{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Diagrama de bifurcação do mapa logístico" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos criar o diagrama de bifurcação para o mapa logístico\n", "\n", "$$x_{t+1} = r x_t (1 - x_t).$$\n", "\n", "Como sabemos, o espaço de estado é $x\\in[0,1]$, e o valor de $r$ é limitado a $r\\in[0,4]$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos usar o módulo `decimal`, para podermos trabalhar com precisão extendida. Especificamos uma precisão de 200 casas decimais." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from decimal import *\n", "getcontext().prec = 200" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inicialmente, criamos uma função para retornar as iterações $x_t$ para $t=0,\\ldots,t_\\mathrm{max}$ do mapa logístico dados $r$ e $x_0$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def iterate_logistic_map(r, x0, t_max):\n", " x = np.zeros(t_max+1) # from x[0] to x[t_max]\n", " x[0] = x0\n", " xt = Decimal(x0)\n", " r = Decimal(r)\n", " for t in range(t_max):\n", " xt = r * xt * (1 - xt)\n", " x[t+1] = float(xt)\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para achar os pontos fixos ou cíclos estáveis que nos interessam, precisamos encontrar quais os pontos atingidos depois que o transiente, que depende do ponto inicial, passou.\n", "\n", "A convergência costuma ser rápida, mas como os cálculos são simples, vamos errar pelo lado da segurança e considerar que estamos no transiente nas primeiras 1500 iterações. Assim, precisamos descartar as iterações do transiente, e reter alguns valores posteriores. Vamos também reter 2500 valores após o transiente.\n", "\n", "Desta forma, temos que iteragir para cada caso 2000 vezes ($t_\\mathrm{max}=2000$) e descartar os valores de $t$ menores que 1500.\n", "\n", "Os pontos cíclicos devem ser independentes do ponto inicial. Portanto, vamos usar um ponto inicial aleatório para $x_0$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def periodic_points_logistic_map(r):\n", " x0 = np.random.random()\n", " x = iterate_logistic_map(r, x0, 2000)\n", " return x[1500:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O processo agora consiste no seguinte:\n", "\n", "1. Escolhemos uma precisão em $r$, isto é, quantos pontos distintos de valores de $r$ devem ser avaliados. Por questão de flexibilidade, vamos também permitir escolher mínimo e máximo do valor de $r$.\n", "2. Para cada um dos valores de $r$, calcula seus pontos periódicos (usando a função acima).\n", "3. Calculados os pontos periódicos, eles são plotados todos para o valor de $r$ a que correspondem." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def plot_bifurcation_logistic_map(n = 500, r_min = 0.0, r_max = 4.0, save=True):\n", " from matplotlib import rcParams\n", " rcParams.update({'font.size': 22})\n", " rs = np.linspace(r_min, r_max, n)\n", " fig, ax = plt.subplots()\n", " fig.set_size_inches(12, 12)\n", " r0 = 1\n", " r1 = 3\n", " r2 = 1+np.sqrt(6)\n", " rinf = 3.5699456\n", " if r_min < r0 < r_max:\n", " ax.axvline(r0, color='red', alpha=0.3)\n", " if r_min < r1 < r_max:\n", " ax.axvline(r1, color='red', alpha=0.3)\n", " if r_min < r2 < r_max:\n", " ax.axvline(r2, color='red', alpha=0.3)\n", " if r_min < rinf < r_max:\n", " ax.axvline(rinf, color='green', alpha=0.5)\n", " for r in rs:\n", " periodic_r = periodic_points_logistic_map(r)\n", " many_r = np.full(periodic_r.size, r)\n", " ax.plot(many_r, periodic_r, ',b')\n", " ax.set_ylim(0, 1)\n", " ax.set_xlabel(r'$r$')\n", " ax.set_ylabel('Periodic points')\n", " plt.grid(True)\n", " if save:\n", " fig.savefig(f'bifurcation_logistic_{r_min}_{r_max}_{n}.png', dpi=72)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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