{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introdução à Teoria Qualitativa de Equações Diferenciais\n", "Neste documento vamos explorar algums aspectos básicos da análise de sistemas dinâmicos representados por equações diferenciais ordinárias. Muito do que será explorado aqui tem relação com o que se conhece como \"teoria qualitativa da equações diferenciais\". Esta área da matemática, criada por [Henri Poincaré](https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9) e [Aleksandr Lyapunov](https://en.wikipedia.org/wiki/Aleksandr_Lyapunov) envolve a análise das propriedades das soluções de EDOs sem necessariamente ter que explicitá-las.\n", "\n", "Vamos aprender como definir um sistema de EDOs no SAGE e resolvê-lo analiticamente, quando possível e numericamente usando o método de Runge-Kutta Prince-Dormand." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display typeset" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def ODEsys(t,y,params):\n", " k1,k2 = params\n", " A,B = y\n", " return[-k1*A+k2*B,\n", " k1*A-k2*B]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Agora fazemos a Integração numérica, Runge-Kutta 8/9 Prince-Dormand. \n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "T=ode_solver()\n", "T.algorithm=\"rk8pd\"\n", "T.function=ODEsys\n", "T.ode_solve(y_0=[500,0],t_span=[0,50],params=[.3,.25],num_points=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vejamos agora o formato de saída da solução." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(0, \\left[500, 0\\right]\\right), \\left(0.25, \\left[464.9639136355884, 35.03608636441148\\right]\\right), \\left(0.5, \\left[434.42876087953675, 65.57123912046313\\right]\\right), \\left(0.75, \\left[407.81632637022733, 92.18367362977253\\right]\\right), \\left(1.0, \\left[384.6226755583144, 115.37732444168543\\right]\\right), \\left(1.25, \\left[364.4086121738929, 135.591387826107\\right]\\right), \\left(1.5, \\left[346.7913615813497, 153.2086384186502\\right]\\right), \\left(1.75, \\left[331.43732253744054, 168.56267746255938\\right]\\right), \\left(2.0, \\left[318.0557500994762, 181.94424990052374\\right]\\right), \\left(2.25, \\left[306.39325006281507, 193.6067499371849\\right]\\right)\\right]$$" ], "text/plain": [ "[(0, [500, 0]),\n", " (0.25, [464.9639136355884, 35.03608636441148]),\n", " (0.5, [434.42876087953675, 65.57123912046313]),\n", " (0.75, [407.81632637022733, 92.18367362977253]),\n", " (1.0, [384.6226755583144, 115.37732444168543]),\n", " (1.25, [364.4086121738929, 135.591387826107]),\n", " (1.5, [346.7913615813497, 153.2086384186502]),\n", " (1.75, [331.43732253744054, 168.56267746255938]),\n", " (2.0, [318.0557500994762, 181.94424990052374]),\n", " (2.25, [306.39325006281507, 193.6067499371849])]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T.solution[:10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A saída é uma lista de tuplas com o valor da variável indepentente ($t$) na primeira posição, e um vetor com o estado do sistema naquele instante." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a=list_plot([(i[0],i[1][0]) for i in T.solution],color='red', pointsize=20, legend_label='A', alpha=.8)\n", "b=list_plot([(i[0],i[1][1]) for i in T.solution],color='blue', pointsize=20, legend_label='B', alpha=.8)\n", "a.legend()\n", "b.legend()\n", "show(a+b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Solução Analítica\n", "\n", "Como o nosso sistema trata-se de um sistema de EDOs lineares, Também é possível uma solução analítica:\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[A\\left(t\\right) = \\frac{500 \\, k_{1} e^{\\left(-{\\left(k_{1} + k_{2}\\right)} t\\right)}}{k_{1} + k_{2}} + \\frac{500 \\, k_{2}}{k_{1} + k_{2}}, B\\left(t\\right) = -\\frac{500 \\, k_{1} e^{\\left(-{\\left(k_{1} + k_{2}\\right)} t\\right)}}{k_{1} + k_{2}} + \\frac{500 \\, k_{1}}{k_{1} + k_{2}}\\right]$$" ], "text/plain": [ "[A(t) == 500*k_1*e^(-(k_1 + k_2)*t)/(k_1 + k_2) + 500*k_2/(k_1 + k_2),\n", " B(t) == -500*k_1*e^(-(k_1 + k_2)*t)/(k_1 + k_2) + 500*k_1/(k_1 + k_2)]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('t k_1 k_2')\n", "\n", "A = function('A')(t)\n", "B = function('B')(t)\n", "de1 = diff(A,t) == -k_1*A+k_2*B\n", "de2 = diff(B,t) == k_1*A-k_2*B\n", "sol = desolve_system([de1,de2],[A,B],ics=[0,500,0], ivar=t)\n", "show(sol)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Atribuindo valores para as taxas de conversão:\n", "# k1=1/3\n", "# k2=1/4\n", "solA, solB = sol[0].rhs(), sol[1].rhs()\n", "plot((solA(k_1=1/3, k_2=1/4),solB(k_1=1/3, k_2=1/4)),(t,0,30))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Valor de A no Equilíbrio:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}214.285714285714$$" ], "text/plain": [ "214.285714285714" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1=1/3\n", "k2=1/4\n", "n(k2*500/(k1+k2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Equilíbrios\n", "\n", "O equilíbrio de um sistema dinâmico se dá quando todas as suas derivadas são igual a zero, ou seja, é um estado do qual sistema não sairá a menos que perturbado.\n", "\n", "No caso acima, $dA/dt=0$ e $dB/dt=0$ ou $k_1A=k_2B$\n", "\n", "Para um modelo simples como esse, escrever o equilíbrio é trivial, mas também podemos usar o Sage para encontrar os equilíbrios:\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Equilíbrios:

" ], "text/plain": [ "

Equilíbrios:

" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[A = \\frac{k_{2} r_{1}}{k_{1}}, B = r_{1}\\right]\\right]$$" ], "text/plain": [ "[[A == k2*r1/k1, B == r1]]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('A B k1 k2')\n", "#k1 = 1/3\n", "#k2 = 1/4\n", "dadt(A, B) = -k1*A+k2*B\n", "dbdt(A, B) = k1*A-k2*B\n", "eqs = solve([dadt, dbdt], [A, B])\n", "show(html(\"

Equilíbrios:

\"))\n", "show(eqs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Um outra maneira de olhar para o modelo, é representá-lo matricialmente:\n", "\n", "$X' = M X$\n", "\n", "onde $X'=[dA/dt, dB/dt]$ é um vetor coluna, $M$ é a matrix de coeficientes do modelo e $X=[A(t), B(t)]$ de dimensões 2x1.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|M=| \\left(\\begin{array}{rr}\n", "-\\frac{1}{3} & \\frac{1}{4} \\\\\n", "\\frac{1}{3} & -\\frac{1}{4}\n", "\\end{array}\\right)$$" ], "text/plain": [ "'M=' [-1/3 1/4]\n", "[ 1/3 -1/4]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|X=| \\left(\\begin{array}{r}\n", "A \\\\\n", "B\n", "\\end{array}\\right)$$" ], "text/plain": [ "'X=' [A]\n", "[B]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{r}\n", "-\\frac{1}{3} \\, A + \\frac{1}{4} \\, B \\\\\n", "\\frac{1}{3} \\, A - \\frac{1}{4} \\, B\n", "\\end{array}\\right)$$" ], "text/plain": [ "[-1/3*A + 1/4*B]\n", "[ 1/3*A - 1/4*B]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = matrix([[-1/3, 1/4],[1/3,-1/4]])\n", "show(\"M=\",M)\n", "X = matrix([[A],[B]])\n", "show(\"X=\",X)\n", "M*X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Se Calcularmos o determinante de M, vemos que com a atual parametrização do modelo ele, $det M = 0$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.determinant()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O Que isto nos diz sobre o(s) equilíbrio(s) do sistema?\n", "\n", "**Exercício:**\n", "\n", "Tente reescrever o modelo, de forma que o determinante de $M$ seja diferente de $0$, e calcule os equilíbrios.\n", "\n", "Se quisermos calcular o valor de A no equilíbrio, fica fácil ver que ele dependerá das condições iniciais do problema.\n", "\n", "Sabemos que a trata-se de um sistema fechado onde o total de moléculas é constante, $A+B=T$. Temos que, no equilíbrio, $$A=\\frac{k_2 B}{k_1}$$ que, podemos reescrever como $$A=\\frac{k_2(T-A)}{k_1}$$ e após algumas manipulações concluímos que $$A=\\frac{k_2 T}{k_1 +k_2}$$ Aplicando os valores de parâmetros da simulação acima:\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "214.285714285714" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1 = 1/3\n", "k2 = 1/4\n", "n(k2*500/(k1+k2))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Espaço de estados\n", "Uma maneira de inspecionar gráficamente o comportamento na vizinhança do equilíbrio é através do campo vetorial. Neste tipo de gráfico representamos o vetor resultante das duas derivadas do sistema, em vários pontos do espaço de estados." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('a b')\n", "solut = line([i[1] for i in T.solution])\n", "ponto_inicial = point(T.solution[0][1], pointsize=50,rgbcolor=(1,1/4,1/2))\n", "vf = plot_vector_field((-k1*a+k2*b,k1*a-k2*b),(a,0,500),(b,0,400),axes_labels=[r'$A$',r'$B$'])\n", "atrator = plot(k1*a/k2, (a,0,300), color='red')\n", "show(solut+vf+ponto_inicial+atrator)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pela figura, vemos que existem infinitos equilíbrios possíveis para o nosso sistema, posicionados ao longo de uma reta: $k_1A=k_2B$. Neste caso, o estado final do sistema vai depender das condições iniciais: $A(0)$ e $B(0)$ . Se plotarmos as derivadas contra os valores de A e B, obtemos o que se chama de \"phase portrait\", onde novamente observamos a reta que contém os equilíbrios como a interseção dos planos." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('a b')\n", "k1 = 1/3\n", "k2 = 1/4\n", "(plot3d(-k1*a+k2*b,(a,0,500),(b,0,400), opacity=0.8)+plot3d(k1*a-k2*b,(a,0,500),(b,0,400),color='red'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Outra maneira de estudar a estabilidade do sistema é através da matriz Jacobiana.\n", "\n", "Na célula a seguir, criamos as versões simbólicas das equações diferenciais para uso posterior, como por exemplo para o cálculo da Jacobiana do sistema. A Matriz Jacobiana do sistema é muito importante para entender o seu comportamento. Se entendemos um sistema de equações diferenciais como descrevendo o movimento de um ponto no $\\mathbb{R}^n$, A matrix Jacobiana, sendo a matriz das derivadas parciais do sistema:\n", "Estudando os Equilíbrios, A matriz Jacobiana\n", "\n", "Seja $f(x)$ nosso sistema de EDOS onde $x$ representa o vetor de estados, A matriz jacobana é dada por:\n", "\n", " \n", "$$\n", "\\begin{bmatrix}{\\dfrac {\\partial f_{1}}{\\partial x_{1}}}&\\cdots &{\\dfrac {\\partial f_{1}}{\\partial x_{n}}}\\\\\\vdots &\\ddots &\\vdots \\\\{\\dfrac {\\partial f_{m}}{\\partial x_{1}}}&\\cdots &{\\dfrac {\\partial f_{m}}{\\partial x_{n}}}\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Jacobiana:

" ], "text/plain": [ "

Jacobiana:

" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "-\\frac{1}{3} & \\frac{1}{4} \\\\\n", "\\frac{1}{3} & -\\frac{1}{4}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[-1/3 1/4]\n", "[ 1/3 -1/4]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "jack = jacobian([-k1*A+k2*B, k1*A-k2*B],[A,B])\n", "show(html(\"

Jacobiana:

\"))\n", "show(jack)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[-\\frac{7}{12}, 0\\right]$$" ], "text/plain": [ "[-7/12, 0]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "jack.eigenvalues()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Neste caso, temos autovalores reais e distintos como um dos autovalores é negativo e o outro é zero, temos que o equilíbrio é uma linha reta de equilíbrios estáveis, ou seja onde quer que as condições iniciais sejam definidas o sistema sempre convergirá para a linha reta. Como vimos no diagrama de fase acima.\n", "\n", "#### Estabilidade do Equilíbrio\n", "\n", "Vamos introduzir um sistema ainda mais simples para começar a examinar a estabilidade de equilíbrios de um sistema dinâmico.\n", "\n", "$$\\frac{dx}{dt}=I-\\gamma x$$\n", "\n", "O sistema acima se chama produção e decaimento, pois $x$ é produzido a uma taxa constante $I$ e decai a uma taxa $\\gamma$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{\\left(\\gamma x_{0} + I e^{\\left(\\gamma t\\right)} - I\\right)} e^{\\left(-\\gamma t\\right)}}{\\gamma}$$" ], "text/plain": [ "(gamma*x0 + I*e^(gamma*t) - I)*e^(-gamma*t)/gamma" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('t I gamma x0')\n", "x=function('x')(t)\n", "dxdt = diff(x,t)== I-gamma*x\n", "sol = desolve(dxdt,x,ivar=t, ics=[0,x0])\n", "show(sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos pllotar a solução para $I=1$, $\\gamma=1/2$ e alguns valores diferentes de $x_0$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(t) = sol(I=1,gamma=1/2,x0=4)\n", "g(t) = sol(I=1,gamma=1/2,x0=0)\n", "h(t) = sol(I=1,gamma=1/2,x0=1)\n", "(plot(f, 0,10,axes_labels=['t','x(t)']) + plot(g, 0,10,axes_labels=['t','x(t)'], color='red') +\\\n", " plot(h, 0,10,axes_labels=['t','x(t)'], color='green'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Temos aqui um equilíbrio de ponto fixo. Qual é este equilíbrio? Para isso basta resolver a equação do modelo quando $\\frac{dx}{dt}=0$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x\\left(t\\right) = \\frac{I}{\\gamma}\\right]$$" ], "text/plain": [ "[x(t) == I/gamma]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(I-gamma*x,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Vimos que o sistema de Produção e decaimento, apresenta um equilíbrio pontual, ou seja qualquer que seja a condição inicial do sistema, ele converge para um ponto onde permanece indefinidamente. Equilíbrios do tipo \"ponto fixo\" não são o único tipo de equilíbrio que se pode observar em sistemas dinâmicos. Mas exploraremos cada tipo de equilíbrio através de exemplos. \n", "\n", "Dizer que um equilíbrio é estável significa dizer que se o sistema sofrer uma pequena perturbação, deverá retornar ao equilíbrio\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d(x) = I-gamma*x\n", "p = point((2,0),pointsize=50, color=\"red\")\n", "a1 = arrow((3,0),(2.2,0))\n", "a2 = arrow((1,0),(1.8,0))\n", "(plot(d(gamma=1/2,I=1), 0,4, axes_labels=[r\"$x$\",r\"$\\frac{dx}{dt}$\"]) + p + a1 + a2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Vemos no gráfico acima que $\\frac{dx}{dt} \\lt 0$ quando $x\\gt \\frac{I}{\\gamma}$ e $\\frac{dx}{dt} \\gt 0$ quando $x\\lt \\frac{I}{\\gamma}$. Logo podemos concluir que o equilíbrio indicado acima é estável. \n", "\n", "Assim encontramos o primeiro tipo de Equilíbrio que sistemas dinâmicos podem apresentar. No caso do sistema unidimensional que exploramos apenas a derivada da solução no equilíbrio nos dá a estabilidade. Mas para sistemas de EDOs temos que recorrer aos autovalores da matriz Jacobiana no equilíbrio. Além dos seus sinais, teremos que saber se são reais ou complexos.\n", "#### Equilíbrio em Ponto de Sela\n", "\n", "Retomando o primeiro exemplo deste documento, para o qual já haviamos determinado os equilíbrios e calculado a Jacobiana, Vamos agora determinar o tipo e a estabilidade do seu equilíbrios. Vamos primeiro recuperar a matriz jacobiana, e reparar que ela é a matriz dos coeficientes do sistema:\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "start_time": "2020-08-10T11:48:59.886Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "-\\frac{1}{3} & \\frac{1}{4} \\\\\n", "\\frac{1}{3} & -\\frac{1}{4}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[-1/3 1/4]\n", "[ 1/3 -1/4]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = matrix(QQ, [[-1/3,1/4,],[1/3,-1/4]])\n", "M" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Agora podemos calcular os seus autovalores." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "start_time": "2020-08-10T11:49:05.344Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[0, -\\frac{7}{12}\\right]$$" ], "text/plain": [ "[0, -7/12]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.eigenvalues()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Neste caso temos autovalores reais, distintos e com sinais opostos. Esta combinação indica um equilíbrio de ponto de sela como observamos anteriormente.\n", "\n", "Vale notar também que os autovalores são as raízes da chamada \"equação característica\" ou \"polinômio característico\" do sistema.\n", "\n", "O polinômio característico de uma matriz $M$ quadrada de ordem $n$ é o seguinte: $$p_{M}(x) = det[x I - M]$$\n", "onde $I$ é a matriz identidade $n\\times n$.\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{2} + \\frac{7}{12} x$$" ], "text/plain": [ "x^2 + 7/12*x" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cp = M.characteristic_polynomial()\n", "cp" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r1 = point((-7/12,0),pointsize=30,color='red')\n", "r2 = point((0,0),pointsize=30,color='red')\n", "(plot(cp) + r1 + r2)" ] }, { "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": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }