EjercicioIteracion1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejercicio de iteración\n",
    "\n",
    "\\begin{equation}\n",
    "    x_{t+1}=R(1-x_t)x_t\n",
    "\\end{equation}\n",
    "\n",
    "Con solución\n",
    "\\begin{equation}\n",
    "    X_{t}=R^t x_0 --X(t)=R^t x_0\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sc\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Iterar ambas funciones, una como una función recursiva y la otra como función de t para diferentes valores de R \n",
    "Describir el comportamiento\n",
    "\n",
    "Hacer una lista y compararlas y graficar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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1.2795595725764075e-07, 1.1516034679642238e-07, 1.0364430018106522e-07, 9.327986049503183e-08, 8.395186661450951e-08, 7.555667360993425e-08, 6.800100111101099e-08, 6.120089683818736e-08, 5.5080803783373824e-08, 4.957272067453099e-08, 4.461544639536872e-08, 4.0153899964347594e-08, 3.613850851681072e-08, 3.252465648973703e-08, 2.9272189888695374e-08, 2.6344970128650847e-08, 2.3710472491134055e-08, 2.1339424736052794e-08, 1.920548185261357e-08, 1.7284933335386733e-08, 1.555643973295603e-08, 1.4000795541857892e-08, 1.2600715811252054e-08, 1.1340644087226614e-08, 1.0206579562754765e-08, 9.18592151272245e-09, 8.267329285507167e-09, 7.44059629544259e-09, 6.696536616072106e-09, 6.026882914105653e-09, 5.424194590004102e-09, 4.881775104523994e-09, 4.393597572623039e-09, 3.954237797987406e-09, 3.5588140041162683e-09, 3.2029325923060004e-09, 2.882639323842501e-09, 2.5943753839796023e-09, 2.334937839523937e-09, 2.1014440506648024e-09, 1.8912996416238618e-09, 1.7021696742421626e-09, 1.5319527042103029e-09, 1.3787574316770814e-09, 1.2408816867984984e-09, 1.1167935167328399e-09, 1.0051141639370509e-09, 9.046027466341167e-10, 8.141424712342296e-10, 7.327282235142615e-10, 6.594554006796338e-10, 5.935098602202772e-10, 5.34158873881221e-10, 4.807429862363057e-10, 4.326686874046727e-10, 3.8940181849572347e-10, 3.504616365096807e-10, 3.1541547274817163e-10, 2.8387392538381623e-10, 2.554865327729087e-10, 2.299378794368718e-10, 2.0694409144560036e-10, 1.8624968226249707e-10, 1.6762471400502733e-10, 1.5086224257923635e-10, 1.3577601830082926e-10, 1.2219841645415472e-10, 1.0997857479530005e-10, 9.898071730488428e-11, 8.90826455655784e-11, 8.01743810018784e-11, 7.215694289590543e-11, 6.494124860162893e-11, 5.84471237376704e-11, 5.26024113608289e-11, 4.73421702222557e-11, 4.260795319801298e-11, 3.834715787657779e-11, 3.451244208759656e-11]]\n"
     ]
    }
   ],
   "source": [
    "R=[0.5,0.6,0.8,0.9]\n",
    "x0=0.9\n",
    "\n",
    "x=[]\n",
    "for j in range(len(R)):\n",
    "    x1=[]\n",
    "    x1.append(x0)\n",
    "    for i in range(0,200):\n",
    "        x1.append(R[j]*(1-x1[i])*x1[i])\n",
    "    x.append(x1)  \n",
    "print(x)\n",
    "           "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TZLgnkuq5i4gUEmS4W+c1VDVyFxGJU1S4m9ksM9tkZk1mdk/Mz+82sw1m9msz+5mZnVX6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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fefcb74bc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(x)):\n",
    "    plt.plot(x[i], label=i)\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}