrlAoFAOKEnCFQqEYUJSAKxQKxYCiBFyhUCgGlJ5HqvX0YkLMAc/2+PQJYN7HcPxCxdUdKq7uUHF1R1zjgv5i2yulnDz7h6EKeD8IIR5cayZc1Ki4ukPF1R0qru6Ia1wQTGzKQlEoFIoBRQm4QqFQDCiDJOB/EXUA66Di6g4VV3eouLojrnFBALENjAeuUCgUijMZpAxcoVAoFKtQAq5QKBQDykAKuBDi/UIIKYSYiDoWACHER4QQPxNCPCyE+LoQYmfUMQEIIf6LEOKJdmx/L4QYiTomACHErwghfi6EcIQQkZd8CSFeL4Q4JIR4Wgjxu1HHAyCE+JQQYlYI8VjUsaxGCLFbCPFtIcTB9t/wt6KOCUAIkRJC3C+EeKQd1x9FHdNqhBAJIcRDQoiv+HncgRNwIcRu4DXAc1HHsor/IqW8Wkr5IuArwIcijsfjG8CVUsqrgSeBD0Ycj8djwL8E/inqQIQQCeDPgVuAy4G3CSEujzYqAD4NvD7qINagBfwHKeVlwI3AHTF5vxrAL0gprwFeBLxeCHFjtCGdwW8BB/0+6MAJOPDfgN8BYrP6KqUsrrqbJSaxSSm/LqVste/+GJiOMh4PKeVBKeWhqONocwPwtJTysJSyCXweeFPEMSGl/CdgMeo4zkZKeVJK+dP2/5dwRWlXtFGBdCm37xrt/2LxPRRCTAO/BPyl38ceKAEXQrwROCGlfCTqWM5GCPFRIcQx4NeITwa+mncDX406iBiyCzi26v5xYiBIg4AQYh9wLXBfxKEAHZviYWAW+IaUMhZxAX+Km3Q6fh9Y9/uA/SKEuBfYvsavfh/4PeC14UbkslFcUsovSSl/H/h9IcQHgd8APhyHuNqP+X3cS9/PhhHTVuOKCWKNn8Uic4szQogc8D+B9511BRoZUkobeFF7refvhRBXSikjXUMQQrwBmJVS/kQIMeP38WMn4FLKm9f6uRDiKmA/8IgQAlw74KdCiBuklKeiimsN/gb4B0IS8M3iEkK8A3gD8IsyxKL/Lt6vqDkO7F51fxp4PqJYBgIhhIEr3p+VUn4x6njORkpZEEJ8B3cNIepF4FcAbxRC3AqkgLwQ4jNSyrf7cfCBsVCklI9KKaeklPuklPtwv3gvDkO8N0MIcdGqu28EnogqltUIIV4PfAB4o5SyGnU8MeUB4CIhxH4hhAncBvzviGOKLcLNnu4GDkop/2vU8XgIISa9KishRBq4mRh8D6WUH5RSTrc16zbgW36JNwyQgMecO4UQjwkhfoZr8cSitAq4CxgCvtEucfx/ow4IQAjxZiHEceBlwD8IIb4WVSztRd7fAL6GuyD3t1LKn0cVj4cQ4nPAj4BLhBDHhRDviTqmNq8Afh34hfZn6uF2dhk1O4Bvt7+DD+B64L6W7MURtZVeoVAoBhSVgSsUCsWAogRcoVAoBhQl4AqFQjGgKAFXKBSKAUUJuEKhUAwoSsAVCoViQFECrlAoFAOKEnDFCx4hxC8LIX7c7iX9fSHEZNQxKRRbQW3kUbzgEUKMSykX2v//YWBeSvnnEYelUGyKysAVCninN80F+HdAPeqAFIqtELtuhApFmAgh/jXuUIdfkFKWhRD/BETeC0Wh2AoqA1e80LkK+GFbvN8CvBx4NOKYFIotoQRc8ULnr4B/L4T4HnAxcFhKWYk4JoViS6hFTIVCoRhQVAauUCgUA4oScIVCoRhQlIArFArFgKIEXKFQKAYUJeAKhUIxoCgBVygUigFFCbhCoVAMKP8/P3BHuhq+NsUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "a = np.linspace(-4, 4, 10**3)\n",
    "\n",
    "for omega in omegas:\n",
    "    sigma = func_sigma(omega, epsilon)\n",
    "    plt.figure()\n",
    "    plt.title(label=f'$\\sigma = {sigma}$')\n",
    "    for gamma in gammas:\n",
    "        plt.plot(a, equilibrium(a, F, zeta, sigma, gamma), label=f'$\\gamma = {gamma}$')\n",
    "    plt.ylim(-1, 10)\n",
    "    plt.legend()\n",
    "\n",
    "    plt.xlabel(r'$a$')\n",
    "    plt.axhline(0, color='k', ls=':')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fundamental-terrorism",
   "metadata": {},
   "source": [
    "There can be several solutions for each parameters. Hence for each value of omega, we will start from a random initial guess. This allows to randomly sample all the solutions (branches) and visualize how they evolve with the forcing frequency. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "preceding-kingdom",
   "metadata": {},
   "source": [
    "## Non linearity effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "verbal-computer",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "omegas = np.linspace(0.5, 2, 10000, endpoint=True)\n",
    "\n",
    "#initialize the array containing the equilibrium solutions\n",
    "sols = np.zeros([len(omegas), len(gammas)])*np.nan\n",
    "\n",
    "#several equilibrium position: want to randomly be on either solutions\n",
    "initguess = np.random.rand(len(omegas))*4\n",
    "\n",
    "#compute the detuning parameter\n",
    "sigmas = func_sigma(omegas, epsilon)\n",
    "\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    for j, gamma in enumerate(gammas):\n",
    "        result = root(equilibrium, x0=initguess[i], args=(F, zeta, sigma, gamma))\n",
    "        if result.success: #if a solution is found, save it. \n",
    "            sols[i, j] = result.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "endangered-bloom",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "accessible-kitchen",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11f784390>"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "cmap = plt.get_cmap('magma', len(gammas)+1)\n",
    "for j in range(sols.shape[1]):\n",
    "    plt.scatter(omegas, sols[:, j]/F, marker='.', s=1, color = cmap(j), label=f'$\\gamma = {gammas[j]}$')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$a/\\bar{F}$')\n",
    "plt.ylim(0, 6)\n",
    "plt.xlim(0.3, 2)\n",
    "plt.legend(markerscale=5, loc='center right')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "respected-relation",
   "metadata": {},
   "source": [
    "For each, amplitude of the non linearity, we find that there might be up to three solutions! For softening ($\\gamma < 0$) non linearities, this appears below the caracteristic frequency ($\\Omega=1$), while it is the reverse for hardening non linearities.\n",
    "\n",
    "The linear oscillator response corresponds to $\\gamma = 0$, for which there is always a single solution and a large amplification at $\\Omega=1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dressed-pattern",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "hungry-enzyme",
   "metadata": {},
   "source": [
    "### phase response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "cleared-hunter",
   "metadata": {},
   "outputs": [],
   "source": [
    "phis = np.zeros_like(sols)\n",
    "\n",
    "for j, gamma in enumerate(gammas):\n",
    "    phis[:, j] = np.arctan2(zeta,(sigmas - 3/8*gamma*sols[:, j]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "committed-implementation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12574d0d0>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "\n",
    "for j in range(len(gammas)):\n",
    "    plt.scatter(omegas, phis[:, j], marker='.', s=1, color = cmap(j), label=f'$\\gamma = {gammas[j]}$')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$\\phi$')\n",
    "plt.ylim(0, np.pi)\n",
    "plt.xlim(0.3, 2)\n",
    "plt.legend(markerscale=5, loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incomplete-blake",
   "metadata": {},
   "source": [
    "## Effect dissipation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "adjacent-suspension",
   "metadata": {},
   "outputs": [],
   "source": [
    "omegas = np.linspace(0.5, 2, 10000, endpoint=True)\n",
    "\n",
    "lzetas = np.array([0.1, 0.2, 0.3])\n",
    "sols = np.zeros([len(omegas), len(lzetas)])*np.nan\n",
    "\n",
    "#several equilibrium position: want to randomly be on either solutions\n",
    "initguess = np.random.rand(len(omegas))*4\n",
    "\n",
    "sigmas = func_sigma(omegas, epsilon)\n",
    "\n",
    "gam = 5\n",
    "\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    for j, zet in enumerate(lzetas):\n",
    "        result = root(equilibrium, x0=initguess[i], args=(F, zet, sigma, gam))\n",
    "        if result.success:\n",
    "            sols[i, j] = result.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "sticky-animation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1258a9050>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "cmap = plt.get_cmap('viridis', len(lzetas)+1)\n",
    "for j in range(sols.shape[1]):\n",
    "    plt.scatter(omegas, sols[:, j]/F, marker='.', s=1, color = cmap(j), label=f'$\\zeta = {lzetas[j]}$')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$a/\\bar{F}$')\n",
    "plt.ylim(0, 6)\n",
    "plt.xlim(0.3, 2)\n",
    "plt.legend(markerscale=5, loc='center right')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "united-heather",
   "metadata": {},
   "source": [
    "The larger the dissipation facteur, the smaller the amplitude response, as in the case of a linear oscillator. All the curve maxima align along a single curve."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dynamic-hawaii",
   "metadata": {},
   "source": [
    "#### Phase response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "gross-hartford",
   "metadata": {},
   "outputs": [],
   "source": [
    "phis = np.zeros_like(sols)\n",
    "\n",
    "for j, zet in enumerate(lzetas):\n",
    "    phis[:, j] = np.arctan2(zet,(sigmas - 3/8*gam*sols[:, j]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "hydraulic-saskatchewan",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x127291090>"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=150)\n",
    "\n",
    "for j in range(len(lzetas)):\n",
    "    plt.scatter(omegas, phis[:, j], marker='.', s=1, color = cmap(j), label=f'$\\zeta = {lzetas[j]}$')\n",
    "plt.xlabel(r'$\\Omega$')\n",
    "plt.ylabel(r'$\\phi$')\n",
    "plt.ylim(0, np.pi)\n",
    "plt.xlim(0.5, 2)\n",
    "plt.legend(markerscale=5, loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "angry-accessory",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
