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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def rhs(Phi,t,omega,omega0,beta,gamma):\n",
" return [Phi[1],gamma*omega0**2*np.cos(omega*t)-2.*beta*Phi[1]-omega0**2*np.sin(Phi[0])]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def integrate(rhs, Phi0, ts, args):\n",
" dt = ts[1]-ts[0]\n",
" Ndim = len(Phi0)\n",
" Phis = np.zeros((len(ts),Ndim))\n",
" Phis[0] = Phi0\n",
" for i in range(1,len(ts)):\n",
" rhs_t = rhs(Phis[i-1],ts[i-1],*args)\n",
" for j in range(Ndim):\n",
" Phis[i][j] = Phis[i-1][j] + dt*rhs_t[j]\n",
" return Phis"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"ts = np.linspace(0.,30.,20000)\n",
"ys = integrate(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x107972d30>]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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chrVxYjDDZ+w9RhHeVGjXiKaVYouibxkAVQ4q65H9pmOWkD9lH6h5JDe2Gcay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\nGqNvUWQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10794d4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"import scipy.integrate"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"ts = np.linspace(0.,30.,20000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1092199b0>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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fCWPhzuKJIzwJNIxnbaDEGfX4ugC3pppjWaTsWeMfJ3kvEcY/VLQAqJwAjfxr\n7k+khyhFlZyEgjJThZaqMeLqDonaaLTr88cHxxFCrdA0gotROmBIagpUSar4g0yeGwtSj6sxBlmP\nfCbcWGg6p8358+2K4yKsBQXSnoXasBoit8jQDCQ6p5WstNGFAG/geq4unwaYMZef9XtO7C+mUi39\naY5xmrf1xpIr4vSwahdF0wC/BmJaMb7vtF3c1yJlzxr/GPlfJIz/NJ9j0GvSPiG0jmUcPVzJqMfG\nOiSUxMUeoRQqmZQe8MQh/ypJGioYJGqDMFycoUlRCkUdUDymuIj7crKyhegZw5XOoUSJxQ5vIDmJ\nuF3QByUSHFZzY3OMVH/paY/hnqn+4r5Eaqo1ZvndCYDM+TdLR/mjRmL9UuewnyQ/pb0z/YIe7Tl5\nbkbRtadU1NaKEARKLI0YDdG0Frm1gZJOYS1S9qzxX4teDXdpzHD+kWENn6USI8caffB856hfh7wc\nIoyvqVIbmWIIq0jCVf2K9JAB3TbpIUWhU6OglMFKJ4+mBm6Q0Y4sRXBcVBTOURooc1iNufWcqTH7\nyGBmZTt6c2BsWLl2ccVUrzxamb5unfAN/1sqoTjDFUqJm8c2GI53MIIGqZhhHCVdtUgi7ouLYtp6\nI6+VeA4tVOqAWaOhz/Zz5uYmiRAMwGaRsneNf0T7UC9VnsW0T/k/xY3GieHKqBMUyHRWJ5P6PR75\npzv4BpkT0XKMpMQNM8oCqcZicHi04aLHYnIm0aILNIgW5od7tMwhR4Gk5bKcow33Pcz0uZmUL5GJ\n++UWe6pfIhhoOG8DGGAMV9vAcc6kGVkGx0glcmNeW5ybiCeXqFQSNJAouM4VVfdoiIrYuSHWihhN\nx84k5zfzWfSByg1YIrxFyh42/rUykZRFPq+MdL04mYeb0AFTql2U/AwvgKDC7fgMoHBtMRGo0D4p\nR8gZDyAx1pUjs4WoPJqxIUIAGPRiNKpvbS8SuXJVSfE/jVrTMJ9ztKHPlsMjrh0nPy3URtzOZpCc\nWjEVxiTlnkZauxb9WB6tTJ3KGumDaNQJ/SLBxRaSpI0xM0a9DZSMjpFbe2l0Xj0/OcKTktzTfB7R\nUjLwitssUvas8V8vaZ+eoznZZvJTLvUcZLqixolhgK8soRK5FgTAURscBcKdU9RGH7TDS1GrutgV\n5D/IHHq9mhu1jFkzXKPI0EhUXNxfzhw73UD+ikFKI0HOgFgdaEiSFm3pKizayRtBgwFcaM+vNph8\nfixNNLMS//h2AAAgAElEQVTtCEcrU6T1JioaeFFGnTpavFnqyeVDWlGREQBJER7ZTqxccq3vdlr2\nrPFfKxO+xw6MSORP0T5aiKpyepG3tvLVbJjfQh9GJyGdU2SlNgg0Y13E3E7NgWFuKCrCari0c5Ti\n9toi1vZ9WB1oe7HLcx2uLaHRhoEz0EOFA7U5xvjvY0kPdgMMc9i3Jc2r6Il5zrFjHDAUVov6ZIBS\nK2/CrKl0j40GgExJbjKyJMaS18nwRcueNf7rJed/bHXIbsJpIThVUW0GM7SVklP1tWkqgkJ61vJI\n6h7zuW8kP7VFV6NWoyGUUA81NyIVUfDA3GK31mun56RwzpvieLkxW6OiOGJUEWHsGM18tTw3cYLW\n0p+c5LZz/q12Cgqu3pGr6Ffok2qXrpUhOzf1m8HC/xZ6SHLeY8qoa3ZEqQYcRfqwSNmzxn9tPINz\nwOGVAUv7tBYng5DMYV300Diaxrp5Kz4YDAiG0Ib0gDZfTfGnxXVsIaqm0FKlSjzX4V7FzTpK5RJ5\nvIPQTjPC1nZAmvy0Ib2QC9ISgfWY9Y1t1ooWzUmkUUwaQXnvS0rTEMUYk58pGOA2mI1nhN7sQLWP\nmTpr5S+azyU9LmKr9BALLq5AshfYy8Z/kmNlkGF5kJG0T1rHCwgopRXWyXx66FM0cFHyk1bUNETN\n6DCRMerjpCKJog2K+7YmsWSFDn2zBrNB+3CJtvr9AOF/iRdVy2A5x5j0yXG8XI7FktRsgQFGH+L+\nwj1ak5+mdoJhjdtxO7Qpg1nc9+XnilJ94PQmrh4K7baT8KXoHOpc/boCq4nU03tMq8msa0UCm6k+\nLFJ25CrOuTc75x52zj3qnLud+P57nHOfd87NnHM/sBPX1GR9MsPKqI+lAb2JatbYuWtL+IYXh2h0\nACAZuGby05y468sloW2+mkH+RqrLEhWlqJVPSvsmumXonBCtNAycZTNYn34J+CRZxBwyowxmuO/W\nta2RYHQYWtGWruJpOVCuXV6/YKdoZ4uKBlnxbuXUwHFggDVwBqA0JuZG2w8Q2mq5htDOGhVZCgAq\nfUhKvFtnTFX7OdK5YeihbSS507lZpGz7Ks65DMD7AHw/gFcDeLtz7tVJs68D+BEAv7fd61llbZxj\ndZgVxp/l/Ivhq2f7JIuYO7bBZuCSULbPKWqTnww1zmkVD5UbCNdJ7y9cL+5XM9Zb4fJ5BJ6b0O2Y\nMEjk3gZmEbdQa5ibJHJLDRIb5isGyVr2GO5RKwkN7SSHHBKBhR7qZ0dxBo5r16LE0hyVBJRm80ay\nvmhH36MF0bdzRUx+LHWMLAhJkT8NlNrl2DTyb1fuyft7UgbBMuZFyk5c5Q0AHvXeP+69nwC4C8Bt\ncQPv/Ve99w8AaI92QbI+mWFl2MfSoIeNiY324eryG+iDUSyKn7RUd2iJ4fDWpkFWHKiVlimmSVIN\n3Wq8dv0SmWbIa0lOceF7C/mbxyzz1fHcUGNJw3eOpmk5RmnMDXSr1X/XFRtSJNjm/Gn9GmV6u3b1\nF0N1MZx/qrP13CRzrczNVjh/yVinyF/KtwXHyCV824iedvKttcKtKQb5s2ulbNfPeuJRFbuJ9nkp\ngCej358qP9uyOOfe6Zw74Zw7cerUqW3d1No4x4FRnz2b3Ur7tKgNjk80GvVW8pOLELgQleGr4yRp\n/DnX32irCm2hLJiqjQK12vdAxGPeSrKSQ/5aEpJ1jEm7NPmphu+tCE9vJ5VmWgxmmwLh+OoEtTJj\nSZG/dczaWTxpPsQ0h4JjbDlQZu0BUHchb9mBWgFVah9Ix+j3Z8LXe3+H9/649/74ddddt62+1iYz\nrIwy9vWHVLUPdcLlNEk6FUZdrqEH+MVOJj+FRdw+WsJIWSSKOmYMXBsFNznefq84i8eE4LhFTITv\nVu5WfgFKef6QhvyVMbd2FnOGMDEexVEVfHRiquIh0K3J0Vo5f2ueg6F9qJ3FRX/y3obQ1pTn6HP7\nNJqGUEr4tstl9YPdNKDUOsnUPDfNdrO5h/doOzLSjuS7qtTzaQA3R7/fVH52VWVtPMPqsF8k0Biu\nfBAZOICmfVqo1cxPctUdbQqEU9TGzk+Od2STTkq7YBSYktAw5vosHpvD4xZ7O89BzWF9REYxZr5d\nc1fs1hZni/M3RlmpYwx9WspbJUfWNIR8JLiVklAV0XMJXy5ivAy+2kp98nqTE1SX0ekQa75dHCED\nJc2op5EERx+njhYIDkrXh0XKTlzlcwBudc693Dk3BPA2AFfkBe2SrE9yrAwzcSHHBk5CUm3USizO\nWft4h+0kPynjET5v9keH+S1FbYWodMK37q9+J61E05jQ6IyIngz0kHWx83x1UqnSpzn6dmJYo4cu\n4x6FCGFkMZhExEgdVWGlulL+m3s3AUex8XROpDdK8joIdzy1OVfUcjryc9YiwXZ5q7xWBspck8Zf\n2GC2a4y/934G4F0APgLgIQDv994/6Jx7r3PuLQDgnPvPnXNPAfhBAP/GOffgdq+rydp4htVRXwjF\niCMHEsUKiytFrbwC1orPH0LlK34eqI1CilKoMkpqHK3kJ8d/s6iHQXqKooZdsZa5aeU5JGdiMHDx\nkcXxWFTDFUr2lHasA02Sn+EeWXRrinZsfHUL3TJ5Kq4un62ESvMmRuqMdd6tJPf26KFm1M3vhk/n\nOr73uF1xPdf4vzVmJnrS82Ou8fdcu2rMhrEsUvo70Yn3/kMAPpR89u7o58+hoIOuiHjvCeQ/b3xP\nVfHYDKEVtdoUNa7i6Ud/n25w0VBKy6hvk/9uo1tdoYf9Hi6NqbemUQaOLm9tRBzRs8t69efxC3bi\ndrzhaib2eY7XZjCbEV4bNHAJPpPD6xsTvtHzWxrUc0HlTQCe3jMnzZX+wpgbNA1BYVHtrJGlNIem\nKLkEDVW5rBUoaVFReb2MyY+lEUI9Zqa6cLcg/xejjGdzzOa+gfzjB1cfndA0cC2uLuE7QzsOwaXh\nu7XMLb5WdY+MQnM16mlyylqZwFIgSpI7RZihbxL5p2MRzuxpXpcPt4cNRGhD/lbqbMgZTAoMEKCB\nSvBJeZPLjYqKsSibt1hKjEa3XG5gEBk46qiKdLdr+Ju0+is9tiT8jTliNBUU8I6MdKAMaGivFVlv\nuPxYmhsIfWonCixa9qTxD69wXB1mZCIrVXyAXnQUVydt029VbRgWO4vMWk6C25CSnHwooJ64H60E\nMHVQbA7BkrgjFqc1ERhfK75HarGnhsa6izVtF84pSl/akzpQbizp/oKqHWPgTDklzsApaFSnsGzo\nNnXKpkiQMHCcflFz0yrh7FvzK7RjLNZoE/BR7SpA1aLO5MRwuHZ7TdEOz1K2ukjZk8Y/vMVrZdQn\nlXpGPAxSoYnFLlW0WNq1SkcFZNbktekt5u3QWEnklv1wZYop0gt9WhWarWgxodt2Mjy+Vn3tdsIQ\n4Ln86hwlJipKk5/h2trGqNCuFRWRerOVklBKb3zrmRSft8fcrBLjHF5xz/Gu2OJzG6LXSo7D31io\n1CGb8KXPPWpV7rXWFL8j15JHs24GSyOE4h55O9JaU8wauBIvbwf2qPGvkX+fNCC1gatRQJ9YdFSE\nICGzFtIz8JPc2fHtCIFPJqURTPh7aiwaSuHQrUWhuaqNrexqtqDbFh0gOND0HKWiv7zVLu6naEs5\nPCpiFByogQYcp06+RLd0aTJBdRHXtlaJNfjv0kG2y2BzYsxSlNxMhrObEpP+tHdEF+346Ncy5nY7\nOQe01c2B4WceUCU0MzPmK/EiF2CPGv/w8vaVEZ3wpY26gOAUo56+NBvgq3g4fpJCH2nICxDURosn\n1xQ1UkACmVkrE7ai0OlbzgZZcRBbq0zRmA+JX6IOyNU+NFpOjIcRtZI0oNCuVaNOJIZZOkcxXGwF\nihHdphRIr0dHgulhe+EetfxK0Y6PGOO5HnFRcgqUuLHMbNVf41S/hDns92LQsDWKVHMmoR0X4XW0\nzzbk0mZh/A+M+tWDi5EFRfuICE5BPeHQrHSBUGfxcIlcanFSCk2FnqYFwhp1uRaaHTOl0ES7UKoZ\n13+zZYopuhX2LFClfdTiNCXXgz4o9AtNidmcBHUmVF4mhmmjTjhGY66IAgNUEjKtKqEiwXE15hg0\ntHdop0eQh2tThQyhj7Td5QKlSRp1s06CS5rLDpSr4uGiaSoyie8rXDttR62VRcqeNP6B8y92+LYf\nMBWWD7IeZtzJhynSM3G8wiImqY12nzSCozarUQotH+8Q7pdFrS10yyi0kufgFgjAVWM0aYO4j7jP\nxl4JKwXSYyIEwsBRY2YroZidwOlcsyiYyNmoSW5uzER+Jb73Rn9Zc/mTz6+KYuS9DTVPXs8h9RYx\nTm9SoBTKsSljTY053WBZXEtZe1WuSKaRuCqeCfGcqQhvq7mBDvlvQ0Kt+QEm4VspYE/ekGJNdnHt\n0uuG39NEYHxPVbutoJ5kfwF1XasCWvMcXMibnh1P7Rvgqngm3GK3cv6tuW72x71tLE0Mh2tbktzU\nYufpIZ3/ZlHrFhK+TQPHtWv2F+6RdYz9pnG1jNkaPVHOm6seiq8VhEoMh8/ldiUroKw9oKDwLNEv\nVcY8mdF6o+2pWLTsSeNfIf9RRioCaeCIsJxN6HBVJcQiptBoU6GZF0XMUp6c340Yo2W2iifhMaux\nWCgLkuOlq33SMYf+6bxEiqzzVsSR9lf8nuwsLn+mzuxJFxJXgULNTfu6bWqDquKh8yGCAyVQq7bv\nw8z5S4aQmJvLr+IJXH4SIRg4f8qok4UHQrkzWfGm5IA4KjUFDcW1+XLn9n4hDijJJ9tOCH1YpOxN\n4x+qfSLk3zT+bY6X5vwJHpPYYk5TG1x9NWPUSSfRPF+HalegmaaycAm5dLFTSW7OMfLIv224xsQi\nNlWgsNEOsdgN1EZaOhr61KpFij755Ke6+5lxoGlUxFEg1JgnCdVlnkMhH5JWldDUVPGilKwFGmzF\nEdr5OvHfNKPz9lzzb9SiqU+tUMA6h+E+rHNjqRKjmAYq2lmk7Enjf2k8Q7/nMOr3qgkfNxSL9th8\nuBbxmEQ7kdqI2tLJT54e0vorfm+H79RYKANHV/u0KSwxiRX1SR0OxlWBFNdSKDEGmVGVKhSdk56j\nFO43jRCoCgtqDtM3iNXtmNMjFYM0ZegAwE5tkLkiMkLQHR41N2lJaNGuDYDoqEjYAEfoNgUamjkg\n/mRbS9FDC/kLieHUMdKRYLH24rmRiiPSa3ec/wIkHOoWTusEmsrPemKGk00pi/R9sTK1QTgdAi1T\ni9N6tg/J3SrJLoB2ZHSdvzU3wNM+l0NZyFVBBr56RiQ1maou0oGmURGT/Gw7k/Yipl6ewxUepO3y\nucc8rQpizilql7cy4IIADdQ+jbTKKPRp0RvrHgjq5fEkQCPaVeWyZMK3HQnGa4o7yp2jxLQINNxv\n245skfPvqn0uXy5uznBgVJxZR4WU9A5fvtKBTshFm8YEaiM2DNxO0qI/GalLCWSqZI+KYto8pmTU\n5VCWUmhqrqkt8NWYlQonLnwvqn0oh2dzjHQJoGu1Y/c2EKeypuOI7z/+mQIhQ4UGlBxtGhWltezc\nG7XSsscwZiqf1TKEQvSr5YqoPRWUbnNHJ6Rjpspl+SqeJuXKHeVO6k1Gz02LOhNyA2n+wrJXYpGy\nI1dxzr3ZOfewc+5R59ztxPcj59wflN9/1jl3y05cl5PTaxNce2AIgK6KoEv7bOeVSOiWTrS1Fzt1\neJm1uoNEKa0QlR4Lzfm3DWt8PEDVzqDQ0oa6IbE4W2fnpOG74PDaiH4reQ7dmZDUGWO4LBUtlIHj\n9lTE1wL4k1bDvaf3mB4PQFIMSQ4htCNzStTcMOXO6dElbGJYSUpTekPlQ+joSaAVCS6fNuqE3hjn\nxgYabDuBFynbNv7OuQzA+wB8P4BXA3i7c+7VSbMfBXDWe/9KAL8G4Be3e11JTl8a49iBEQDZIGlh\nmKyA8iKmFqfUTqtM4FAKx93aeUwisWhAy5xCp2Ohxxy42/ra1S5potqH2ttAVqooPHm4D0veZEgh\ns7yd4JMrX2Qnb034kuCC47WNBolOctMOlMoV8Tu+m0Y9PapCGjNVjq0laKm8iVThZMl7pZRr0b+N\nLiTXKLPu013uuxH5vwHAo977x733EwB3AbgtaXMbgDvLnz8A4I0uzpLsoEzzOZ46u4EbDhXGX074\nNh/GLDWE4aERVTwNAyctTkWhqcVenQdPIXoiWUmiFMoQGsL3dKt8dV3jJi8gnWsj0ptTUZG0iNuo\ntX18MM3dUiWhFgca+O9m8pM3cNRzpmrZNdAg51fkhC9gN+q0A6WS4TbKQkTqypHcImgg5nBIREWU\n87Y5RuuaotYKtV+o+Lt+T47cqBzjImUnrvJSAE9Gvz9Vfka2Kd/8dR7AsbQj59w7nXMnnHMnTp06\ndVk388y5DRwY9fGmV90AgAsp6ZI9fteitjh5pHc5yc/ZvG0wARql8MhMR/RcIredQ8hab9Syl+zZ\nUCuXaE77o94gFv6OWpwmZEY6WiLBRzhGCanTu05lx0iClVlbv6xJ83oselQ07Ge2vAnTX3ss/Bqg\noukxYQg1GtAaIYS/ox0jVQll4/Lba4+qhCocaFoxFY8zHte+TPh67+/w3h/33h+/7rrrLquPlx1b\nxcd/6r/EG0vjX53NTilMQ7GKNiSC2w4yI7nbqJ2Rlgq/07xjWq9t5zEtSSyq6iYYrhilUFUb9IYn\nwfhr+ZU5PTdctc+22rUWcU7kBoicEhExUvpA502EHBWVKzKgWyui5+r8acfIIH9lDVAUCG3Ubbvm\n6bXH58csAIhzeHThATE3BvqRYgZqvdklnD+ApwHcHP1+U/kZ2cY51wdwDYDTO3BtUpaHTc+ZKmuY\n8DSpCdSoGygeWrrzs0a3FApunmtS9BH3FxRaqe4geEyARylk1YaFxyQiBI4LDt/F7dJ7DIhFc7QU\nZWHdzk9FWeF3mv+mkuG2MVOUGJU3icfZGAvJ5RNzqGzeoqqCpFcGpsiRH3OKbh1Z50/ngLjNW+21\n0iyLJjZYUhHjFgsKtPxYKJelSzj1CIFMcm/FSRAb6orvZLC5SNmJq3wOwK3OuZc754YA3gbg7qTN\n3QDeUf78AwD+zKdH+C1QUmUldw8yVARnCLVzSGoDV1e01A83qhPvBQQgVzCE/q38pCmpKfDaaX+h\nj3gsvXR3I/ESDWtFC4Ucqc1b1JZ6wJ7wJZF/3n5vKp1foSmVog/ZeVN0jnTOjcXAkQn7GVXF06Zz\n+IRv+10HFp48lJim+RB+zHKhgNUxUseMhP6pfJttrdgiQa6dtSijPZa2HVmkbPsqJYf/LgAfAfAQ\ngPd77x90zr3XOfeWstlvAzjmnHsUwE8BaJWDLlIGWTPJR1EH1cOYNZ2EBemJVUFxf4Thol4ZyJ3x\nQS1Oqs6fNQoWHlMwcCm65R0j4fAaJYA8VaJRFrVRMCxOjuoi2lEOz8p/F/fVdIzhXbfx/bXbUbmi\ndlTEGa7UeVMvRy/a0QlaE6InQUP7XRWTWfu65Ma2sAZ6xFrROH+yoCDoTUpV9pj+9Io3bme4NeHb\nruIhABpBkVI7yBcp/Z3oxHv/IQAfSj57d/TzJoAf3IlrXY6kG3FIZMbw1fH2ckAOUUmkRzxcuqac\nchKpwjTD97DYrQk5W8KXiiTaiF5MfjaiGB4Fx9em8iHhd0s7sqIlpzeDUTty2/RQXcUT0CxJBxDR\njhTm63w1FRXx6FbjycPvJs5/Cw40HMHcj3TDFBVJVCoFBqiIkawekp03Cy4ojp6gzjjkf83ygBxz\nAQDqs4ja1+UB0Gg/JnwXJSnCpSiLIcG9F4u9zRm32hFG3cpjhj61Cobwd42dyqEqiLhHa5kbVaZI\nRQjxfVXtCOMBNB2euKOTWMTUBiWtWqRqF405nAd/uY6RMkjm8F3oj6ZzCAqEGjPpoGT6kWpXjyV1\nUERVF+UYqRJOiSJtOUZmrrUSYSPwCtfWyruLsTAJ32TM1LsJyOIIpsKJYxA0qmuRsi+MfyvhOxcW\ncaqojIHTkpDW0r7wuxbyht+10tHQn3XDU3y9MC5ubjSFHhEJX+tmsKmAzCazNlVCjZncX2A4toFz\nEnE/4WcW3Sb5C8rBU+0AvYrHWv1FoWWgPWa2XJYp1bXoAwkuSIdHVxkB+l4c6qgKbq208nxEuWz4\nO7KCTgFo4dqsk5/Z1hRJfSZtFyX7xvibKYvEwKXtpJMrtY0rVu6WrWhJ+W+WDrDtB+DCaJbznylI\nzxjtSEduaFSEGBUZ2lGleNIiTh2ZOSoy9hfuPUg/66HnaApEM3A1tdGudiMdsvH5tSur6N3KFqMu\n5oqUNRXucUKslVbEmDxnroginRvqEL1wXTI/ZnSMrANN1lR6tMoiZX8Y/6SkcZrPK66yarNFFNxe\n7K5R6UCiFEahB61qJJuTEKuCCI6X4/Jb0Q6HWlOkZ0SO6ZEIVJkii1q5RaxU+4hREbmIDSWcRgdK\nJQxJOocr6e0bjXU6N1LS3EidAcC4UXxAVULZop16z0Izn5XOdV30YBuz5Tmnm62octnQH71GKUCV\nvI+BSuQSQImuOqMB0JVK9gL7xPiPkkXClbkBKTJrK741NA5tNaQH8OG71cBR1Ibl1XRkWL6FqCgd\nc6hwmaTGI2uWANZlirrhai1iyUlsYRE38hzWKEZAeq1FbOwvrQoKfVLolko2N6/bPlM//B0VWbY5\nf4qaol+Ik455TCR8uX0f6ZoK96ztD6naKXmT8HdayXHoTzt+IrQDUFUK1mPhOP+44o2nCzVwsUjZ\nF8Y/XSRcbXz4rmpHlK9ZI4TQ9nKoCClEJUtMmcUeDBx15nlol46FzHOQ0U4b3Rb32E5eUxxm4ZDl\nTV7xWOLrAnq0wzlabhcyt3M3nZv2s6M26W0tYkxlxBlCirJIDDBAo1u6P0MlG1XuzJRwUo47bUet\nvXDtdG7SqqAwFnJXrAKo+LxJahuKnykaKb4eQNM5NS289SKKSd7eiLlI2R/Gn1AEKjQO38XtqGNv\ngXaEQIVr3CJuRx1GdJsaOKHSwfu6GmhGnHnOj4WvTNDyIeHaLTqAmJu0Dps6Rylc21K1Mew3X5PI\nJdfrfEPsGOkXm4T7r6/Ng4aWwzNEjJTxCH1qVUFUO4n2od8/0a72CeMUx0Lx1YThshrM0FabayBQ\nuERUZAUDCucv6Vc6FprOsYFDsuKNoM4WKfvH+CcPrd8KtWlem6WHDIawvYhtCVpRoQ01zqkjq0vI\nDNGOQG2kySkawWWt/AqFblPEZd3kpYXlk3TMCr0nVQXF7cLPlhJOSm+CvpkcKOfkyaiI2jQmJ3zZ\niDEZM18VRNeoW5KfVATKjZnSm3YkSD/nNvDi154lD0OvFapyyUZ1cbvcO85/h6UdUkqJGlmh64em\nG7hUoamXclDtJMMV7/BlueDUwDFlblyVhWWxU4gQaC86Cd2akpAc1cWMJcyxlFyP+5Eolfj7MJb2\nIXoEIiTOAHLOtXIxVMIw9Gni/LfiQA0gpHageTVeqp2Vr+Yq4zjaJz3Vk4wYWS7fGBUpToItokie\nc9gPwRZRJPNtyhV1xn/npY2QhPp9hf+mjmPgEr4D6rpJVVC4thXdmqqCkkXH5hCSxV70KeVDbNxt\namg4eoguU7w8qis1NNZFbI0QQltLIpfaGQ608xwUrRjuJeWMqXtsl3ByCd/mibXamMfJ3JgRvcGB\nssURaXTCUCDpfg4p+iU5f+btZWFuaidBgwY1smQLQmimwTI3i5J9YfyppM6AqLAI3wWhqjYA2iBR\nHru1y5BT6KQdh1IGTG6APUogbxpCNuGbcLfUuSaALVnZik6kZHjUjq324cJ8rvwwLE4hbxK3Y9Ft\nVfbYnG8eLevURsFXN89wsjnQ9o70qp1Bb8I9hhyQSp2llBg318oa4PJj1mofst0WIkHyRUqEIwtH\nVcTtNDCgzWGap2L1qwUaOuO/o0Jxnix32ziIjUatKaKnDr8CqOQUrdBUu3Cdxj0m2++lOn8gpn0U\nlFL2E6qC2AonS+KOiGJIx0i0cw6tXEy7HVOmaDRcPOfP0XvJmA2GUEK36UY5HlzYnERsPKiXnlP3\nyDnGNHqS+PS4XbhHUxGFAIAuR7+4qqB0TUmlnuF68b22x9JE6tKO9HTMYwo0ENHTuEv47rxQddPW\n0j4qLE8XHafQ6f4CTqFHVnSbKqCwEzgeC6fQ6SLOlaqgFM2whssSIRCLc5j1WpRY8ezah95pexEk\nqqTRrkqmts9yAVLHKFQFKfx3uEZ7bmyUGGswCQNHnY8Ufy+VEsffS/tN4nYAbbiCI29XQtH60OS/\nGUCVvJuApR/TqNsIBvjNZVnjezVv0hqzfN3w865B/s65o865jznnHin/P8K0+7Bz7pxz7o+3c73L\nlfRQJiostyY/Q9t2iEqF+cmuRSaSaKMZGY2mnCyfvE7DfCVCYGrot2Tgkjp/6xxSm4TCtZtJbhlx\nWcNyDd22nIRwjEDcX2hrTeRaCgVYCiQ1mOax2PRB2nsRtws/p3MTktzt6i8baNhWVVDLmeSmMWtG\nfaroDU0Dtp9zr+fItbKb6vxvB3CP9/5WAPeAP6f/lwH8z9u81mULlXjt9+QFAsicv7Xm3VIhwyc1\n5Y0hXP13q2qDzSHQ7WzJT3qT17CfqaiHHHNOK/5Wk9xptY+WrGSPiGadBHM0QYsC4RK5OiXW2ihH\nVA+FsaVJ0vje07HUcyNTZ61KKIavDtcOR4tzeS+zYzToDZUDsl6XHHMKqIR8G1DngFhwkayVQNNS\n7+UlQeQuon1uA3Bn+fOdAN5KNfLe3wPg4javddkyyHoNrpymfQh+0qhYFKcX+tSy/lR/bFVQolg8\nxxvC7eaGJy3PwSWGyfcgS4g+PSjOwFeLkUTDIRd9U7mB0E8x5q0Zda1clnOMoU+tKgigN/1xeyUu\nCzQoSD016loUI71ONL5e2ERoAUpb4fIteQ6p3dzXr5Bk5yZxeDUlxjhGTW84gMZQXem+ol1D+wC4\nwQ8gbUMAACAASURBVHv/bPnzcwBu2E5nzrl3OudOOOdOnDp1apu3VkubK5fO4S53xeZz8nS/0F+r\n8oVbnCYumOLJaWeSjgMQEndaEiugHoUOqMZiQK0tmsZcy8452ixx3HRuYKtjDg5Rr3mXq0DCZ9rx\nDqGdNWLUTsIM9xjvataqfaxlilWEUEaEWkFB5RgtUYxA51jAQErh8qAhfc7lPfYuc24Sh1ftneHW\nlOIkwjVanP8VRP7qm7yccx8H8BLiq5+Jf/Hee+ecJ9qZxXt/B4A7AOD48ePb6iuW+MEtDQpUlSpB\n+tJnziiE/ky17ITBlBJ887lHr0TY3GIHDFU8yS7DrfLfLMq0GC7KkRmpLnKBRI4762WlYaWip3TM\ntoQcR+dw+wa4uZkm+mAqZ+QcI5EY5uY63NtSL4uiE6ZUdyY7stSBcvQQ62gtFKkYMTYjPJOjFfIm\nxRjmWB5m4KqCWrkizYGqieFUvwQ7Qq2BK4j8VePvvX8T951z7nnn3I3e+2edczcCOLmjd7dD0g7Z\n9EPJpMU+yNqh53Y5fwCYzucY9TJR8eN74xK0rUiHcRLW0r4wlpjH5KIiumRPp7qkvRJAgaQqx009\nk+R1ijzn35wb6cyXuB8uCR8+C/rAvVoz9Lk2nlW/22vZ+egJqOeGeol6PLZ6565C5yT6oNFD1Vxz\nayWlfUwOlMkBZbYKuvTNfGZApext0JLmgSLV2oVrNOaGucdFyXavdDeAd5Q/vwPAB7fZ30KkbTR5\n+mWap8bDUknAl4SmSSeOC46vySk+u4tVSTpZDRz3rth0LFuhh9hFTHDBomOMjLVkCIOB47hWa/QU\njlq2LOJRY27os4LCtdt0jrHahzn9Mx7LZNbeo1HcS2jnG2NOdTHN7WgGTss9hWvEieGtJHzJM6GI\nyJLTL6AJlOgzpmwAiI+S5efHRWMADZR2U7XPLwD4PufcIwDeVP4O59xx59xvhUbOuU8C+PcA3uic\ne8o59w+3ed0tCRX2akjdutgB3iClVUZSWVr4PlxbamfmMRWFTs/f1xRaq3QI1zCVeiZzyG1waaNM\nnmIDomfMUmJ09MRW3eSGRUw4Rs4QWjj/rcxhPBY2euo3UbCUhIyvbXXyoV/NyWuO0VpQEL+PQUr4\nAk0ARB25wXP+NHUWoia1AEDJPQFNOyJVTC1KVNpHEu/9aQBvJD4/AeDHot+/ezvX2a5QKCB9kxcQ\nFL9pWLlQ1lLdYa1gMEcmBEoReUwlORXahkXJ8ZihXYqWbbkB2xlAk9kcB5fa6kiF25JjjJPX3I7h\ncL24X23M3MaodCyqwTSE+XEit1dGH6uj9txQiVd6HOVRzVajnjcRvdaOo9jCZ1ZnEo9ZooeAgJIz\nNm/S0psZnWjmo+mdoUjFNRU5RqlialFy5a50FSV+5+icOY0PoBVae2hFv3Jyqjo0iqM2CHQroZkY\nSVlRT3E/CmoVxkxRG/zc+MaYtSR3uFcxfG9ERcT9EQnfQUbvGA79hPsrPmf2LCR5E4pWiat4NAfa\nPNjNltvh5zCcv1/PDQlW+m3+G2g7RoBD6oqBUzj/VnWagabhCgAoSpPLm5jaEdcN952OIx4DlzcJ\nn6XAS42ehDlclOwL4x8j5vAaNvqhuWqRS4s4Rv7VJg6Bo49pGpGyyGVFrTaaNJAez2O28xf0WMbJ\nmLWacskxxpUg1RvELItuC1GR2N9MMR4cd8skDVsOT+G1xblOd3zndK6oVU3DbfIiqQ2LIfRkuWxo\n2ypT1PRhi+205HVxbXpNpS/jkUpH42uy9BARTVOv1qwo0jT6VYCSCC4yW8S4KNlXxn+az1VDmKIe\nDo1aHlp6XpDG3ca7DMUQNVcW+xZCVDpZKUc7mkKHa+dVKGsYC8NXt8NyW7TD0UPpS1WsEV5V864g\nuNpJ0OWowWhwh+jFY5nOZMNFgQFOr4sxyHMDpPogR4xjwxwWKDh5u9o2nl/g7XWqqx1N0w45vS7d\nrhhLuwBAc3haGWyH/BcsMQrgtnmHdibah+T0eEOolZhS6EPkMRtOot2u33Nwrp3E0jh6lcdM+1MW\nscZ3xmPWaJ8K6TFjppLX1HjTl6rUyU85wuNq3sM9tjf1tJOLg76rrssdoheuCyRO3jCH49kco4Hu\nQLm5CX22IjxjtMNVqIVNf9wheqG/cG/cG8SAdqmuNeErldXG/XHRdGjbPleLyR2a1l7WeHYAPYeL\nkn1h/Gvk79XF3q72kZ2ElPxsvQBiNieNAqWoFqqEU2jnXEMBuSMRgLCIk/JIY0WLVoEi8p0EJ8tx\nxmk7Klkf7rvB8TIILubeNTCQ6oMWCUpVQeH01lDyCPCGNe6LzXMk+sBVTFFJ8z43N/FYBCcfRwi1\n4SIcXnQKZ+gvPVcrXBewg4aYHjIlfBV6aGxyjPWxGxPp+fXbJePUfA8yV11XKpddlOwL4x8vJmtl\ngshjZnWFjJYUC9cNfXL7AeJrapu8YvqFMuhAYWhS/pvkePv1WKTqjkFGID0CZTbm2pLgC8o/zUnj\n0cqHMBFCuLYlfC8MXHKYHWOQtBNU29eVwYX3RWWHRjfFfXGIvrWreTbHaKCDi/GUn8NGqacxWTme\n0W8QS9tJEUIzOhfaZe254UqT42ty9BC1W5kHDa41FmsynI2K8rRd+/ktSvaF8Y93vMolnBFKUQxh\nSPRaUXBVx2tMOlnC/Mms2NlJSYpauVA2RssaPdRCKQqHaqKHlPwFxWtzCyR+efxklrOLuEjs1w5v\nmPVa5bJFO1uSmzoWRHt+49L5UEYhXKM5ZhvtY0H+Y2auw31ryc9w7bbhkqPp4CRIB5XFeiM7nfia\nk5kMGrZaPs05idBnOhaNy5fonHiuq7npkP/OSowW9DJFmyEEykWs8KKhL4njpdCtmExtoB4Dgtsq\nx8uF+VtYxOMoytLyHPN5QYOIu5qja3NjSZPX1HWrMUf9cQtuROiDtWRPi9zGU16/0iox7jnXBi5E\nMfRY6lNeY+TPg4ZmBRYHGowGzmoII/rFAqgaUZGBOpsw1UPtndx0ZVU15rhAQQINCYjcTlS0KNkX\nxr9R6ikoFpmo0Xjtqp28dVzeSdpEeuNZTiL6FKVI4XvK0fNoJmtVbSwxdI41lA3XtCzisUIPpUlu\nbrGHv7eE7+kipiiVVjvh+VEUCDmHBGiQkP9kNsesBA4iulXmJhxaOIm4d4veiCiY0AeOIk03jWmA\nSsqbxHMTomnb8Q78iZkpApei6UaUJYKQvOqv+Ix+fpa5WZTsC+MfK8JYUKw4fJcrHWokJXF1MUrR\nUHV8TU6xUpQyznkEF1NY3PsGwphTZGYNZc1RkUJ1SQnDFj0kGOs4eS06iWTMFqMgcrzGRRxHbha9\nUfMmVX81yrREeOMpHz2lyN8SIWjPr6I9FQokXFOMLBvAq4impQh0Gj0/toon0W0xH1KtKT5iJOeG\nydkE+lhyoIuSfWH8Y/QoIfoGx6tUgRRtbAhuPJvbEGFQGAnRZ9ZFnDU4euq64b5jHrPfc2RlQkOh\np3r4Hs8NhaSa7fiEYYuvntEVU9U9NhYx3a45ZjpJGvqbRos9/G2rXVbvVtaQHhAcntBfBBpMc22M\nijSqBGgWClgjSw35e1+Utlpon+lsjk1pzFl7DsXcU6TbIqKPdFt2oHWhgBVccPdIOfku4bvDEu8K\nFKsx+hFangZjzdMv03gRm8N8OdkFBFShGyRRAROFliKEeLHzicAapYwtaDR2eMYwX9rw1JgbDvk3\nxswjs2Yi19ZOSgw3HJlguOKSYxk01EluyShQp3ryOaBmpYqI6A1zneaA+kxieNCYG4NjVABV7Rij\nSEKpOivuUTbWY8vay5qVcexc95tRtzaWhiPrkP/OCs3R02HYNPHYGrqtUYoQeubejPTCG8QkgzRu\nKDSnqC4ai2IwjcgRKBXVsohjh6eUH8qhcT3XITEs7cDUyh7DtZulglYHyhsPoKT3pDJF45hHDYNp\nc7TFWDTQELezURaSIbQ4nZp+8fLcEKCB3jcQ5iY3OdCKpplaIzxbtCMmzbOsOTcZX2YNAOM8330J\nX+fcUefcx5xzj5T/HyHavN4599fOuQedcw845/7H7VzzciTUcBfcu3AgU3T2SjBwWmmmxahPlFB2\nkNmMQvj7HTVcCYKTjEe4R5OB0yiL2GAKoXE8N9V1WUeWmRxZA9GLRt2ZUHDTMRocnsb5R6dwSvpV\nnauf5xVokKq/xvkW58ZoCKUE8iAycKIjs4IBoh3VX5XknhX5BtHhZQmdwziJ+HiHSS7kntLoSaDY\nLGNZlGz3SrcDuMd7fyuAe8rfU1kH8L94718D4M0Aft05d3ib192SxC+fqEs4+YOWCmUpFJry2APS\nwNG7G4GSuxVQcFyKJ9FDoa1FseLktRzKNlGKZuAai1hwjGPFcFkXe5zk1uYmrmjR0W1c+bK9HAKV\nv9BKLsU8R3QKp2YUgrGWHDKwBaTeQLfGCEGgC0eN6FdPco9V6qxG9JIDjccyK988Z0L0osPLGmuP\nLxRwjSQ3W03WpwpHdo/xvw3AneXPdwJ4a9rAe/8V7/0j5c/PoHjV43XbvO6WJWw20Uo94+QUlyCi\nPLaOUnijEJ83o232SBNtYpniFhGclgisx2Lgv420z7iB/GWKQeNFGyV2YljeLMWTULAlSZpWLvWI\n9wiE+wMMiVyyEkp+fhKqDp9bxxLO1ReT4XGlirCPhDJw1lwRmeeIdjVrayUgdRU0tKJfgVaMo2kF\nKAWHxzuJrNEu/tsrIdu90g3e+2fLn58DcIPU2Dn3BgBDAI8x37/TOXfCOXfi1KlT27y1pgReTyq5\nbD40QQniRaxUgQB6Eguoqyxq2kA2SFV0wtbvJ0adXcQuiXZkdBvm0MJ/S2MmF7GwmKa5Fw1maNfg\nq5X+AL26ozKEQmVVvKs5UHFkxEhRWFTEGOmXCd3mckko0Eb+Ev8N1DprygEpkWXcjksM08URfFTU\noAsVx7g5lfUrLXqQqsSaVJdxDrW5jmkfZj0vQtQ3eTnnPg7gJcRXPxP/4r33zjlPtAv93Ajg3wF4\nh/d+TrXx3t8B4A4AOH78ONvX5UjYsKMhf6DmbqV68qqdIZRtGHUlRLWilJr/ligQW/gO6A4vXezS\nggvt8rl8LHZoJ3H+QJ3ktlIb8zm/+afor/n+WXXM2iKOnTxzRlGrvykfxVDUmWTUxwb9aoIGnrJo\nJJuN+hCSmvR1m8balDSXomnj2gv3GIOQJeFYkPMbUwBKHi2OBKfy/pBwjxOJHqrmOq+oOAo0LEpU\n4++9fxP3nXPueefcjd77Z0vjfpJpdwjAnwD4Ge/9Zy77brchIXlX7dQUNluNZzk2jclPUxIr19Ft\nWJx6KNszcYRbruIpqQitaiMsOotRCLSQvSpIonNkqiT0GaNqy7lHYtljZjOEo75tbgbGqGgrtM8o\nRLS54iT6Payvz0z8d3Vt5RgIoMwBKVEWEBwZr1/9rIee0416Vh5Xbl0r47jEVNwcaAENtjLYJjOg\ng8jg5K8k3w9sn/a5G8A7yp/fAeCDaQPn3BDAfwDwb733H9jm9S5bBv0m508pYTAWm9O5WiED1EZh\nkDGhbHi4Uzt3q4X5o36vWkjcOMLntpLQLRr1CKVQEr9LYDzN4Ry9US4+f19D/iHakbjgql0c5rOO\nLKvaaGcFAcXz27ToQ/n8JCcW+pOcd13FY3XyuVhNFtqNZzKqBgh94MZC5IAoCWtqPMtFeqgai2LU\nnXMY9XvYnEZ6I0VFhrUXckVaNdloEL31zpgDEtulerPLjP8vAPg+59wjAN5U/g7n3HHn3G+VbX4I\nwPcA+BHn3P3lv9dv87pblhCy1e+pbRuksAt2c5aLhnC5chK5aFj7WQ/DrIeNaS6iGSBWfFmhlwdZ\ndd2iP7kdoJUpNjlZFekp7eISO6liCqgRV22Q6D6XyrFoiz1Qe9pcLw972Jw1q7q46wL6c27z5Mx1\nQ3+lfvUcfc57uHbTcMkOT+P8U71RqQgFjaaRm/TsAFTPj9PDcE+WCK8Yi27Ul4dZ6XS2tvak5zcr\nT/KVophRw+HJZwABugNdlKi0jyTe+9MA3kh8fgLAj5U//y6A393OdXZCipCteHDOgUTqYXFuTGSU\n0m7HP7SlQYFStNCzaKeHssvDrNkfc49Lg+J4h1k+Z0/MjK8znsmL04puQ1ttIYV2jSoeRvmXwxwa\nUPA099iYKHM4yMrjuOVSvOVhbPx5Bxq45PFUNpihP02/gOL5bUQOT6QslOohoBjzRjmOoj8+NwDo\njizds8A/uzBm3cCFI0mkpHljLMKeiqrdJF4r/BoYG9aeFQwsxwzCLMc1ywOyXTqH3DgWJVfW1VxF\nGfRDorR4UQqlWOnD5c7DqRaxQg+FtlakXiiqvNiXBxnWJ1GIqhiaC5uzsh2tWCtlu/WJHO2EzwPi\nEhdx1lN5ciB2eApqHRZzY6HEAODSuBwz62izqt1s7tkS08pwlYaGn+vi8/WpPIfBSWwYUPBKpTey\nY1wqUbBFH+I51JB/oKYs+jARHGM8hzryd2rEAQBLw9L4C7v1w7UbUbewnhtrT3PeUxn0hTGvl/PN\nPrt+7SSkdouSfWP8w3EH4sNoLXbZyATFkjx2jVL0RWyhh5YS1COF+QBwbn3SuOdWfw2F5se8MiyC\nxAr1KMhfq5gK97hudYwxZaFwrRcVhxcWcajwUA3XRJ6bCjSUBoS7v16v4KvDWKTFXoEBg+Fan9gi\nwQZVokR4F8fK3AyTueH0ethcKzLy76kRB1DSPvGYOSc/tK0pq35VRn2cF8eMKGBgQ1kr1dxMZmJk\nuSjZP8Y/SvhyR7tWnH8I35mH4ZyLOFQN3WaR8eBD2ZWAPqy0j0GhAeCc0cCFxcQpdDNC4MvXgGaJ\nnbiIh31sTHJsTHL0nBxux5SFVmZ6cbMcs7KIK+Nvcoz8cw6OsW4njbk0XIoDrQyXsJs6jGVzmmND\nOIgwtJvkc6xPZBASjPglNWIMY55hY5JXzoC6LlDqlyHhO50ZoukWUBLmxrCmVoYFl782VkBDS29k\nMBCiCW6uY71Zn+RV/1dK9o3xj3f4cmfbx7SPVN0BBMQ1M7WrUfXOKPQ0rxWVo6aC4Tq/LiuqlfYJ\nc7M+KRZ7UFxK4h250phXhllhPKaF4ksc7+YkrwzXCmNoauMfFrFs/M9WUZHG3crGOg7zrc95c5qz\ndedFu17hGKeFo+USwyulHm4ocxPQ6Nm1SdmOfn5bncONybx6fpTE0fS64CTCtSu6UIoYh3U07ZyB\n9lH2QCyl+qCsqTNlO5YWjvRmfTLjn0mkN5tTeW4WIfvK+IdkkoqCLQhukJVJLB4th3Z1wlBGhMEo\nADKCA4DT5SLWENe5DZn2Ce0ujqeYzT173aDAm9NcRHpAc8OaNjfrk2AUeGeSzg137Zr2mVb3QUm1\niC8Vc7M60hentB8gpgE3p/y58aHPjWmBwDmjULfLsTGZiXO9VM5hQP6cEbbqTRo9aZHg2qRw3txY\nBlkPg8yVY1H0JgulujZKLKBlFjSktI9CYQXjzznlMIdBb7gxB8daGPU5q9tZoAHLsUj6sAjZN8Y/\nlHpKiCtN+EqGK1TxaCi4XsQ5ixSKdgUFsjaWF3FluNbGAHgEVynq2lTuLxgFRaHDIl6f5FgXkB5Q\nIzjVwJVUV4F6dLRcIX9lu/z5jVk5Fm1uJo3fqfsDgLNl9MQ9v16vpgHXlDEHGlAzhMFwaXMYEsNh\nbrg+lwap3shzGOhCPpKoc0re13rJXTtEMdyzC9eezObYmM6wOpLBwOa00ENtrjenc6xPyihZiX5P\nG8FApTeKfl0aTzHJ5/oaKGk7CTQsQvaP8S/LACVkViG98mGs7sDiXIpQyqqIbnuVEiwPMvLQtPge\nT6/JxjoY09OXysXOKHSl+AodEMaybkAp4ciBApnpjnF9MsOK0C4s4rXJTKRAAp0XEJwWbmtjrh1j\nMYcHFIMUjLoIBirDNVNAQ78ymJKjXRkWNOCFzSmckDdZrkCDbNQD4j63rhj/dA6VaGc8M+hN+T5p\ne1SkONDEWHNrwL6mbGMOiVytv9DHegADnfFfjMQn/Gnla+fXp/Ce9+xAM/TUDOamMczP5x7n16dq\nO6AOPTWkV6EZDqUMmwaOQz1AocSXxjNMZnMT7bM+man9FZTFXESOFQJfm4jRU/X8jKg1oGCNOjtj\ncIw1hcVzvKGdhf9eHvZMFNtSpA8rSt6kGIs85kFl/OUxW/UwfFdHO1KuqCj1XB9bAZUMGpYHAQBN\nMMx6bK4v3FNYAxqiV6On8qiKMDciDTiMoqKO9lmMDLJ66z/3MEIp3gtK+AfUFShr2mIvF/HaRAtl\nSwVcG6tGAYgMkpHj5e4xhMIaBVL00Y8Shjp3uzY2oOBJwWtLyDG8BvLM2kRONPebhoub77ZR5wxh\ncQTFCwolFsZybn2CuZcNYUz7aGjZRvv0q7HYULBMAwYHGqguDjT0eg5Lg55KgQCFjl0azzDJ5zpd\nODNERcMaUGlOByjWAIf6AUIfFIr0jJI3cc5hZdhX9Sv0sT6ZqRHeImR/Gf+8SCZJ6HFpkKl8OlAn\nctcnuapYG9NcRTPhwb9waaKiHqBQaIkCqRU/0D7yIq4NnBzFnDYs9prz11HwugkFR4tYiTiAwnBp\npaOhP4BfnKGk97SC9MJYQn8aXbhpMOqV3kxltBzTdqLTMeaKUs5fcyinDaBhaZiZKJDwjlzLWpnk\nc1way/pVP+exTLlGaw8Q6KEtUqQ22qePswamYRGyb4x/OJRpU6m6WRr0zIv44mZBgWiKVUcIMucP\nFIqqOR3AjvRq2kdbxHJuACiUOLTTENx4pudNVoYF1XVhc2qiNs4qYw589fmNKVaGfbEKBNARXLh2\nnQiUn8tpE2joRXy1YDyGGbwHzq9PKvqCu78wFumZxHoz7PfI402AKGm+rke/ZnTbiBB0vbE4xjAW\nS7vTCqCK9SHrOWFHbk0jARqit0VFy8Msirq7TV4LkZVBv+ITtTrs6uGaF7uMerwvEmiyogbe0a6o\nItpKkpWao9DK18J3FsVfGRb9ea/MYaAsLtkMl4b8w3enLo7lZxJoJEO0Ey9i7bmctvDfgwyXNgsK\nRHSMjTHryL8AAzpo0OZwqZ/BuWIOi/5thksrb7XM4YHRABc3SwpEcYxAqTfK/QEGJxHlvaS8STio\n0eLI4jFrCXtLTmkRsm+Mf0AwZ9YnoqKuDPuR4vPtVkf96hhd6aGFqODSWC9fA6BzvIO6P6ndqER3\na5Pi7Uli3fQww1pVRqlX+8T3S8mh5UHdnwGZrU3kCCFU2VzcnInP7lB5gJY21/2sh2G/h4vlRjlp\nca4O+9VZQVqEp21CAwqHV13XYJAubsp1/uG7S+OZ7ExGdX9SrqHXczg46pufXzU3UoQw6lebxqS5\nPrTcr+bQ4hgvjuWxrAzjtSI40EgPtY1Wy8N6zNpzNrWL5lCKuhch+8b4h4c/mc3FnZXXLA+qQ7Kk\nh3Y4OqlPbLdSt5MU/+BSrZySol4T9XdgiW/nnKvucXnIo5ni2nWf0iKOF+ShJfqkwvQ70bBG1+JO\nPgSaYxbbLduuC9TPb2WYsRRI2qf0nOPnJzmeuL+DwvOL20lzHd+TdW4OCe3i7weZYytktnLteK1Y\n79G6pqQ1ELcTI46oD6mcN77HrNzbwcmhqE9pzCvGNbAI2Zbxd84ddc59zDn3SPn/EaLNy5xzny/P\n8X/QOffj27nm5Ur88KWEb/wAJKR3+DIMkrTYj64Mq5+PrPD9HRz1EWzV4ehvyGuX/UjGI72euIij\n6x0W7tFqaOL+rO2k+1saZBVnfWhZXsTh/g8rCy4e50FhHo+s2ubmcuZaancknkPh/kb9rFoDmvEP\n19OM0RHjPcbzIV07vv9rBN2O+5Oe32GjHg6yHg6WRv8a4dnF175meSACKqtuW5/fImS7yP92APd4\n728FcE/5eyrPAvhO7/3rAXwHgNudc9+wzetuWWLjLx3bEBsNGY3aFnusBEdXeYVuLCRB8Xs9Z16c\n4fsjq8oiLu/r4KjPVg8Bzfu3OjxpzEetxt+IHIF6AR1RHOPh5eJ7aa7jdqN+T6QE4uuFvyH7axh/\nazt+zI1nohmuZZvDC3OogYugN4NMRsFHLgM0SAAonjdrf1I7ADi8agUDw1bflBwtr+ccKsdCidWB\nLkK2a/xvA3Bn+fOdAN6aNvDeT7z34/LX0Q5c87IkDsUlaiM8AOfsBkkyNNcY28VRgaaAoR9VUZdt\nhjB8rxkPq/E/ZFzERw/YUE/suLVFfE3pvDXDVSM4W4Sgz6HN0MSGy4ropf6WBhn6ZSioggGj4apA\ng6oPxfcHl2QUfI3ReR8yrhVrJNHPelVxh3UN6KBhoF63uMeinwPDPrtbH2iuKa3PnZbtGuIbvPfP\nlj8/B+AGqpFz7mbn3AMAngTwi977Z5h273TOnXDOnTh16tQ2b60pMWqzcK0rA5kLjpXkiIBuDxvR\nR6wgmoELHKW2OIMCqgiu7EeiuYCmokpccHPMNuR/7ADfLjYs2lgOGQ2X1agHh6jtvozvS0pKx89W\nisi2glrn3gOQo6yiz1Jv1HY25H90dQSAfiVqLHE/EqdudRJW4BWLda1YaR+tvyMR8hfbGQHVIkSt\nLXLOfRzAS4ivfib+xXvvnXOe6sN7/ySA15V0z390zn3Ae/880e4OAHcAwPHjx8m+LldiwyZxt0EJ\ntIt/w+Gl6udDxsTdNxxeVnot5KXWdkfkdtcfKhbntYJhBYDrDxZj0RT12gMj031949GV6uejwuKM\nHbJ1zDcp7QLSu1Fpd8OhYsyS0wGAG68p2k3nc7FdmGtNXnKo1psw75TEDuSmwytsOwCYl8qq6Vd4\nX7M21zcfLb7XjFHQq56iOGEOAYgRwk2RPt9wiJ+bmJrU1kBeTo46N6UD0+Ym3Jc2N9cfCmtKnpt4\nbUpgcxGiIn/v/Zu8999C/PsggOedczcCQPn/SaWvZwB8CcB378TNb0Vi5Cahj79z7SoA/UEcHc0X\nkwAAB7BJREFUOzDCLcdWcPxlR8QH3Os5vOYbDqHfc7j+oGwg3vr6IhVy6w0HxXbf96oiwPompd1r\nX3oNAOCblXavu7lo94aXHxXbverGop/vvvVasd2R1SFWhhledmxFDHkB4A23FNeUFjsA/A/f9lIA\nwCtvOCC2+/uvKO7tVS+xzY11Dt/0KjKoreTvltf7DmUOj6wOcd3BEV56eFnVseMvK+onbjwsz83/\n9B3fCAD4JmVu/t4rjgEAblXaffNLDgGox87J628+DEDXm1deX1zvu14p683qqI9jq0Nce2AknqgL\n1GO5STH+b3vDzQD05/ydpd684np5br71pmLMr7rxkNguzN0bX3W92O7W6w+i54BXXLcqtluIeO8v\n+x+AXwZwe/nz7QB+iWhzE4Dl8ucjAL4C4LVa39/+7d/ud1LOro39y376j/3LfvqP/X1fOyO2e827\nP+z/1Z89ovb5/IUNf3ZtrLb72gtr/otPnVPbvXBx09Ruczrzn/zKKT+fz8V2eT73n/jb5/1klqt9\nfuaxF/zGZKa2+/zXzvhzaxO13SPPX/BfP72mtnv67Lp/+LkLarszl8b+xFdPq+02JjP/qUf0uZnP\n5/4vHj5pmptPP3rKX9jQx3z/18+a9OGxkxf946cuqe2ePGPTm7NrY/95QaeDbEzsevPpR0758VSf\nm3ufOO0vbU7Vdvd//ax//vyG2u6R521z8/z5Df/Ak/rcnFuf+M889oLabmMy8599/LTPc11vPvmV\nU35zqq+Vv3r0BX9uXdebB58+b5obqwA44Q3223l/+eyKc+4YgPcD+EYAXwPwQ977M8654wB+3Hv/\nY8657wPwqyiYFAfgX/mC3hHl+PHj/sSJE5d9b6l47/Hyf/IhAMCf/x/fi1uu5T1tOHtfC9k66aST\nTl5s4py7z3t/XGu3rf3E3vvTAN5IfH4CwI+VP38MwOu2c52dkNiQaxTDlX6dWieddNLJlZYre5jE\nVZbbXv8NePi5i51x76STTva97Cvj/6s/+K3It0FzddJJJ53sFdlXxr+f9fbXgDvppJNOGNk3B7t1\n0kknnXRSS2f8O+mkk072oXTGv5NOOulkH0pn/DvppJNO9qF0xr+TTjrpZB/Ktnb4LlKcc6dQ7Bq+\nXLkWwAs7dDtXU/bKOIBuLC9W2Stj2SvjALY3lpd576/TGr1ojf92xTl3wrLF+cUue2UcQDeWF6vs\nlbHslXEAV2YsHe3TSSeddLIPpTP+nXTSSSf7UPay8VdPDt0lslfGAXRjebHKXhnLXhkHcAXGsmc5\n/0466aSTTnjZy8i/k0466aQTRjrj30knnXSyD2XPGX/n3Judcw875x51zt1+te9nO+Kc+6pz7ovO\nufudczv3WrMrIM6533HOnXTOfSn67Khz7mPOuUfK/49czXu0CjOW9zjnni6fzf3Ouf/mat6jRZxz\nNzvnPuGc+7Jz7kHn3E+Un++65yKMZTc+lyXn3L3OuS+UY/nZ8vOXO+c+W9qyP3DODbW+tnTdvcT5\nO+cyFO8I/j4ATwH4HIC3e++/fFVv7DLFOfdVAMe997tu44pz7nsAXALwb73331J+9ksAznjvf6F0\nzEe89z99Ne/TIsxY3gPgkvf+V67mvW1FnHM3ArjRe/9559xBAPcBeCuAH8Euey7CWH4Iu++5OACr\n3vtLzrkBgE8B+AkAPwXgj7z3dznn/jWAL3jvf2OnrrvXkP8bADzqvX/cez8BcBeA267yPe1L8d7/\nJYAzyce3Abiz/PlOFIv1RS/MWHadeO+f9d5/vvz5IoCHALwUu/C5CGPZdVK+d/1S+eug/OcB/FcA\nPlB+vuPPZa8Z/5cCeDL6/SnsUoUoxQP4qHPuPufcO6/2zeyA3OC9f7b8+TkAN1zNm9kBeZdz7oGS\nFnrRUyWxOOduAfBtAD6LXf5ckrEAu/C5OOcy59z9AE4C+BiAxwCc897PyiY7bsv2mvHfa/Jd3vv/\nDMD3A/hHJf2wJ8QXfONu5hx/A8ArALwewLMAfvXq3o5dnHMHAPwhgJ/03l+Iv9ttz4UYy658Lt77\n3Hv/egA3oWAw/u6ir7nXjP/TAG6Ofr+p/GxXivf+6fL/kwD+Awql2M3yfMnVBs725FW+n8sW7/3z\n5YKdA/hN7JJnU3LKfwjg//Pe/1H58a58LtRYdutzCeK9PwfgEwC+E8Bh51x48+yO27K9Zvw/B+DW\nMks+BPA2AHdf5Xu6LHHOrZaJLDjnVgH81wC+JP/Vi17uBvCO8ud3APjgVbyXbUkwlqX899gFz6ZM\nLP42gIe89/8i+mrXPRduLLv0uVznnDtc/ryMomDlIRRO4AfKZjv+XPZUtQ8AlKVdvw4gA/A73vuf\nu8q3dFninPs7KNA+APQB/N5uGotz7vcBfC+Ko2mfB/DPAPxHAO8H8I0ojuv+Ie/9iz6Ryozle1FQ\nCx7AVwH8rxFv/qIU59x3AfgkgC8CmJcf/18ouPJd9VyEsbwdu++5vA5FQjdDAcjf771/b2kD7gJw\nFMDfAPhh7/14x66714x/J5100kknuuw12qeTTjrppBODdMa/k0466WQfSmf8O+mkk072oXTGv5NO\nOulkH0pn/DvppJNO9qF0xr+TTjrpZB9KZ/w76aSTTvah/P+RrwF1pfGuQwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1092199e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x109d79550>]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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q6TgAutolTZZVz5GrYjTKJiQSW0chIHHF6VELWau+CP8/CBLnql3SaIZ19BmF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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109cb21d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,30,20000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.9))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10a60c5c0>]"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6tV5k25yHQo6JTAXy8QAtQ9JrZJoeeZewtKnRlE10BoCbe97ypydAykMDRAL0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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a0c1278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6,3))\n",
"amp = np.max(ys[:,0])\n",
"ax.plot(ts,ys[:,0])\n",
"ax.set_xlim([25,30])\n",
"ax.plot(ts,np.sin(ts*2.*np.pi)*amp)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10a0bd5c0>]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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lat22SoN3XquQsw1Qbr3q3xMRYiGvLd4sUnoiyytTqICx5nSRgAfZYrOiKFZq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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a0bd4a8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,30,20000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,1.06))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10aab3668>]"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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3Q6dZ3b8QHb4imoEtLfi2Fi0Od9nwxJAX56YWsL/DQoeuGoxBq8ZOhwnXfBsr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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a3d3470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,30,20000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,1.073))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"#ax.set_ylim([-9,-7])\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10b5ce160>]"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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u9radr9SNwATZOoSszkKorXU2/Px6GVuGwOrGlMzoUkXirAck6AqShSpKtYbS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\n6ARBED0CCTpBEESP8P8DGoJu0md65iYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b5ce240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,30,20000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,1.0826))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"#ax.set_ylim([14.8,15])\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10aacf908>]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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IOfaRXMSeXUcAAjOClG+MrGTZ9VYWajFGDn1rHpcFA/NYYxB0LJOfeL+LbnfFDt8lYWdh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\njuM4DYg3f8dxnAbEm7/jOE4D8j+pIrrGQcxjcgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ae4b2e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,60,40000)\n",
"ys = scipy.integrate.odeint(rhs,[0.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"#ax.set_ylim([14.8,15])\n",
"ax.plot(ts,ys[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10d0b5d30>]"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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BHDPedsVu4j3Hz7ekYZTAuGIj8xLosQJmyIJgAriV/kUGcBIslwMMa2BmQY8D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\nJFyHSOSfkJCQcB0ikX9CQkLCdYj/B+DT6l++nvXgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ba330b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,60,40000)\n",
"ys2 = scipy.integrate.odeint(rhs,[0.9,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"#ax.set_ylim([14.8,15])\n",
"ax.plot(ts,ys[:,0])\n",
"ax.plot(ts,ys2[:,0])"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10dfbc9b0>]"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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oWCO9jr39FddM9qEk3oKwCpiqlJqolPIBVwJL4vwbQj8IHbvtDnoZL0Ukv/u/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\nBEEQTEQQBEEQBEAEQRAEQTD5/wHbqcNCmKhNDgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ddda860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,100,2000)\n",
"ys1 = scipy.integrate.odeint(rhs,[-np.pi/2.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,1.105))\n",
"ys2 = scipy.integrate.odeint(rhs,[-np.pi/2.+1e-10,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,1.105))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.set_yscale(\"log\")\n",
"ax.plot(ts,np.abs(ys1[:,0]-ys2[:,0]))\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10e3f4e48>]"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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egcEmEs9UaJBU88tuHURUld9ecBL/vm5ASNu2SE1xLFKH2qgcbvG6ujnXPp1a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\nWglApgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e23b748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ts = np.linspace(0.,100,2000)\n",
"ys1 = scipy.integrate.odeint(rhs,[-np.pi/2.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))\n",
"ys2 = scipy.integrate.odeint(rhs,[-np.pi/2.+1,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,0.2))\n",
"fig, ax = plt.subplots(figsize=(6,3))\n",
"ax.set_yscale(\"log\")\n",
"ax.plot(ts,np.abs(ys1[:,0]-ys2[:,0]))\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"gammas = np.linspace(1.06,1.087,200)\n",
"ts = np.linspace(0.,600.,600,endpoint=False)\n",
"ts[0]=0.\n",
"Nlast = 100\n",
"phis = np.zeros((len(gammas),len(ts)))\n",
"for i, gamma in enumerate(gammas):\n",
" phis[i,] = scipy.integrate.odeint(rhs,[-np.pi/2.,0.],ts,args=(2.*np.pi,2.*np.pi*1.5,2.*np.pi*1.5/4.,gamma))[:,0]"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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bbmHv3r2MjIzwkY98hHXr1rFr1y6GhoZ4+umn09JGliR1YwAT/oZhzDrl+gB4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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ea37e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6,3))\n",
"o = np.ones(Nlast)\n",
"#ax.set_xlim([1.08,1.085])\n",
"for i, gamma in enumerate(gammas):\n",
" ax.scatter(o*gamma,phis[i,-Nlast:],color=\"black\", s=2.4)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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