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@jakoblorz
Created May 29, 2020 17:23
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Bifurications and Lyapunov.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Bifurications and Lyapunov.ipynb",
"provenance": [],
"authorship_tag": "ABX9TyNyQxOMQf2cL7N+VS2bTDOW",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/jakoblorz/f044ba71ba18e0858e861fecbe505c78/bifurications-and-lyapunov.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "A0m7lXGNee8f",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "SK0hJ-OhfITs",
"colab_type": "code",
"colab": {}
},
"source": [
"def logistic(r, x):\n",
" return r * x * (1 - x)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "YEOR4ygffMdc",
"colab_type": "code",
"outputId": "406eeb79-d752-4088-b3e1-ae64bfd8a7fb",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 283
}
},
"source": [
"x = np.linspace(0,1)\n",
"fix, ax = plt.subplots(1, 1)\n",
"ax.plot(x, logistic(2, x), 'k')"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fbaec0e7390>]"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
},
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "q0S-_rjEfZW5",
"colab_type": "code",
"outputId": "00fe3b98-d10b-4152-d684-1b9bf1a3a80f",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 391
}
},
"source": [
"def plot_system(r, x0, n, ax=None):\n",
" # Plot the function and the\n",
" # y=x diagonal line.\n",
" t = np.linspace(0, 1)\n",
" ax.plot(t, logistic(r, t), 'k', lw=2)\n",
" ax.plot([0, 1], [0, 1], 'k', lw=2)\n",
"\n",
" # Recursively apply y=f(x) and plot two lines:\n",
" # (x, x) -> (x, y)\n",
" # (x, y) -> (y, y)\n",
" x = x0\n",
" for i in range(n):\n",
" y = logistic(r, x)\n",
" # Plot the two lines.\n",
" ax.plot([x, x], [x, y], 'k', lw=1)\n",
" ax.plot([x, y], [y, y], 'k', lw=1)\n",
" # Plot the positions with increasing\n",
" # opacity.\n",
" ax.plot([x], [y], 'ok', ms=10,\n",
" alpha=(i + 1) / n)\n",
" x = y\n",
"\n",
" ax.set_xlim(0, 1)\n",
" ax.set_ylim(0, 1)\n",
" ax.set_title(f\"$r={r:.1f}, \\, x_0={x0:.1f}$\")\n",
"\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6),\n",
" sharey=True)\n",
"plot_system(2.5, .1, 10, ax=ax1)\n",
"plot_system(3.5, .1, 10, ax=ax2)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "vQVwdOTxfkcZ",
"colab_type": "code",
"outputId": "ae77d85a-b9e6-463c-826b-e3917b91f3ce",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 657
}
},
"source": [
"n = 10000\n",
"r = np.linspace(2.5, 4.0, n)\n",
"iterations = 1000\n",
"last = 100\n",
"\n",
"x = 1e-5 * np.ones(n)\n",
"lyapunov = np.zeros(n)\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 9),\n",
" sharex=True)\n",
"for i in range(iterations):\n",
" x = logistic(r, x)\n",
" # We compute the partial sum of the\n",
" # Lyapunov exponent.\n",
" lyapunov += np.log(abs(r - 2 * r * x))\n",
" # We display the bifurcation diagram.\n",
" if i >= (iterations - last):\n",
" ax1.plot(r, x, ',k', alpha=.25)\n",
"ax1.set_xlim(2.5, 4)\n",
"ax1.set_title(\"Bifurcation diagram\")\n",
"\n",
"# We display the Lyapunov exponent.\n",
"# Horizontal line.\n",
"ax2.axhline(0, color='k', lw=.5, alpha=.5)\n",
"# Negative Lyapunov exponent.\n",
"ax2.plot(r[lyapunov < 0],\n",
" lyapunov[lyapunov < 0] / iterations,\n",
" '.k', alpha=.5, ms=.5)\n",
"# Positive Lyapunov exponent.\n",
"ax2.plot(r[lyapunov >= 0],\n",
" lyapunov[lyapunov >= 0] / iterations,\n",
" '.r', alpha=.5, ms=.5)\n",
"ax2.set_xlim(2.5, 4)\n",
"ax2.set_ylim(-2, 1)\n",
"ax2.set_title(\"Lyapunov exponent\")\n",
"plt.tight_layout()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x648 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
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