{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring the Lorenz System of Differential Equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this Notebook we explore the Lorenz system of differential equations:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\dot{x} & = \\sigma(y-x) \\\\\n", "\\dot{y} & = \\rho x - y - xz \\\\\n", "\\dot{z} & = -\\beta z + xy\n", "\\end{aligned}\n", "$$\n", "\n", "This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\\sigma$, $\\beta$, $\\rho$) are varied." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we import the needed things from IPython, NumPy, Matplotlib and SciPy." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "from ipywidgets import interact, interactive\n", "from IPython.display import clear_output, display, HTML" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "import numpy as np\n", "from scipy import integrate\n", "\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.colors import cnames\n", "from matplotlib import animation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the trajectories and plotting the result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\\sigma$, $\\beta$, $\\rho$), the numerical integration (`N`, `max_time`) and the visualization (`angle`)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):\n", "\n", " fig = plt.figure()\n", " ax = fig.add_axes([0, 0, 1, 1], projection='3d')\n", " ax.axis('off')\n", "\n", " # prepare the axes limits\n", " ax.set_xlim((-25, 25))\n", " ax.set_ylim((-35, 35))\n", " ax.set_zlim((5, 55))\n", " \n", " def lorenz_deriv(x_y_z, t0, sigma=sigma, beta=beta, rho=rho):\n", " \"\"\"Compute the time-derivative of a Lorenz system.\"\"\"\n", " x, y, z = x_y_z\n", " return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n", "\n", " # Choose random starting points, uniformly distributed from -15 to 15\n", " np.random.seed(1)\n", " x0 = -15 + 30 * np.random.random((N, 3))\n", "\n", " # Solve for the trajectories\n", " t = np.linspace(0, max_time, int(250*max_time))\n", " x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)\n", " for x0i in x0])\n", " \n", " # choose a different color for each trajectory\n", " colors = plt.cm.jet(np.linspace(0, 1, N))\n", "\n", " for i in range(N):\n", " x, y, z = x_t[i,:,:].T\n", " lines = ax.plot(x, y, z, '-', c=colors[i])\n", " plt.setp(lines, linewidth=2)\n", "\n", " ax.view_init(30, angle)\n", " plt.show()\n", "\n", " return t, x_t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's call the function once to view the solutions. For this set of parameters, we see the trajectories swirling around two points, called attractors. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x151379a668>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, x_t = solve_lorenz(angle=0, N=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using IPython's `interactive` function, we can explore how the trajectories behave as we change the various parameters." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x151b4fd6d8>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))\n", "display(w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The object returned by `interactive` is a `Widget` object and it has attributes that contain the current result and arguments:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "t, x_t = w.result" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/plain": [ "{'N': 10,\n", " 'angle': 0.0,\n", " 'beta': 2.6666666666666665,\n", " 'max_time': 4.0,\n", " 'rho': 28.0,\n", " 'sigma': 10.0}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w.kwargs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [], "source": [ "xyz_avg = x_t.mean(axis=1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/plain": [ "(10, 3)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xyz_avg.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Average $x(t)$')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x151379a2e8>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(xyz_avg[:,0])\n", "plt.title('Average $x(t)$')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Average $y(t)$')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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