{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# The Lorenz System" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The Lorenz system was the first dynamical system known for exhibiting chaotic behavior. It was developed as a simplified model for describing atmospheric convection (E N Lorenz 1963). The dynamical system consists of three variables, denoted $x, y, z$, obeying the equations:\n", "\\begin{align}\n", "\\dot{x} &= \\sigma (y - x) \\\\\n", "\\dot{y} &= x ( \\rho - z) - y \\\\\n", "\\dot{z} &= x y - \\beta z\n", "\\end{align}\n", "These variables roughly represent the convection rate and the horizontal and vertical temperature variation in a fluid layer. There are three parameters, $\\sigma, \\rho, \\beta$, representing the Prandtl number, the Rayleigh number, and the relative dimension of the fluid. These dynamical equations are now known as the \"Lorenz equations\"." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "The Lorenz system is the classic example of \"deterministic chaos\". In Lorenz's own words, such chaos happens \"when the present determines the future, but the approximate present does not approximately determine the future.\" In other words, the dynamics of the system is deterministic, as it is the solution to a set of differential equations, whose solutions are uniquely determined by initial conditions. However, the solution is very sensitive to the initial condition, such that tiny changes in the initial values would lead to dramatic differences in the long term." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "To examine such unusual behavior, we will numerically solve the Lorenz equations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate as intgr\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [], "source": [ "def lorenz(xyz, t, sigma, rho, beta):\n", " \"\"\"\n", " Lorenz equations, with parameters as arguments.\n", " \"\"\"\n", " x, y, z = xyz # parse variables\n", " dxdt = sigma * (y - x)\n", " dydt = x * (rho - z) - y\n", " dzdt = x * y - beta * z\n", " return [dxdt, dydt, dzdt]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Steady states and stability" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The steady states of the Lorenz system can be found analytically. If we set the right-hand side of the equations to zero, the solutions will be:\n", "\\begin{equation}\n", "x^* = y^* = z^* = 0, \\quad \\textrm{or} \\quad x^* = y^* = \\pm \\sqrt{\\beta (\\rho - 1)} \\;\\;\\&\\;\\; z^* = \\rho - 1.\n", "\\end{equation}\n", "There is a trivial solution at the origin, and a pair of solutions that are located on the same constant $z$ plane and symmetrical about the $z$ axis." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "If the parameter $\\rho < 1$, the two nontrivial solutions would not exist because of the squareroot. In this case, we may expect that the only steady state at the origin is stable. Let us verify this by solving the equations from some random initial values." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "sigma = 10.\n", "beta = 8/3.\n", "rho = 0.5\n", "\n", "T = 10. # total time to run\n", "dt = 0.01 # time step\n", "time_points = np.arange(0., T, dt)\n", "\n", "repeat = 10 # number of trajectories to plot\n", "sol0_list = []\n", "\n", "for r in range(repeat):\n", " init = np.random.rand(3)*2-1\n", " sol0 = intgr.odeint(lorenz, init, time_points, args=(sigma, rho, beta))\n", " sol0_list.append(sol0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These solutions represent trajectories in the 3-d (x,y,z) space. To visualize them, we can plot the projection of these trajectories in the (x,z) plane." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "for r in range(repeat):\n", " sol0 = sol0_list[r]\n", " plt.plot(sol0[:,0], sol0[:,2]) # plot trajectories projected onto the (x,z) plane\n", " plt.plot([sol0[0,0]], [sol0[0,2]], 'b^') # blue trianble labels starting point of each trajectory\n", "plt.plot([0], [0], 'rx') # steady state at the origin\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$z$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be seen that all trajectories do converge to the origin." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "When $\\rho$ is larger than $1$, the pair of nontrivial steady states appear, and the steady state at the origin is no longer stable. Let us visualize this situation." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "sigma = 10.\n", "beta = 8/3.\n", "rho = 2.\n", "\n", "T = 10. # total time to run\n", "dt = 0.01 # time step\n", "time_points = np.arange(0., T, dt)\n", "\n", "repeat = 10 # number of trajectories to plot\n", "sol1_list = []\n", "\n", "for r in range(repeat):\n", " init = np.random.rand(3)*2-1\n", " sol1 = intgr.odeint(lorenz, init, time_points, args=(sigma, rho, beta))\n", " sol1_list.append(sol1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x1 = y1 = np.sqrt(beta*(rho-1)) # nontrivial steady state\n", "z1 = rho-1\n", "\n", "plt.figure()\n", "for r in range(repeat):\n", " sol1 = sol1_list[r]\n", " plt.plot(sol1[:,0], sol1[:,2]) # plot x as a function of time\n", " plt.plot([sol1[0,0]], [sol1[0,2]], 'b^') # blue trianble labels starting point of each trajectory\n", "plt.plot([x1], [z1], 'rx') # steady state at the origin\n", "plt.plot([-x1], [z1], 'rx') # steady state at the origin\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$z$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the system is bistable: the trajectories flow to one of the two nontrivial steady states depending on the initial values." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, this is not the whole story. When the value of $\\rho$ becomes sufficiently large, the two steady states also become unstable, and the system becomes \"chaotic\". We will explore this situation below." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Irregular oscillation and strange attractor" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Lorenz first observed this strange behavior when he used the parameter values $\\sigma = 10$, $\\beta = 8/3$, and $\\rho = 28$. Let us reproduce his observations." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "sigma = 10.\n", "beta = 8/3.\n", "rho = 28.\n", "\n", "T = 50. # total time to run\n", "dt = 0.01 # time step\n", "time_points = np.arange(0., T, dt)\n", "\n", "repeat = 10 # number of trajectories to plot\n", "sol2_list = []\n", "\n", "for r in range(repeat):\n", " init = np.random.rand(3)*2-1\n", " sol2 = intgr.odeint(lorenz, init, time_points, args=(sigma, rho, beta))\n", " sol2_list.append(sol2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The first strange feature of the solution that Lorenz noticed was an irregular oscillation. To see this, let us plot one of the variables, like $x$, as a function of time. We will show just one of the solutions." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x2 = y2 = np.sqrt(beta*(rho-1)) # nontrivial steady state\n", "z2 = rho-1\n", "\n", "plt.figure()\n", "# plt.axhline(0, color='k', lw=1) # steady state at the origin\n", "plt.axhline(x2, color='k', lw=1) # one of the nontrivial steady states\n", "plt.axhline(-x2, color='k', lw=1) # the other nontrivial steady state\n", "plt.plot(time_points, sol2[:,0]) # plot x as a function of time\n", "plt.xlabel(r'$t$')\n", "plt.ylabel(r'$x$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "It looks like the solution oscillates around one *unstable* steady state for a number of times, then switches to oscillating around the other one. However, the behavior is *aperiodic*, as we can see that the number of times it goes around each steady state varies with time, in an apparently random fashion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also visualize the solution as a trajectory projected onto the (x,z) plane." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(sol2[:,0], sol2[:,2]) # plot trajectories projected onto the (x,z) plane\n", "plt.plot([sol2[0,0]], [sol2[0,2]], 'b^') # blue trianble labels starting point of each trajectory\n", "plt.plot([x2], [z2], 'rx') # steady state\n", "plt.plot([-x2], [z2], 'rx') # steady state\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$z$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "The trajectory seems to circle around each steady state many times, filling out a region that looks like a butterfly." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "Let us now visualize all the solutions as trajectories in a 3-d plot (you may turn on the interactive mode, so that you can rotate the plot to see from different angles)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "# uncomment the following line to turn on interactive mode\n", "# %matplotlib widget\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(projection='3d')\n", "for r in range(repeat):\n", " sol2 = sol2_list[r]\n", " ax.plot(sol2[:,0], sol2[:,1], sol2[:,2])\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "ax.set_zlabel(r'$z$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "It can be seen that, although the trajectories never stop at any steady state, they are confined to a finite region that looks like two thin disks joined together at an angle. The center of each disk is one of the unstable steady states. Each trajectory circles around on one disk for a certain number of times, and then moves onto the other disk and repeats. The structure formed by the two disks is an \"attractor\" in the sense that all trajectories starting from any initial values will eventually converge to the same finite region and exhibit the same aperiodic behavior. This structure is quite befittingly called a \"strange attractor\". To mark its strangeness, it is mathematically shown to have a fractal dimension of 2.05 (a little \"thicker\" than 2D disks)!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Sensitivity to initial conditions" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "Another important feature of the chaotic dynamics is the extreme sensitivity to the initial condition. This is sometimes referred to as the \"butterfly effect\", perhaps inspired by the butterfly-looking trajectory in the Lorenz system. It says that a butterfly flapping wings in one place could cause a tornado later in another place faraway, which is a metaphor for the chaotic nature of weather systems. We will examine such sensitivity below." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us add a small perturbation to the previous solution at a given time, then solve the equations onward with these perturbed initial values. We will add the perturbation when the solution has settled onto the strange attractor, say at $t = 20$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "t1 = 20. # time to add perturbation\n", "init0 = sol2[int(t1/dt)].copy() # value of original solution at given time\n", "init1 = init0 + 1e-6 # add very small perturbation\n", "time_points1 = np.arange(0., T - t1, dt)\n", "sol3 = intgr.odeint(lorenz, init1, time_points1, args=(sigma, rho, beta))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us plot the two solutions side by side to see how they differ." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.axhline(x2, color='k', lw=1)\n", "plt.axhline(-x2, color='k', lw=1)\n", "plt.axvline(t1, color='r', lw=1, label='perturbation')\n", "plt.plot(time_points, sol2[:,0]) # original solution\n", "plt.plot(time_points1 + t1, sol3[:,0]) # perturbed solution\n", "plt.xlabel(r'$t$')\n", "plt.ylabel(r'$x$')\n", "plt.legend(loc='lower left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "We see that the solutions started very close to each other after the perturbation, as one would expect. However, deviations began to be visible around $t = 35$, and then the trajectories quickly diverged from each other. In fact, later there were times when one trajectory was going around one steady state, while the other trajectory was going around the other, i.e., being as far from each other as possible within the strange attractor." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us examine how fast the solutions diverge by plotting their difference as a function of time." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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RAuDrQKwx5qZAl0ctbNVtdjLiwsd825wJX3/2IM8faOSrV63g0z7fOKva7Fgt4m1GGr6RljfbOTs3gcqWk/0X4L5pDPdfANR4aiTD/RcAqzJiCLYKD7xRgX3QyeaCBO+5zPhwv2scQRYhPXbsjXo8l6xI4Rfby2m3D5IQGTLh4/bVdrI6MxarRbzHClOi+N2uNhptfTR3D4z5Vh0fGcK2L1w45bJfsyaDe587zJO7aylt7Ob96zMBON9zM/7F9jIcLsOGnLHBkZ0QwYMf3UhqTBghQe5/H77Xk50wMkhvWJfJirQYb1/VaDFhwZzl07x088bsCcsdFRrEz27bwCtHmvjQ5lzv8dzESJ757HtIigpFRCZ8/pmaEzUOEXlIRJpF5NCo41eKyFERKRORrwAYYyqMMXcEpqRqMXm3up2Lvrede549dOoHn6H+IScveSaAPfBG5YjhoJWtdjLjwr03p6z4CEKsFu+kvqq2kcGRHR9Bd78DW6+7yaamvZfk6FAiQk5+TwwLtrJ1eQr7ajsJDbJwYeHJZp3shAi/ZkVXt/eSFR9O0BTD9Zo16Thdhj+9WzfhY/qHnBxu6BrRIQ3u4OgfcrHtoHtY6pk2x0SFBnH16nSe2F1Lz4CDogx330NmXDiFKVH8raQJi8Cm/IRxn3/pytQRN/tTWZ4WTWjQ2NrG6bigMIlvXreKqNCR3//X58SPCa3pNieCA3gEuNL3gIhYgZ8DVwFFwG0iUjT7RVOL1d9L3DfyJ3bXzvhSDhUtdgYcLj60OYfWngGe9XTYgvsbfZ5PMFgtQn5SJOUtPfQOOmi09ZOfOLLGASfnctS0945ophr2pSuWszY7jm9et4rY8OARz+/oHZpwFd3Ratt7yfFj5M6KtBjOyYvn4bcqJ5xAV9Jgw+EyrB/VFFWY6q5t/endOqwWoSj9zNvxb954ctLiOXkng+q6tRmAu4/B9+9HzZHgMMa8DrSPOrwJKPPUMAaBJ4AbpvqaInKniBSLSHFLi/8rcip1qOHk5LCZ3udiuN3+I+flclZmDA+95V7B1hhDVaudvFH9B0tSIilvsXs7ipf4dLYOf9scbm6qbe8bNziWp0Xz58+dz4c254w4nj08l2OKzVXuYPKvPf3fr1xBg62fu3+/l5q2sbWb3Z4RU+ty4kYcX5rsWbaksYvClCjCQ8782/vm/AQ+el4uN52dNaI/5c4tBXzx8mV89wNrzvg9Fpo5ERwTyARqfX6vAzJFJFFE7gPWi8hXJ3qyMeZ+Y8xGY8zG5OSxoyuUOpXDDV3csC4DEbxj+mfK8aYeb03ixvVZHGvqoa6jlzb7IN0DDm/H+LAlyVHUtPd6h9SelXHym7fvXI4Bh5MGW59fTRfeGssUmqtsfUN09g6NG0yTOScvgW9dv4o3jrew5Xuvcs+zh0ZMCnz1SDMr02PGdHDHRgR7O4VHN2OdLhHhWzecxfdvXjuiXyAs2Mo/X1o4oran3OZd57gxpg24K9DlUAtbz4CDjt4hVqTFcLDOxhE/1lc6Hcebu8lLjCA0yMoFno7Zt8pavTf8JaOGby5JjsLpMjx/oIHosKARHd+x4cFEhwZR19FHfUcfxkCuX8Ex9bkcteOM2Jqqj74nj/euSuNHLx3jt29XkxIdypDTxYc251Jc3cFdFxWM+7z3r8/k4bequG5Nht/vqabHXA6OesB3WEGW55hSM67Rs6xFRlwYK9KjpzTv4Ewcb+phWaq7GaYwJYqU6FDeON7KOk8bf9GoCWPDTSq7qzq4vCh1xDdlESEzPpza9l7KfSYHTlVSVAhhwZYRQ3onMhwcp9sZmxYbxrduWMX2Y838wLPMx69er8BlDDedPf6oonuuKeL2zbnjzoVQs2MuN1XtBgpFJF9EQoBbgecCXCa1SAyvh5QZF87SlGhq23tnrIN8wOGkqs3OMk/Hr4hwwdIkdpS3cbDeRnJ0KMnRoSOeU5QRQ2acu5Zxw7qx37yzEyKo6+jzzrIefu2pcE8ijJhSjaPmDIMD3E1C3795LdesSeecvHgGHC4+vDl3xEgxXxaLaGgE2JyocYjI48BWIElE6oBvGmMeFJG7gb8BVuAhY8zsbXGlFrXhtZQy4sJZkhyJy7hHNw0vezGdKlrsuIx7ctuwCwqTeHpvPX/e1+Ad3ePLahEe+fg5HGvq8S5H4SsrPpy3ylo51tRNRmyYd8LbVGVPcS5HTXsvcRHBxPj5+qNdWJjMhYXJDDpcHGvqHlPDUnPLnAgOY8xtExzfBmyb5eIoRUNnHxaBlOjQkxPuWnpmJDiOe0ZG+dYKLlh6cjbw1WeNDQaAwtRoClPHL092fAS9g052lLexKsP/m3BWfMSIfSMmMtFQ39MVEmTxa16ECow5ERxKzTX1nX2kxYQRZLVQkOxZ4qOl5xTPOj1lTd1YhBFNMykxYfzi9g3UdfTy3lXjB8dkhkdGtXQPcE7e+JPXTvX8rn4Htr6hSecw1LT36o1+EdLgUGocDZ19ZHj6ECJC3Ivrlbf4v6XqVBxr6iEvMXLMjOKrV6ef9mv6ruE0vGugP4b7LOo7+iYMjv4hJ7XtvdwwTlOaWtg0OJQaR6Ot37ucN7iHw5bPUI3jeHO3d0b0dEmNCeM/b1hF/5DLu4ChP3xnnw8vw+F0GSyCdwRXVdvYvhm1OMzlUVVKBYTLZWjs7PfWOODkHhhT3bluqgYdLqraeilMmf6b7z+dl8entow/F+JUsuNHzj63Dzi46Huv8rGHd+PyrN47PGt9abKOcFpsNDiUGqXVPsCg00Vm3MlZywXJkfQMOGjudu91cN9r5Xzq0eIJ11qaqvKWHpwuw7IZ6HQ/E3ERwUSGWKn2rKz7ZlkrdR19vHashb97FmM83tSDCN4+ILV4aHAoNUpDp3sobnrsyBoHQHlzDw6ni++8eISXDjfx/7aVntF7Dc9IXznHgkNEWJcTxw7PGl2HPRMg02LC+N9XjmOMoaShi/ykyHH3llALmwaHUqM0eGeNjxMcrXZKG7sxxn0TfeztGn79RsWUXveJd2q45Vc7Ryzqd6SxmxCrZU6uh3TpilTKmnuoaOmhpKGLpSlRfOm9yznc2MX2Yy3sq+1gffb0rBel5hcNDqVGafBZbmRYakwokSFWypq6ecezSdIfP3MeVxSl8t2/HfU+ZyId9kG+8ecSdlW287VnDnr7So6c6GZpStSsbBTlr6tXp2O1CE8W11Ha2EVRegzXr80gJTqUrz19kNaeQTbmaXAsRnPvX6tSAdbQ2U9EiHXEMFQRYU1WHLsq2ymuavdszRnBN64rwhjDfa+Vex9b19HLCwcaR3Sk//6dGgadLm7fnMObZa38+o1Kb3PPivS51Uw1LC02jEtXpHD/6+XUd/axKiOGkCALHz431zuz/vKi1ACXUgWCBodSozTa3HM4Rm+9edHyZI6c6Oavh06wyTOpLis+gvevz+SJ3bU0d7tvph956B0+9/s9/PbtasA9Suvxd2o4tyCB/7jhLC5ensyPXj7GofouWnsGxt3Peq740OYchrdAH96n/OPn5/HBjVl896Y13v201eKiwaHUKA2dfePun33JihTvz+cWJHp//szWpTicLh56s4qGzj4qPBMFv/1CKdsONvLasRbqOvr40OZcrBbhC5cto3fQydeeOQjgDaG5aEthMmfnxrM8Ndq7Um90WDDfvWktH5xkT2y1sOkEQKVGabD1syJt7PpOy1KjuXh5Mu9Wd3CZTxNNflIkV69O57G3q739Io/dsZkfvnSUz/5uDwDZCeG8d5X7OWuzYlmSHMnBehsFyZFzeqVXi0V46tPn4TJmynuKq4VP/yUo5WPA4aSle2DEiCpfD3xkI2995RISIkNGHP/s1qX0DDj4xp9LiAoN4rwlifz+U+dyy8ZschIi+NEH13mXFBERPn9pIUlRIXzpiuVjmsTmGotFNDTUCFrjUMpHk809wS89bmxTFUCQ1UL0ODfRoowYLl2RwitHmlmVEYPVIlgtVr5z0/j7Vd+wLpMb1mVOX8GVmkX6NUIpHw02z1Dc2PFrHJP5wmWFxEcEc8cF+dNdLKXmFK1xKOWj0TZ2DsdUrcmKY+83rpjuIik152iNQykf4y03opQaSYNDKR8NnX3ERwQTHqLrLyk1EQ0OpXz4buCklBqfBodSPhpt/dpMpdQpaHAo5cNd4/C/Y1ypxUSDQykPW98QXf0OMrWpSqlJaXAo5VHb7t4nIzcxIsAlUWpu0+BQymM4OLITNDiUmowGh1IeNRocSk2JBodakPqHnJzwbDY0VdXtvcRHBBMTFnzqByu1iGlwqAXp7t/vYct3X+Xoie4pP6e2vZccrW0odUoaHGrBsfUN8XJpM4NOF4/urBr3Md39Q2OO1bT3ajOVUlOgwaEWnLJmdy0jJiyIv+xvYMjpGnH+yeJaVt/7dx55q9J7bMjpor6jT2scSk2BBodacMqb3Vu33rV1CV39Dkoaukacf8yzF/jPXi2jf8gJQHWbHYfLzOnd+JSaKzQ41IJT3tJDiNXC+9e7N0oqrmr3nuvsHeRgvY1NeQm09gzywoFGAI419QDu7WGVUpPT4FALTnmLnbykCNJjw8mMC2dvbaf33M7yNoyBL713OUuSI3myuBaAY03diMCSZK1xKHUqGhxqwalo6fEGwNrsWA7W2bzndld1EBpkYV12HJeuTGVvTSf9Q06ON/WQkxChy6krNQUaHGpBGXS4qG7v9QbH6sw4atp76bAPArCnpoO1WXGEBFnYlJfAoNPFvtpO9tZ0cFZmbCCLrtS8ocGhFpSa9l6cLkNBciQAa7LcYXCw3kb/kJOSBhsbcuMBOCc/AYvAU8V1NNj62ZSXELByKzWfzLs9x0WkAPg6EGuMuSnQ5VFzS3mLu5N7uMYxXIs4WG8jLNjKkNNwtic4YsODWZMVx5/21AFwQWFSAEqs1PwzqzUOEXlIRJpF5NCo41eKyFERKRORr0z2GsaYCmPMHTNbUjVfVbS4h+IO1zhiw4PJT4pkf20nrx5txmqRETWLGze4R16dW5CgHeNKTdFs1zgeAX4GPDp8QESswM+By4E6YLeIPAdYgf8e9fxPGGOaZ6eoai771l9K6Ol38J0PrMFiEe/x8pYeUqJDifZZb2p9dhzbDjWyq7KdcwsSiI04ee7Dm3PJS4xkbVbcbBZfqXltVoPDGPO6iOSNOrwJKDPGVACIyBPADcaY/waunc3yqfmhoqWHh9+qAuDq1elcvCLFe67cZ0TVsH86L5dn9tXTP+TiUxcWjDhnsQhbliXPeJmVWkjmQud4JlDr83ud59i4RCRRRO4D1ovIVyd53J0iUiwixS0tLdNXWhVwbxxv9f78h90n/+kYY6hosbMkJXLE49fnxPPMZ8/n95/czNblKSilzsy86xw3xrQBd03hcfcD9wNs3LjRzHS51Ow5cqKbuIhgbtqQxSM7qugZcBAVGkRLzwC2viEKksb2VazLjpv9giq1QM2FGkc9kO3ze5bnmFLjOt7UzbKUaLYsS8bhMuyt6QCgTJcNUWpWnLLGISI5U3ytTmNM16kfNsZuoFBE8nEHxq3Ah07jddQiYIzhaFM316/NYH1OHBZxzwa/sDCZY03uVXGXperoKKVm0lSaqn4DGEAmeYzBPWLq0Ukeg4g8DmwFkkSkDvimMeZBEbkb+BvukVQPGWNKplAutQg1dQ3Q3e9gWWo00WHBLEuN9tY4jjX3EBseTHJ0aIBLqdTCdsrgMMZcPF1vZoy5bYLj24Bt0/U+av7r6h+iwz5IbuLIju6TtQp3c9T6nHieP9CAy2UobexieWo0IpN9x1FKnakp93GIyE9msiBK+frsY3vY+v3tHKq3jTg+ujlqfU4c3f0OSk90UVLfxfqcuNkuqlKLjj+d490i8hcRiQQQkfeKyFszVC61iPUOOnizrBVj4JEdVSPOHW/qITEyhMQod3PUBk9QPPhmJYNOl3c5EaXUzJlycBhj/i/wOLDdExj/Cky6PIhSp+PoCXetIiEyhBcONNI76PCeO9bcTaFP53dBUhRJUSE8vaee8GAr5y/V9aaUmmn+NFVdCnwKsANJwOeNMW/MVMHU4lXa6A6Of718GX1DTt6tdnd+u1yGYye6WZEW432sxSJ8/tJCAD6zdQmRofNuapJS844/TVVfB+4xxmwFbgL+ICKXzEip1IL3+rEWPv/4Xmy9Q2POHTnRRVRoEDesy8BqEXZVuLd+re/swz7oZHnayHkaHzkvj2PfvsobIEqpmTXlr2fGmEt8fj4oIlcBfwT+MRMFUwvbvc+VUNFqJzcxgi9esXzEudLGLlakuYfbFqXHsMcz3Ha4CWu8CX4hQXNhLqtSi8OZ/N+2BDgyXQVRi0fPgIOKVvfy508V1+F0nVwRxhjDkcZuVqS7w2Fddhz7aztxutwT/0An+CkVaH4Fh4isF5HviUg18APcTVZK+aXSs2fGtWvSOdHVT3FVu/dcXUcf3QMOVqa7+zHW58RhH3RS1tzDvtpO8pMiRyyZrpSafacMDhFZJiLfFJGjwANAK7DVGLMZaJ/82UqNNbxL38fPzwNgt09wHPE0Rw13gA8vTrinpoPiqnY26nBbpQJuKn0cR3CvJ3WTMebgqHO66qzyW3lLD1aLcFZmLIUpURR7Rk2Bu39DBFZ4OsDzkyKJDQ/mwTcr6egd4j1LEwNVbKWUx1Saqm4EKoG/i8hvReQ6EdG2AnXaKlrs5CREEBpkZX2Ouw/DGPd3kCMnushNiPAOqxURLlqWTFlzD5EhVi4vSgtk0ZVSTCE4jDHPGmNuBZYCfwXuBOpE5GEgZtInqwWtf8g5ZkmQqShv6aEgyb0G1drsODp6h6ht7wPgcEPXiHkaAF++agXvW5fBj29dT5TO01Aq4PyZOW43xvzeGHMdsALYCRyYsZKpOe9bfynh2p++yUuHm6b8HKfLUNFqZ0mKe2TU8F7f++s6sfUNUdXWy+qs2BHPyYwL58e3rufyotRpK7tS6vSdyX4cLwIv+pw/3f041DxkjOGFA40APPZ29ZRv6vUdfQw6XCxJdtc4lqdFExJkYX9tJ/ERIQCsGRUcSqm55Uz34xg+PqX9ONTC0WYfpKvfQWiQhbfKWunqHyJmCsNky1vdI6oKkt01jmCrhVUZMRyos3mH2a7O1OBQai6b1f041MJR094LwG2bcnhkRxUHam1cUHjqBQbLm93BsST55CS+jbnx/GZHNTXtvazPiSPOU/NQSs1Nuk6DOi01be7guG5tBiJ4lwU5lfIWO/ERwSREngyHW87JZtDp4kRXPzednTUj5VVKTR8doqJOS7UnOFZlxJCfFDnl0VUVLT0jahsAS1OieeyOzVS327ntnKluca+UChQNDnVaqtvtpMWEERZsZVVGLHuqp17juGRF8pjjFxQmcQG6l4ZS84E2VanTUtPWS05iBABF6THUd/aNu0S6L1vfEK09A2NqHEqp+UWDQ52WmvZechM8wZHhnrB3uHHy0dgVLWM7xpVS848Gh/Jb36CT5u4Bcn1qHAAlDZP3cxxv8gRHigaHUvOZBofy2/BQ3GxPjSM5OpSU6NBT1jiONXUTGmQhx/M8pdT8pMGh/Fbd5t5PIzcx0nusKCOGww2nCI5m94gqq2W8uaRKqflCg0P5bbjGketTc1iVEUNZcw/9Q84Jn3e8qVt371NqAdDgUH6rae8lOiyIuIiTS4yclRGLw2XYW9M57nO6+odotPVTOM5+4Uqp+UWDQ/mtuq2X3MQIRE42OV20PJno0CAef6dm3Ofsr+0EdAFDpRYCDQ7lN/dQ3MgRxyJCgrhtcw5/OdAw7izyPdWdiJzcClYpNX9pcCi/OF2Guo5e74gqX3dfspSEiBDufa4EYwwH6jq9IfJ2RRvLU6O9K+AqpeYvDY5FrKmrn6pWu1/PabT1MeQ03jkcvmLCgvniFcspru7g2X313P7rXVz70zf5W8kJ3qlq59KVKdNVdKVUAGlwLFIul+Hm+3Zy5U9e54Stf8rPG14VN3eCuRi3nJPNstQo/s8f9tPd7wDg0799F6tFuG2TLmCo1EKgwbFIHWqwUdPeS/+QiyeLa6f8vKrh4EiKHPe81SJ87uKl3p9f/7eL+eLly3j8U5vJiteJf0otBLo67iJV4pmslxUfzrN76/n8pYVTel5Vm52QIAvpMWETPuaa1ensqe7g8qI0chIj+OcpvrZSan7QGsciVdVmJ9gqfPS8PCpa7VNurqpqtZObEIFlktnfQVYL37rhrCntCKiUmn80OBap6lb3yKjNBQkA7K5qn9Lzqtrs5E3QTKWUWhw0OBapqjY7eYmRrEyPITTI4p2gNxmXy1Dd1kveOCOqlFKLx7wLDhFZKSL3icgfReQzgS7PfGSM8c7+DrZaWJkew8EpbP16oqufAYdLaxxKLXKzGhwi8pCINIvIoVHHrxSRoyJSJiJfmew1jDGlxpi7gA8C589keReqlu4B+oac5HlWt12TFcuhehsul/E+xtY3xLaDjQw5Xd5jw3M+8hI1OJRazGa7xvEIcKXvARGxAj8HrgKKgNtEpEhEVovI86P+pHiecz3wArBtdou/MHiH1HqanFZnxmIfdFLhMxnwS0/t57O/28P9r1d4jx1t6gZgqW7EpNSiNqvBYYx5HRjdC7sJKDPGVBhjBoEngBuMMQeNMdeO+tPseZ3njDFXAbdP9F4icqeIFItIcUtLy0xd0rxU1Tay5rDas/Dg8PIgnb2D/ONIMwAPvVnpXSq9tLGLhMgQUqJDZ7vISqk5ZC70cWQCvjPQ6jzHxiUiW0Xkf0XkV0xS4zDG3G+M2WiM2ZicnDx9pT0DxhhePdJMZ+9gQMtR3WbHahEy48MBWJocRViwhQN17uB4pbQZp8vwb+9dTpt9kBcONAJQ2thNUXrMiFVxlVKLz1wIDr8YY7YbYz5vjPm0MebngS6PP3aWt/HxR3bzyd8UB7Qc1W29ZMWHE2x1f/xBVgurMmI5UNcJwIslJ0iPDeMzFy1hSXIkT+yuYcjp4lhTNyvTdT8NpRa7uRAc9UC2z+9ZnmMLzuvHWwEoru6gwx64Wod7SO3IDu7zChLZU9NBeUsPrx1r4cqz0rBYhGvXZFBc3cH2oy0MOFxsyIkPUKmVUnPFXAiO3UChiOSLSAhwK/BcgMs0I0oaTg553VXZFpAyGGM8czhGzsW4eWMWIsL1P32TQYeL69dmAHDZylSMgf98/jAAmwsSZ73MSqm5ZbaH4z4O7ASWi0idiNxhjHEAdwN/A0qBJ40xJbNZrtlS0WLnqrPSsAgcbuwOSBk6eofo7neQO6rGkZsYyZeuWI590MmN6zNZ76lZnJUZQ2pMKDXtvWzKTyAhMiQQxVZKzSGzusihMea2CY5vY4EPrXW6DCe6+rkhKYP8pEhKG7sCUg7viKqksbO/P7N1CR85L5eIEKv3mIhw6zk5/PK1cr6gixUqpdDVcWdNS/cATpchPS6cFWkxI5qtZtPwJL6chPEn8UWGjv0n8X8uX8bnLy3EOsnChkqpxWMu9HEsCo22PgAyYsMoSI6ktqOPQYfrFM86fS6X4Y/v1lHe0jPieGWrHYtAzgQbMU1EQ0MpNUyDY5Y0epYtT48NJz8pEqfLUNPu37at/vhbyQm+9NR+bvrlDu8EPnAHR3ZCBCFB+tErpU6P3j1mSUOnp8YRF0ZBsnvJjvKWmQuOHeXuUVsdvUM85bPDX2WrnXxdpFApdQY0OGZJo62f8GArseHBFCS7b9wVMxgcB+ptbM5PYGNuPL/cXo7TZdxDcVvtukihUuqMaHDMkkZbH+lxYYgIMWHBJEWFUtnac+onnoZBh4vSxi7WZsfxT+fl0mDr50BdJy3dA9gHnd7gUkqp06HBMUsaOvvJiA33/l6QHDljNY5jTd0MOlyszoxlS2EyFoHXjrVQesI9d6QwRZcNUUqdPg2OWdJo6yM9Nsz7+5LkyBHLmE+n4U2Z1mbFER8ZwurMWN4qa/WufluUETMj76uUWhw0OGbBkNNFc/fAiOAoSIqi3T7oXSn3129U8K2/lIzYTOl0HaizERseTHaCu4Zz/tIk9tZ08lZZK7mJEcSGB5/xeyilFi8NjlnQ3D2AMZAeN7KpCtwjq9rtg3z7hVIefquKh3dUnfH7HazvZE1WrHf58wuWJuFwGXaUt7GlcG4sMa+Umr80OGZBo2co7ogah2dIbmWrnT3VHQDEhgfz/7aV8uKhxtN+r/4hJ0dPdLM6M9Z7bFN+AivSorFahFvOyZ7k2UopdWq65MgsaPBM/svwqXFkx4cTbBUqWnowQLBV+McXL+ITj+zm688c4oLCZKI8y3987OF3CLJY+MXtG045ce/IiW6GnIY1WSeDI8hq4Q+fPo+uviGy/ZwxrpRSo2mNYxaMV+MIslrISYigvKWHd6s6WJURS2JUKPdev4o2+yCPvV3tfq6tj+1HW3i5tIn/feX4Kd/roGczptVZcSOOu/s8NDSUUmdOg2MWNNr6iQ4NIjpsZKf02qw4dpS1sbe2g7Nz3cuYr8+J5/yliTz8ViUDDie7KtxbtK9Mj+Hn28t49WjzpO+1r9ZGYmQIGT4hpZRS00mDYxY0dLon/422dUUK3QMOhpyGc/JO7qz36S1LaOoa4M/7GthV2UZ0WBBP3XUeK9Ji+Len9tM+ye6Be2s6WJ8Tr/uCK6VmjAbHLGi09ZPuM/lv2NblyQRZBKtFOG9Jkvf4hYVJrEyP4f7XK3i7op1z8hKICg3ihx9ci61viG8+N/4+Vx32QSpa7WzIjZupS1FKKQ2O2dBo6ydjnBpHTFgw275wIU9/5j0j5laICHddVEBZcw+VrXY25ycA7uaqf76kkL/sb+A/nz+MfcAx4vXeqXI3a52t+4IrpWaQBscMG3A4ae0ZGLfGAbAsNZq12XFjjl+zOp3hLTAuXpHiPf6ZrUu4fXMOD75ZyY2/2EHvoANb3xAAr5Q2ER0WxIZcDQ6l1MzR4bgz7MQ4Q3GnIshq4fFPnUtFq51lqSfXlgq2Wviv96/m4uUpfPLRYtbc+3ecxvD1q1fy/IFGrjornWCrfh9QSs0cvcPMsPrOkzv/+WtzQSK3bcoZ99xlRalcszodh8tgDHz7hVIGHC4+tSX/jMqrlFKnojWOGdbQeXo1jqm459oikqNDuXljFr/dWc1Fy5JZkaYLGCqlZpYGxwwbnvyXNgPzKtJiw7j3+lUA/M8H1kz76yul1Hi0qWqGNdj6SIoKISzYGuiiKKXUtNDgmGH1nf0z0kyllFKBosExwxo7+0bs/KeUUvOdBscMMsZMuNyIUkrNVxocM6irz4F90EmmNlUppRYQDY5psKuijUt+sJ0dZa0jjjfYPHM4NDiUUguIBsc0uO+1cipa7Nz7lxKMOblneF2HBodSauHR4DhDxhjeqWwn2Coca+qhpKHLe666zQ5Arm6gpJRaQDQ4zlCjrR/7oJN/uWwZwVbhmb313nPVbb3EhAURFxE8ySsopdT8osFxho439wCwMTeeC5Ymjdihr6rNTl5SpG6qpJRaUDQ4ztDxpm4AlqZEsTEvgYoWOx2eHfpq2nvJTYwMZPGUUmraaXCcofKWHhIiQ0iMCvXuG76npoMhp4u6jj7yErV/Qym1sOgih2foeFMPS1OiAFibFUewVdhd1UFOQgROlyE/SWscSqmFZd7VOERkq4i8ISL3icjWQJbFGMPx5pPBER5iZU1WHLsq27yjq1ZlxAayiEopNe1mNThE5CERaRaRQ6OOXykiR0WkTES+coqXMUAPEAbUzVRZp6KlZwBb3xCFnuAA2JSfwME6G7sq2wkJsrAkWWscSqmFZbZrHI8AV/oeEBEr8HPgKqAIuE1EikRktYg8P+pPCvCGMeYq4MvAt2a5/COUeUZUFaac3Np1c34CDpfh8Xdq2JyfQJBu46qUWmBmtY/DGPO6iOSNOrwJKDPGVACIyBPADcaY/wauneTlOoDQiU6KyJ3AnQA5OeNvv3qmvMGRerLG8Z4lSWTGhVPf2ceNGzJn5H2VUiqQ5kLneCZQ6/N7HbB5ogeLyI3Ae4E44GcTPc4Ycz9wP8DGjRvNRI87E8ebeogODSIl+mR+hQRZeOLOcylr6WHrsuSZeFullAqouRAcfjHGPA08HehyABxv7mZpatSYCX7ZCRFk6zIjSqkFai40wNcD2T6/Z3mOzXllzT0sTY469QOVUmoBmQvBsRsoFJF8EQkBbgWeC3CZTqm1Z4DWnkGWp0Wf+sFKKbWAzPZw3MeBncByEakTkTuMMQ7gbuBvQCnwpDGmZDbLdTqOeZYa0eBQSi02sz2q6rYJjm8Dts1mWc7U0ROe4EjV4FBKLS5zoalqXjrW1E1cRDDJ0ROOCFZKqQVJg2MKqlrtXP+zNylv6fEeO1Tfxcq0GF0yXSm16GhwTMGjO6s5UGfj0h+8xscefoeqVjuHG7u8q+EqpdRiMu/mcQTCP440eX/efrSFO9p343QZNuZpcCilFh8NjlM4Yeunqq2XLcuSqW3vJSs+nDeOtxJsFc5bkhjo4iml1KzT4DiFnRWtAHz5yuWsyoilqaufjz+8m4+dn0dokDXApVNKqdmnwXEKO8raiIsIZmVaDACpMWFs+8KFAS6VUkoFjnaOT8IYw47yNs7NT8Ri0dFTSikFGhyTqm3vo76zj/cs1b4MpZQapsExibfK3f0b79FOcKWU8tLgmMRz+xrITghnia6Aq5RSXto5PolvXl9Ec9eAzg5XSikfGhyTWJEWw4q0QJdCKaXmFm2qUkop5RcNDqWUUn7R4FBKKeUXDQ6llFJ+0eBQSinlFw0OpZRSftHgUEop5RcNDqWUUn7R4FBKKeUXDQ6llFJ+EWNMoMsw40SkBag+zacnAa3TWJxA0muZexbKdYBey1x1JteSa4xJHn1wUQTHmRCRYmPMxkCXYzrotcw9C+U6QK9lrpqJa9GmKqWUUn7R4FBKKeUXDY5Tuz/QBZhGei1zz0K5DtBrmaum/Vq0j0MppZRftMahlFLKLxocSiml/KLB4SEi2SLyqogcFpESEfmC53iCiLwkIsc9/40PdFlPZZJruVdE6kVkn+fP1YEu66mISJiIvCMi+z3X8i3P8XwR2SUiZSLyBxEJCXRZT2WSa3lERCp9Ppd1AS7qlIiIVUT2isjznt/n3WcybJxrma+fSZWIHPSUudhzbNrvYRocJzmALxpjioBzgc+JSBHwFeAVY0wh8Irn97luomsB+JExZp3nz7bAFXHKBoBLjDFrgXXAlSJyLvAd3NeyFOgA7ghcEadsomsB+Defz2VfoAropy8ApT6/z8fPZNjoa4H5+ZkAXOwp8/DcjWm/h2lweBhjGo0xezw/d+P+R5QJ3AD8xvOw3wDvC0gB/TDJtcw7xq3H82uw548BLgH+6Dk+Xz6Xia5l3hGRLOAa4Nee34V5+JnA2GtZgKb9HqbBMQ4RyQPWA7uAVGNMo+fUCSA1UOU6HaOuBeBuETkgIg/Nh2Y38DYj7AOagZeAcqDTGOPwPKSOeRKMo6/FGDP8ufyX53P5kYiEBq6EU/Zj4N8Bl+f3RObpZ8LYaxk23z4TcH8R+buIvCsid3qOTfs9TINjFBGJAv4E/Isxpsv3nHGPXZ433xDHuZZfAktwN5M0Aj8IXOmmzhjjNMasA7KATcCKwJbo9I2+FhE5C/gq7ms6B0gAvhy4Ep6aiFwLNBtj3g10Wc7UJNcyrz4THxcYYzYAV+Fuot7ie3K67mEaHD5EJBj3jfZ3xpinPYebRCTdcz4d9zfFOW+8azHGNHluXC7gAdw34XnDGNMJvAqcB8SJSJDnVBZQH6hynQ6fa7nS07RojDEDwMPM/c/lfOB6EakCnsDdRPUT5udnMuZaROSxefiZAGCMqff8txl4Bne5p/0epsHh4WmjfRAoNcb80OfUc8BHPT9/FPjzbJfNXxNdy/A/Ho/3A4dmu2z+EpFkEYnz/BwOXI67z+ZV4CbPw+bL5zLetRzx+Z9acLc/z+nPxRjzVWNMljEmD7gV+Icx5nbm4WcywbV8eL59JgAiEiki0cM/A1fgLve038OCTv2QReN84J+Ag542aICvAf8DPCkid+Bemv2DgSmeXya6lts8wwoNUAV8OhCF81M68BsRseL+ovOkMeZ5ETkMPCEi3wb24g7KuW6ia/mHiCQDAuwD7gpgGc/El5l/n8lEfjcPP5NU4Bl31hEE/N4Y86KI7Gaa72G65IhSSim/aFOVUkopv2hwKKWU8osGh1JKKb9ocCillPKLBodSSim/aHAopZTyiwaHUkopv2hwKBUgIpIlIrcEuhxK+UuDQ6nAuRTYEOhCKOUvnTmuVACIyAW41wzqBLqBG40xFQEtlFJTpMGhVICIyIvAl4wxc34BPaV8aVOVUoGzHDgS6EIo5S8NDqUCQESSAJvPjnlKzRsaHEoFRh7QEOhCKHU6NDiUCowjQJKIHBKR9wS6MEr5QzvHlVJK+UVrHEoppfyiwaGUUsovGhxKKaX8osGhlFLKLxocSiml/KLBoZRSyi8aHEoppfzy/wEdj6ohkKSG7QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "diff = sol2[int(t1/dt):] - sol3 # difference between solutions, 3d vector\n", "diff = np.sqrt(np.sum(diff**2, axis=1)) # magnitude of difference\n", "\n", "plt.figure()\n", "plt.plot(time_points1 + t1, diff)\n", "plt.yscale('log')\n", "plt.ylim(5e-7, 2e3)\n", "plt.xlabel(r'$t$')\n", "plt.ylabel(r'$|\\Delta x|$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see that there is a roughly linear increase in the log plot, which eventually flatten out because the difference is bounded by the length scale between the steady states. If we fit the increasing part to a line, we can find the rate of divergence of the solutions, which is the so-called \"Lyapunov exponent\" of the chaotic system." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "slope, intercept = np.polyfit(t1+time_points1[:1500], np.log(diff[:1500]), 1) # fit line\n", "t_array = time_points1 + t1\n", "d_array = np.exp(np.polyval((slope, intercept), t_array)) # calculate line\n", "\n", "plt.figure()\n", "plt.plot(time_points1 + t1, diff)\n", "plt.plot(t_array, d_array, '--', label=f'Lyapunov exponent = {slope:.1f}')\n", "plt.yscale('log')\n", "plt.ylim(5e-7, 2e3)\n", "plt.xlabel(r'$t$')\n", "plt.ylabel(r'$|\\Delta x|$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse of the Lyapunov exponent sets a timescale over which small errors in the initial values are amplified to render predictions of the future unreliable. For example, this \"Lyapunov time\" for typical weather models is on the order of 10 days, which means weather forecasts are inevitably inaccurate beyond a week or so." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Orbit diagram and bifurcation" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Finally, let us study how the behavior of the solution depends on the parameters. It turns out that the chaotic behavior is exhibited when $\\rho > \\rho_H \\equiv \\sigma (\\sigma + \\beta + 3) / (\\sigma - \\beta - 1)$. On the other hand, when $\\rho < \\rho_P \\equiv 1$, the origin is the unique stable steady state. In between $\\rho_P < \\rho < \\rho_H$, the origin is unstable but the other two steady states $(\\pm \\sqrt{\\beta (\\rho - 1)}, \\pm \\sqrt{\\beta (\\rho - 1)}, \\rho - 1)$ are, so the system is bistable. The location of the steady states and the behavior of the solutions in general can be represented by an orbit diagram shown below. To make this diagram, we vary the value of $\\rho$, and for each $\\rho$ value, we solve the equations from random initial values; then we plot the position of the trajectory at every time point (after some initial period by which the solution has settled down)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "sigma = 10.\n", "beta = 8/3.\n", "\n", "T = 100.\n", "dt = 0.01\n", "time_points = np.arange(0., 50., 0.01)\n", "\n", "rho_list = np.geomspace(0.1, 1000., 401) # list of rho values geometrically spaced\n", "sol_list = [] # list of solutions of Lorenz equations\n", "\n", "for rho in rho_list:\n", " init = np.random.rand(3)*2-1 # random initial values\n", " sol = intgr.odeint(lorenz, init, time_points, args=(sigma, rho, beta))\n", " sol_list.append(sol)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rP = 1 # onset of instability at the origin, pitchfork bifurcation\n", "rH = sigma * (sigma + beta + 3) / (sigma - beta - 1) # onset of chaos, Hopf bifurcation\n", "\n", "plt.figure(figsize=(8,6))\n", "plt.axvline(rP, lw=1, ls=':', label=r'$\\rho = 1$')\n", "plt.axvline(rH, lw=1, ls='--', label=r'$\\rho = %.3f$' % rH)\n", "plt.axvline(28, lw=1, ls='-', label=r'$\\rho = 28$')\n", "for i in range(len(rho_list)):\n", " rho = rho_list[i]\n", " sol = sol_list[i]\n", " y = sol[int(t1/dt):,0]\n", " x = [rho] * len(y)\n", " plt.scatter(x, y, s=0.1, c='k', marker='.', edgecolor='none')\n", "plt.xscale('log')\n", "plt.xlabel(r'$\\rho$')\n", "plt.ylabel(r'$x$')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "It can be seen that the stable steady state at the origin \"bifurcates\" into two steady states at $\\rho = 1$. (This is known as the \"pitchfork bifurcation\" where one fixed point splits into two.) Then at $\\rho_H \\approx 24.737$ the two steady states undergo another type of \"bifurcation\" (known as the \"Hopf bifurcation\" where a fixed point becomes a saddle point) that leads to the onset of chaos." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }