{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dinâmica do \"Spruce budworm\"\n", "O modelo da Larva do pinheiro, é um modelo clássico em ecologia. Sua dinâmica, influenciada pela predação de pássaros, é dada pela seguinte equação diferencial:\n", "\n", "$$\\frac{dB}{dt}=r_B B\\left(1-\\frac{B}{K_B}\\right)-\\beta\\frac{B^2}{\\alpha^2 + B^2}$$\n", "\n", "#### Exercício 1:\n", "Explique o significado dos termos desta equação." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%display typeset\n", "# dBdt: variação da população de larvas ao longo do tempo (indivíduos/tempo)\n", "# r_B: taxa de crescimento da população de larvas (1/tempo)\n", "# B: população de larvas (indivíduos)\n", "# K_B: capacidade do sistema (indivíduos)\n", "# beta: taxa de predação (indivíduos/tempo)\n", "# alpha: eficiência do predador (indivíduos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercício 2:\n", "Escreva o modelo em forma adimensional. Há mais de uma maneira de se adimensionalizar este modelo. Distcuta as opções e justifique a sua escolha." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-B*R_B*(B/K_B - 1) - B^2*beta/(B^2 + alpha^2)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('B t R_B K_B beta alpha')\n", "dBdt = R_B*B*(1-B/K_B) - beta*(B**2/(alpha**2 + B**2))\n", "pretty_print(dBdt)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Fazemos:" ], "text/plain": [ "Fazemos:" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " ; e , onde " ], "text/plain": [ " ; e , onde " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "-A*R_B*u*(B/K_B - 1) - beta*u^2/(u^2 + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pretty_print(html(\"Fazemos:\"))\n", "show(html(r\"$(R_B B \\alpha) / \\alpha$ ; e $(B^2 / \\alpha^2) / (\\alpha^2/\\alpha^2 + N^2/\\alpha^2)$ , onde $u = B/\\alpha$\"))\n", "# Teremos:\n", "var('B t R_B u K_B beta A')\n", "dBdt = R_B*u*A*(1-B/K_B) - beta*(u**2/(1 + u**2))\n", "pretty_print(dBdt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Multiplicamos tudo por $1/\\beta$ e fazemos $v = (R_B \\alpha) (1/\\beta)$\n", "\n", "Teremos:\n", "$$\\frac{dB}{dt} \\frac{1}{\\beta} = v u \\frac{1-B}{K_B} - \\frac{u^2}{(1 + u^2)}$$\n", "Fazemos $K_B = y \\alpha$ e substituímos. Como $u = \\frac{B}{\\alpha}$, teremos:\n", "$$\\frac{dB}{dt} \\frac{1}{\\beta} = v u \\left(1 - \\frac{u}{y}\\right) - \\frac{u^2}{(1 + u^2)}$$\n", "Passando o $\\frac{1}{\\beta}$ para o outro lado, teremos:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(u*v*(u/y - 1) + u^2/(u^2 + 1))*beta" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('beta t v u y')\n", "dBdt = beta * (v*u*(1 - u/y) - (u**2/(1 + u**2)))\n", "pretty_print(dBdt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sendo que só o beta ainda está com dimensão, sendo esta indivíduos sobre tempo.\n", "\n", "Logo, fazendo $z = \\frac{\\beta t}{\\alpha}$, teremos a adimensionalização" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-u*v*(u/y - 1) - u^2/(u^2 + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "var('z t v u y')\n", "dzdt = (v*u*(1 - u/y) - (u**2/(1 + u**2)))\n", "pretty_print(dzdt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercício 3\n", "Mostre que $B=0$ é um equilíbrio instável." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[B == -1/3*(1/2)^(2/3)*(K_B^2 - 3*(R_B*alpha^2 + K_B*beta)/R_B)*(-I*sqrt(3) + 1)/(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3) - 1/6*(1/2)^(1/3)*(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3)*(I*sqrt(3) + 1) + 1/3*K_B, B == -1/3*(1/2)^(2/3)*(K_B^2 - 3*(R_B*alpha^2 + K_B*beta)/R_B)*(I*sqrt(3) + 1)/(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3) - 1/6*(1/2)^(1/3)*(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3)*(-I*sqrt(3) + 1) + 1/3*K_B, B == 2/3*(1/2)^(2/3)*(K_B^2 - 3*(R_B*alpha^2 + K_B*beta)/R_B)/(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3) + 1/3*K_B + 1/3*(1/2)^(1/3)*(2*K_B^3 + 27*K_B*alpha^2 - 9*(R_B*alpha^2 + K_B*beta)*K_B/R_B + 9*sqrt(1/3)*sqrt((4*K_B^4*R_B^3*alpha^2 + 8*K_B^2*R_B^3*alpha^4 + 4*R_B^3*alpha^6 + 4*K_B^3*beta^3 - (K_B^4*R_B - 12*K_B^2*R_B*alpha^2)*beta^2 - 4*(5*K_B^3*R_B^2*alpha^2 - 3*K_B*R_B^2*alpha^4)*beta)/R_B)/R_B)^(1/3), B == 0]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Equação original:\n", "var('B t R_B K_B beta alpha')\n", "dBdt = R_B*B*(1-B/K_B) - beta*(B**2/(alpha**2 + B**2))\n", "pretty_print(solve([dBdt == 0], B))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fccoelho/Downloads/SageMath/local/lib/python3.7/site-packages/sage/plot/graphics.py:2420: MatplotlibDeprecationWarning: \n", "The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", " x_formatter = OldScalarFormatter()\n", "/home/fccoelho/Downloads/SageMath/local/lib/python3.7/site-packages/sage/plot/graphics.py:2445: MatplotlibDeprecationWarning: \n", "The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", " y_formatter = OldScalarFormatter()\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Gráfico:\n", "plot(0.5*B*(1-B/20) - 1*(B**2/(1**2 + B**2)),(B,0,18),ymax=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercício 4:\n", "Quantos equilíbrios existem além de $B=0$?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# Além de B = 0 existem 3 equilíbrios (com autovalores complexos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercício 5:\n", "Plote o diagrama de bifurcação deste modelo, utilizando $β>0$ como parâmetro de bifurcação." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fccoelho/Downloads/SageMath/local/lib/python3.7/site-packages/sage/plot/graphics.py:2420: MatplotlibDeprecationWarning: \n", "The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", " x_formatter = OldScalarFormatter()\n", "/home/fccoelho/Downloads/SageMath/local/lib/python3.7/site-packages/sage/plot/graphics.py:2445: MatplotlibDeprecationWarning: \n", "The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n", " y_formatter = OldScalarFormatter()\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "forget ()\n", "\n", "import numpy as np\n", "\n", "def drawbif(func,l,u):\n", " pts = []\n", " for v in np.linspace(l,u,100):\n", " g = func(beta=v)\n", " xvals = solve(g,x)\n", "# print(xvals)\n", " pts.extend([(v,n(i.rhs().real_part())) for i in xvals if n(i.rhs().real_part())>0])\n", " \n", " show(points(pts),axes_labels=[r\"$\\beta$\",'$B$'],gridlines=True, xmin=0)\n", "\n", "var('beta')\n", "R_B = 0.5\n", "K_B = 20\n", "alpha = 1\n", "f = R_B*x*(1-x/K_B) - beta*(x**2/(alpha**2 + x**2))\n", "drawbif(f,0,3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.3", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": 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