{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Qualitative analysis and Bifurcation diagram Tutorial in R\n", "\n", "*This tutorial assumes you have read the [tutorial on numerical integration](http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/Numerical%20Integration%20Tutorial%20-%20R.ipynb?create=1).*\n", "\n", "\n", "\n", "## Exploring the parameter space: bifurcation diagrams\n", "\n", "Bifurcation diagrams represent the (long-term) solutions of a model as a function of some key variable. The idea is that, as this parameter changes, the solutions change in a \"well-behaved\" way, and that helps us understand better the general behavior of the model.\n", "\n", "In this tutorial, we are going to study a simple predator-prey model (the Rosenzweig-MacArthur), and see how the amount of resources for prey ($K$) changes the dynamics.\n", "\n", "### The Rosenzweig-MacArthur consumer-resource model\n", "\n", "This model is expressed as:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= rR \\left( 1 - \\frac{R}{K} \\right) - \\frac{a R C}{1+ahR} \\\\\n", "\\frac{dC}{dt} &= \\frac{e a R C}{1+ahR} - d C\n", "\\end{aligned} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rosenzweig–MacArthur model solutions\n", "\n", "We use the same method as before to integrate this model numerically:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##Loading the necessary libraries\n", "library(deSolve)\n", "\n", "### Rosenzweig-MacArthur model###\n", "\n", "## ODE system to be integrated\n", "RM <- function(t, y, parms){\n", " with(as.list(c(y, parms)),\n", " {\n", " dR = r*R*(1-R/K) - a*R*C/(1+a*h*R)\n", " dC = e*a*R*C/(1 + a*h*R) - d*C\n", " return(list(c(R=dR,C=dC)))\n", " })\n", "}\n", "\n", "##initial parameters\n", "parms1 = c(r=1, K=10, a=1, h=0.1, e=0.1, d=0.1)\n", "\n", "##initial population sizes\n", "y0 = c(R=1,C=1)\n", "\n", "##running the numerical solution from time 1 to 1000\n", "out = ode(y=y0, times = seq(from=1, to=1000, by=0.5), func = RM, parms = parms1)\n", "\n", "##plotting the solution\n", " matplot(x=out[,1], y=out[,2:3], type = \"l\", lwd=2, lty=1,\n", " col=c(\"blue\", \"darkgreen\"), xlab=\"Time\", ylab=\"Population size\")\n", " legend(\"topright\", legend = c(\"Resource\",\"Consumer\"), \n", " lty = 1, lwd=2, col=c(\"blue\", \"darkgreen\"))\n", "\n", "#### For jupyter notebook only\n", "options(jupyter.plot_mimetypes = 'image/png')\n", "####" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the parameters chosen above, the long-term (asymptotic) solution is a fixed point. Let's see this in the phase space, that is, the space of Predators ($P$) vs. Prey ($V$). We note that the arrows are \"circulating\", but always point inwards, and so the trajectory moves toward the middle, to the fixed point." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "## Phase space flow and fixed points\n", "##first we need to calculate the coordinates for the vectors\n", "xs = seq(from=0.9, to=1.3, length.out=7)\n", "ys = seq(from=0.94, to=1.04, length.out=7)\n", "coords = expand.grid(R=xs, C=ys)\n", "## And then loop over all coordinates to calculate the derivatives at that points\n", "dvs = matrix(NA, ncol=2, nrow=nrow(coords))\n", "for(i in 1:nrow(coords))\n", " dvs[i,] = unlist(RM(t=1, y = coords[i,], parms = parms1))\n", "\n", "##now we plot the trajectory\n", " plot(x=out[,2], y=out[,3], type=\"l\", lwd=2, col=\"blue\",\n", " xlab=\"Resource\",ylab=\"Consumer\", xlim=c(0.9,1.3), ylim=c(0.94,1.04))\n", " ##and add the vector field\n", " arrows(x0=coords[,1], y0=coords[,2], x1=coords[,1]+dvs[,1]*0.5,\n", " y1=coords[,2]+dvs[,2]*0.5, length=0.1, lwd=2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Messing a little with the parameters...\n", "\n", "Increasing the carrying capacity $K$ from $10$ to $15$, we now see oscillations..." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# now K = 15\n", "##Messing a little with the parameters\n", "parms2 = c(r=1, K=15, a=1, h=0.1, e=0.1, d=0.1)\n", "\n", "out2 = ode(y=y0, times = seq(from = 1, to = 1000, by=0.5), func = RM, parms = parms2)\n", "\n", "##plotting the solution\n", " matplot(x=out2[,1], y=out2[,2:3], type = \"l\", lwd=2, lty=1,col=c(\"blue\", \"darkgreen\"),\n", " xlab=\"Time\", ylab=\"Population size\")\n", " legend(\"topleft\", legend = c(\"Resource\",\"Consumer\"), lty = 1, lwd=2,\n", " col=c(\"blue\", \"darkgreen\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, looking again at the phase space plot, we now see that the flux (the arrows) inside circles outwards, towards a limit cycle, and the arrows outside points inwards. The limit cycle corresponds to the periodic solution we just saw." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "In arrows(x0 = coords[, 1], y0 = coords[, 2], x1 = coords[, 1] + : zero-length arrow is of indeterminate angle and so skipped" ] }, { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##calculating the vectors again\n", "xs = seq(from=0,to=6,length.out=8)\n", "ys = seq(from=0,to=2,length.out=8)\n", "coords = expand.grid(R=xs,C=ys)\n", "dvs = matrix(NA, ncol=2, nrow=nrow(coords))\n", "for(i in 1:nrow(coords))\n", " dvs[i,] = unlist(RM(t=1, y = coords[i,], parms = parms2))\n", "\n", "##The trajectory\n", " plot(x=out2[,2],y=out2[,3], type=\"l\", lwd=2, col=\"blue\",\n", " xlab=\"Resource\", ylab=\"Consumer\", xlim=c(0,6),ylim=c(0,2))\n", " ##and vectors\n", " arrows(x0=coords[,1], y0=coords[,2], x1=coords[,1]+dvs[,1]*0.5,\n", " y1=coords[,2]+dvs[,2]*0.5, length=0.1, lwd=2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The bifurcation diagram\n", "\n", "We have seen the solutions for two values of $K$, $10$ and $15$, so we want to plot those as a function of $K$. In the second case, there are oscilations, so instead of taking all of the solution, we just pick the minimum and maximum of the solution (after a long time). When the solution is a fixed point, the minimum and maximum should coincide." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "##plotting minimum and maximum population sizes with different K values\n", "\n", "##object with the line numbers we will use for the following plot\n", "lines = (nrow(out)-500):nrow(out)\n", "\n", "##creating an empty plot\n", " plot(0.1, type=\"n\", xlim=c(0,20), ylim=range(out2[lines,2:3]), log=\"y\",\n", " xlab=\"K\", ylab=\"Min and Max population\")\n", "\n", "##points for the K = 10\n", " points(x = c(10,10), y = range(out[lines,3]), pch=21,bg=\"darkgreen\", cex=3)\n", " points(x = c(10,10), y = range(out[lines,2]), pch=21,bg=\"blue\", cex=3)\n", "\n", "##points for the K = 15\n", " points(c(15,15), range(out2[lines,3]), pch=21,bg=\"darkgreen\", cex=3)\n", " points(c(15,15), range(out2[lines,2]), pch=21,bg=\"blue\", cex=3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a very poor bifurcation diagram: it has only two points in $K$! Let's try with many values of $K$.\n", "\n", "What happens when we change the carrying capacity $K$ from very small values up to very large values? For very small values, the resource is not going to sustain the consumer population, but for larger values ok $K$, both species should be benefited... right?" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "## this block calculates solutions for many K's, it should take some time\n", "KK = seq(from = 0.5, to=25, by=0.5)\n", "rminmax = matrix(NA, ncol=2, nrow=length(KK))#resource minimum and maximum\n", "cminmax = matrix(NA, ncol=2, nrow=length(KK))#consumer minimux ans maximum\n", "\n", "## Loop over all values of K andd get min and max population sizes\n", "for(i in 1:length(KK)){\n", " parmsi = c(r=1, K=KK[i], a=1, h=0.1, e=0.1, d=0.1) \n", " y0 = c(R=1,C=1)\n", " out3 = ode(y=y0, times = seq(from = 1, to = 1000, by=0.5), func = RM, parms = parmsi)\n", " rminmax[i,] = range(out3[(nrow(out3)-500):nrow(out3),2])\n", " cminmax[i,] = range(out3[(nrow(out3)-500):nrow(out3),3])\n", "}\n", " plot(x=KK, y=rminmax[,1], type=\"l\", lwd=2, col=\"blue\",ylim=range(rminmax), log=\"y\",\n", " xlab=\"K\", ylab=\"Min and Max population\")\n", " points(x=KK, y=rminmax[,2], type=\"l\", lwd=2, col=\"blue\")\n", " points(x=KK, y=cminmax[,1], type=\"l\", lwd=2, col=\"darkgreen\",ylim=range(rminmax))\n", " points(x=KK, y=cminmax[,2], type=\"l\", lwd=2, col=\"darkgreen\",ylim=range(rminmax))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well, the first prediction was OK (notice that the plot above uses a log scale), but for high $K$, the minima of the oscillation go to very low values, so that the populations have a high risk of extinction. This phenomenon is the so-called **paradox of enrichment**.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Consumer-resource dynamics in a seasonal environment\n", "\n", "A special type of bifurcation diagram can be used when we have parameters that oscilate with time, and we want to see how this interacts with the system. Let's consider the Rosenzweig-MacArthur equations again, but now we make $r$, the growth rate of the prey, oscilate sinusoidally in time:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= r(t) R \\left( 1 - \\frac{R}{K} \\right) - \\frac{a R C}{1+ahR} \\\\\n", "\\frac{dC}{dt} &= \\frac{e a R C}{1+ahR} - d C \\\\\n", "r(t) &= r_0 (1+\\alpha \\sin(2\\pi t/T))\n", "\\end{aligned} $$\n", "\n", "We integrate this in the usual manner:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "### Consumer-resource dynamics in a seasonal environment ###\n", "## time sequence \n", "time <- seq(0, 2000, by = .5)\n", "\n", "## parameters: a named vector\n", "parameters <- c(r0=1, alpha=0.1, T=80, K=10, a=1, h=0.1, e=0.1, d=0.1)\n", "\n", "## initial conditions: a named vector\n", "state <- c(R = 1, C = 1)\n", "\n", "## R function to calculate the value of the derivatives at each time value\n", "## Use the names of the variables as defined in the vectors above\n", "RM2 <- function(t, state, parameters){\n", " with(as.list(c(state, parameters)), {\n", " r = r0 * (1 + alpha*sin(2*pi*t/T))\n", " dR = R * ( r*(1 - R/K) - a*C / (1 + a*h*R) )\n", " dC = e*a*R*C / (1 + a*h*R) - d*C\n", " return(list(c(dR, dC)))\n", " })\n", "}\n", "\n", "## Integration with 'ode'\n", "out <- ode(y = state, times = time, func = RM2, parms = parameters)\n", "\n", "## Ploting with matplot\n", " matplot(x = out[,1], y = out[,2:3], type=\"l\", lwd=2, lty = 1,\n", " col=c(\"blue\", \"darkgreen\"), xlab = \"Time\", ylab = \"Population size\")\n", " legend(\"topright\", c(\"Resource\", \"Consumer\"), lty=1, lwd=2, col=c(\"blue\", \"darkgreen\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, even with small $K$, the solutions oscilate due to the oscilation of $r(t)$.\n", "\n", "Now we use a tool that is an all-time favorite of physicists: the resonance diagram. It works exactly as a bifurcation diagram, but the parameter that is changed is the period (or frequency) of the external oscilation." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Zep9ERKQy1FdwbVFf6MG8NxOBa4CWEh+/IbAdMBJYPojzSsOxw4Df4/8/PgzsB64z3Zpqla0PzMJ/gF0CfBrcHamWJCIikXZgNbAP8LeUa0lVoYvv0r4YLwlpvIZTwjlHVvm8UtNsAti80C1hCdgWaVdU++xzYNlYd5dv6KJCEZGa0FBdOMpVbPSKRgjQaVCAljzmwG6PXRh3QtoV1Q87Amxx7L27A2xs2lWJiDS5pg/QhUJzX/dL/xSgJY99IRYAf552NfXHtgF7LvYePg+2fdpViYg0MQVo6jdAlzLms7pwSMpsV7BVIfi9BDY67Yrqk40CuzkWopeCHZV2VSIiTUoBmvoM0KVOnKIALSmyEWD/CoGvE2yvtCuqb+bAzg39oS30j/4+mvJbRKTaFKApHqBrYVa/Qor11S5UpwK0pMhmxlpMv5x2NY3DPkJunGj1ixYRqb6mD9BQuDW3VsMzFK6rWL0K0JISOyYW8O4DK3UYRCmJbQP2bOw9fgFsh7SrEhFpEgrQQb2EZ+i/tTntkUQUoJuevZ/cyBELwCalXVFjsjFgt8VC9BKwj6VdlYhIE1CArkOl9Hm2Eh5bKQrQTc0OChe4RX10j0i7osZmGbBvkRsvOhu21S9aRKRyFKDrVKkhWgFaqsg+BrYyBLkusClpV9Q87MjQAh21Rt8FtlPaVYmINKimD9C1OIpFKUodvk4BWqrETsCPtGFgq8GOTbui5mPbkhv1JGqNvhNsv7QrExFpMArQ9B00azVA1zIF6KZjp5EbWm052OFpV9S8bDTYDLA1sSBtYA/67jSaClxEJAEK0PTdX1gBeuAUoJuKnRvrf7sM7OC0KxIA2xTsovCBJh6knwH7DFhr2hWKiNQxBWj6HrVCAXrgFKCbhn0rFszeBtsz7Yokn60X/p3ezgvSr4KdDTY87QpFROqQAjR9tzorQA+cAnTDMwf201gYmwu2Y9pVSV9sZAjMr+cF6QUhYI9Lu0IRkTqiAE3ffZ8VoAdOAbqhWRvY9bEA9iLYZmlXJaWyIWCngL2UF6QXg30PbKu0KxQRqQMK0BQPyArQ5VGAblg2lN4TdzwNtkHaVUk5rAXseLAn84K0gT0XwvQH0HjSIiKFNH2AluQpQDckGwH2p1jIetT3r5X6Z/uC3V4gSBvYW2C/ADvWdwMREREUoKUCFKAbjq0L9kgsVP1FYaoR2fZg/w32d3LDEsaX5WC/AzsZbP20qxURSVHTBehio2z0t0jpFKAbim0I9s9YiLrFd+WQxmYbgE0NLdMrCoTpLrC/gv0X2A7N1dXDhoFtGVrujwX7XOjy8nP8DJA/BBubdpUiUlEK0CUuUjoF6IZgGfzFZotioek6mn384GlsSQdHch5N9D7YCLCjwK4JXToKdfVYCnY/2E/APgX2nvoN1TYC7BCwc8AuAPsl2L2hb/jiIq8/f3kD7GNpvxIRqZimC9BSeQrQdc92wM9cFw8EF9VvIErAVLZhKr+ggy46MDq4jw4mpF1W9VkL2H5gPwJ7oZ8QuSQEzx+DfRJsa2pyJkQbB/bR0HL8d9aexbGUZTXYa/SeSt3Afo26u4g0ooYK0DX4i7kpnQJcAYwC3k25FhkQGwp8Hfgv/C8HgFnAGeB+n1ZVqZrGtmT5GvBJoCXv3jeAY5jBQ9UvrFbYtsC+wG7A7sD7yP3fKWQJ8DjwD+Al/Hv4mr9171S21ohNBPYLy/7Ae4FiHw5XAnOBN/OWucC83K1bGDv+Z4ELgWhs7beAz4H7TcIvRETS0w6sBvYB/pZyLYNWboCOumi4vO3BHLOZKUDXJTsEuBzYOuzoAi4CzgO3PLWy0tLBdvgPE8eRC85Z4AagE/h02LcG+DwzuLzqNdYkawN2xIfpKFTvCLSV8OSV9IRpXgfm4APqnNy6WxA71xjWDr7DgSF5+4YCewAH4MP+1hTWhQ/3fwUeAP4O7q0S6i7ANgAuA46K7bwNOA3c3PKOKSI1pOkDdH5YLtTfWSF6YBSg64qtB1wAnEju//o/gGngnkitrLR0sB2Or2B8it7B+fcY32QmT4THTQMuJtfaej0ZpnEVK6pec82zdnzLdBSqdwN2oO+W6mpYCTyCD8t/xQfmhH9n2bHAJcD4sGMx8EXgGnC6vkakfilA5z23v23pnwJ0XTAHfAb4MRCN57wM+AZwCbjutCpLxclsTyv/XTA4O77BdJ5c6zmT2Z0MNwKbhj1P0s3RXMMr1Sm6nlkrsAGwCbBhWDYFJgEbARsDEyHRizWXAg+G5QHgUXBrEjx+EbYu/tucE2I778Z/SJ1V+fOLSAUoQOc9VwF68BSga55tg/83Oii281bgLHBz0qkpJVPZATi3QHC+iQzf5Cr+3efzT2Z9Wvg1cEjY8w6OTzGdP1as5qZhGXzI3hgfsDcCxuL/aMV148NxvsXkRlJ6CXgm3Q+GdgS+m9RGYce7wFeAy8BlUytLRMrRUAG6HMWGtSu2Lf3TKBw1y9rAzgVbGRslYC7YZ9KurOo62JwOfksH3WFUDQsjbFzHZN4zoGOdRysdXJh3nK+iD96yFhsdRrSJT1Tzf+FiTBGpHw01Cke5io35rHGgy6MAXXNsItgX84Yd6wa72P9BbyI+7P4XHSyPBd5OOvg5U9lmUMfu4JN08G7suLdwAs31/kqJ7GCwl2M/jyvApoMd0NTDRYrUDwXooK8ALQOjAF0TbCjYcWB34meNi49N+xTYnmlXWHVTeD9TeTIWcLNM5RecUnRUhoGbxo508GLsHM+HbiIieWwE2E9Ze9r018KY1DulXaGIFKUALYlTgE6V7Q12Bb1nEIyW5/DTDjfRLHrANIYzhe/HJkExOniRKT39lpN1AqPp4KbYuZbRwXEVOZc0APsA2G1hMpb8n9l/gn0FbNP+jyMiVaQALYlTgK462zD0bX6+wB/gRWBXgu1LTc4CV2EdHEkHc2JhdhUdnMdZa40VnDTHFL4Z62OdZSo/qcJ5pW7ZWH89gt0Nli3ws/wPsLPBxvd/LBGpsIYK0M0XDmqTRuGoChsBHA18FjiQ3hNKdAJ/AH4O3AEuf9SCxncqG9LFxfSeyOJ+Mpza78gaSZrK4RjXk5uV7hmMz/aMJy1SkG0KfCos7827M/r5/hVwGziNPS5SfQ01CocCdG1QgK4o2wk4Az+1dH4r/5P40Pyr3jO2NZHzyPA6p5Phu1jPBXzvAF9mBleTxnUNJ7MFLfwGPxseQCeObzOJ73M+XVWvR+qMvQ8/hvQn8UP6xXXhh+j7J/BsuP2n3+f0f0ukchSgJXEK0ImzNnxL6pnAfnl3zse3RF0L7ukqF1ZbprEjWa4C9ortvYFWzuQK0v1AcR6tzOWLGN8mNwPfI2T4bFVbxKWOWQb/838CcAy5bzUKWQ38C3gOeAYfrp8FXtUMiCKJUICWxClAJ8Y2AKbh39NJsTu6gduBmcAfmr6l6RyGsYxz8ZNSROH0VYzTmckfUqxsbT7k/wLYOexZheNbTOJHnI8m05AS2RDgUHz/yx3w3Tw2p3dXrkLexQfr2cAbYXkTeB2YB8wBt7xCRYs0EgVoSZwC9KDZ3vjW5qPJBUKAhcAM4Apws9OorOZM5oNkuAzYMuzpwvETHOdzFbXZN/QkhtLKt4EvEgUex720MJkrmJVmaVLPbDiwPT5M7wDsGLbzu330Zyk+UL9J75D9Jv530DvA2/7WrUykdJH6owBNaX0iFc5LpwBdFhuG7+N4BrBr3p3/AC4FfgNuVbUrq0mnMp4uLsRfZBV5hCzTuJqn0iprQKaxL1muJQr/jqUYX2AGM1OtSxqMjcUH6qilejtyU6OPGuTBV9ATpnkbH7Dj22/jA/lSYElYlgLLFL6lzjV9gC61L5gCdOkUoAfENgdOBaYA68buWA3cCFwC7qE0KqtRjilMwfFDoj6gjqVk+RobcVnddYM4nZGs4Uf4nxv/e8ZxJ510cC3zUq1NmoCNwLdQT8QH6on4cL1hbN8G9P4mLCmdFAzWLMX/7VgErAJW5q0vDrcF1tW/W6pGAXoQz5XCFKD7ZG34H7jDwpI/29gb+PdvOrj5VS6utp3C1nRzOfSaAOUOujmda5iTVlmJ6OA/gKvxgQVgMcbnmMl1KVYlEtgEYDz+Q/464Xa9vO389ZYUCl0DLMcH6lX4QN6FD9pd+HAePWYFPgBFj4m2O/F/uyw8j9hjohDfFfaBgnuzUoAexHOlMAXotdjG5ALzodAzvFrc/cAlwC1Nf1FgPt9n+KvAueRawl7DOJOZ3J5iZck6jXF0cjF+lAXP+A1wIUt5jBvoTq02kQGzMfggPQ7/O280/u9CtD42th6/L9o/DBhR9bLLlx/AwQdwwwf2NeH+qLV9Cb5lPd7FJX672K+7+vpWrXkoQA/iuVKYAjTWDuyLD8yHs/ZECABZ4FH8hAg3gvtn9eqrIx0cjHEFjq3Dnm4cP6ONb3JZg/7/msrRGJcD6/fs8/2jH8C4hwz3Momn6667ikhZLB6m89eH4sfDj68Pi6234QN5CzAGH3pGxB4zCmit3mspyzJ8qF4clkX93Ebry8AtSqPgJtH0ARoUopPWpAHatgA+iA/Nh1B4KvMFwB/xoflP4BZWr746M431yHIBcCK5n83HyDCNq3g8xcqqo4MJwGXAx4s84m3gfox7yXAv03m2esWJNBqLgnQUrFvJXWA5Fv87KArkQ4Dh+BF0xoTHjMaH9Oj5LeS+aRwTHjs8PHcMuVb3oRV8UXFRC3i868kSfENO1N2lG9/yDb1b0QnrnWE9G54bibq1RKKW+Pxzl7oddZeJLAVXi9++NX2A1kWEyWuSAG0bAQcDB4Vl0wIP6gYeAe4Ky+P6Oq4EUzgWx6XkWmBX4Pg2i/lx03VjOIkNaGE/HIcC/4Ef67eQBcD9OP4P40Fm8DhpzLooIgNgQ/BBekxYxtI7YEfr48J9Y2Pr4+h7Mp1GFQX/SNRNpr/tVcB54JJqgFGAruCxm1WDBmjbADiQXGDeusgD5+Fbme8C7gb3TlXKawRT2IUMF2Ac1LPPuI0sZ9b9RYJJ8dOCR/8HD8aPlFDI2xgv4XgZeBl4CeNlHC8xA12cKtIwLB6q8wN2K7kW8EKt41HLe9Sq7sJzI1GreSRqja9XvwJ3Qv8PK0nTB2hJXoMEaFuX3oF5+yIPXAo8ANwL3AM8pSuyB2gyu5Phm8AR5H6O38BxFtP5XYqV1b5pbEu25//ogcT7TRf3Lo6XyfISGV7GwgIvsZQ3uaHX16kiIgVY1J88MoLewx32tx11iYnk90ePusVEog8Ckfww3992G/AVcH8v8GLKoQAtiavTAG2jgQPIteztSOFpcZcDD+ID873AYzXaP6v2dbAX8A3gw7G9ncAVrOTrXN/TH09K45jGe+nmABw74ido2Qo/zm9/UzzHvY3/JmU+MBdjAY65wHwc84A36WIB1/BW0i9ARKROKEDH5LcaKpCXp04CtA3H/8ePAvNuFL4aexXwd3KB+WFwnQUeJ6Waxr4Y38D4YGzvGhzX0ML3NZ11wo6lnVFsjmMrXE+o3jIsm1P+JBlr8H2vFxANx2VhUgwXhuOKtjMsIhvuz7KEdpbW7FTrIiL9a6gAXe5QNMW+btfoHA3F2oH340fIOAjYi959uyKd+Av/7sEH5r9r+uyEdHAgjm+GLgeRVcBMuvmB+jlXiO+S8XxYejuWFtZlYzp7wvQkHONxbIgxHt/HegN8/8l87fiJXzbq2ZP/2zLatrDu8G3hWaADyF3BvzK2voroSn5jBY7V5K7sX4XRewrozFqjAkTnjI8cEK8pPnpCYUYLjgzGixgvMIQXG3bYRBFpeuUE6Hh4zv/Vb7Fbhei6Y63Arvh+oQfjx2UuNCh/N/AkPjDfAzwITn8okzSVQzG+CewX+4lbiXEVxg+5mrnpFdfk/Kgms8JS3AmMZgST6A7h2jGeLBNxbICffW4MjjFkw23pFxsNDUvh0QQKHaHYb+pSlfr4eBPKGqCD14EXgBcwXsDxPMYLbMQszkeTH4lI3arERP5CDusAACAASURBVCpqhR64lLpw2FBgD3w/5v2AvSk8FrMBz5ELzPdrsPkKmcJhOL6B/7eILMf///iRRoNocCcwmnbG0NprmK4xGKNxjAOGk2UIrudK/+g2utgouo0uNsq/6Cj/IqO0rAFewbfwv4DjKVq4jyt4I+W6RKRy1IWjzvXVltLgod9GALvg//Meim9hLjYo/SvA/+Ev/vs9uNerUmIzmsIuOD6GnwDkfbF7lmFcRpYLdPFZk7i+Z4ri6jmLIXQxfMDPW8jytUYfOYdhLGEbXFhgG4z3hPV4i3k7sG1Y/G/lLmAKL+K4H8d9dHOvvmkRkVrVTC3QA/nSstq1V6gF2tbBh+WohXlXin9o+jfwV/zwcveDU9/aSplGG93sj+NI4GPkTyjjp6C+mDVcyC94O5UaRZJ2MuuTYRvgPdATst+DsSWFr60A40XgPjLcX9FAPY02WsK3byt7WvihlWFYXiODMYJMSReR+m8LqiXT0++90lZgvWbNK49b69uR0hkO6zX28kCtIpN3XcDa5+j7/TRWky3p/V7G0AF2VxrKKi7sp7761FAt0IOdSKWvnnW1FKBLrSut+isQoO3nwGeK3JkFnsGH5QeAv4JT14BKmswoHIfh+E/gcAr3X30CuJE2Ludy1EVGmsN5tPIGu+M4AONA/DdjhbqSge9LfT9wH238jSwtZBmLMRbHmBCqxpBhbOhb3nt/buIM6D31tEgjiU8xPhgrMM5kJrckcCxosABdThcOR++LBYs9phb1V1f8tdW7Pfu4by6+i8YCfP/aRnnNtWUyk2jhYxhH4kcxyW+N6gQewHErWW5jJrOrX6RIyvzFhA+F5Qc9gdpfzHwAvQN11DVkaq82PZd3a3nrIs2lhWSmLB+H4yhILEA3lGYZB3og3UrS6IJSiRboLYEL8Ff7bwxs1s8TXgceiy2PgFuYTC1N4DwyzGFrWtgd2A1jX2B31v5/tAy4C+NW2rlLLc0i/TiPVuawBxkOwIfqfSjeQh23CGMJjsX4IfuiWz/kX9QNIRMbus9Yim+9A8disqGzgD9GX5Lp1pAGo4VMzzTVtagzDK/YP8cyuvK6SzjayJTw/6X/rjlDyRYcmtLLDKBbieuZInwwxpAd0GRPxWrp65uYFRg/TbBxp6FaoGs18CatCbtw5LN18BOf7BpudwO26OdJL+LHd344LE+C05TFUVh24X107IZjF6zoH6E3gNsxbmU493Jxnf6hFakFUaB27ID/Y+yDsWMxxhJaWMxVBca4FpG0KUDXqSa8iLA/Nho/6sNusWVbik9h3IkP1Q/iR+h4DHgOXCN/SeqYytZYz/uzez9hGfwQXU8Bd+O4hen8A32RLCIiza2hAnQpfaDzuzSUGgRqLZyXUn+t1Vxhbik+DD+Y22dj8WND7xlb1g93tgHbh2Va2DcfLGql/qu/dbXdwnoOw1jMRNqYRDfjcGHJMpEMkzDG4fuPTQQ2xPL6Lvf+H9SF4wWiri+Ox1jDP7gWzcQoIiLSoJpxHOgmC8kD5RYDd4clsC3w03jviZ/aexdyF8RNAD4aFoBVYA8B94Xl4apO630SG9DCJriwGJtCzzIJWI9lZGjBj0WSf9FR3x8P1+BHL8n1FV/CM2uNhSsiIiINrZQAnR84FUCbjnsFP2rHr/y2teNDdLyVesvw4KH4C30ODNurwB7Gh+n7gYfADWx8y8mMgl7LOmTYAGMzHJtAz7Ip8QszBt5pYgkwH1iIsZAMCzEW4HiFbp5gGU8rLIuISOOzscAacNUYW7wuldMCXa8TqVTbKEp/fwc+C1iq3BpyFxYGNoF1nzmcrmH7Qdd+ZLq3omWVo23pUDKdB9C+5ABa1kDbsi6Gf302o16bxbinFzD2X2/TsnoYforhsbBWWC4+FE9p/8PeBWYDs3HMIR6QfTh+iywLWcZChWMREUmWZfBjkEfGkvvrNRo/5BzhMZkCj4n+BsaPE19vCceB3mObx9fbyI1cE398fm35f28N7HRwVxR/fc2rGbtw9CeJDwBb4i+2G+gxkvvQcTJ7kuECHCMK3NuFKzBDloX9FuowMriemaJacLSHd6cdC/v9cDxtAyi9Ff/+bNnfA0s0D3gNeA3jNRyzccwCXiPLa8zknYTOIyIiqbOR0HOdyjp9rPc3xFupjVzFhnmLB17w335Gw9zFA2s9c/hvm6WAUgN0oS/DNapAcS8DO1L6OI8fB75Kku9pC9fTV0gtdqZqzzPZPSQsw6BrOGTbVpLpXkDb0tkMfWsWjrcxFgILgWVhnNZlZJhHJ6/pYj0RkXpj48jNCjmuyG18PR6OS5lGvVmsgJ5hUZdDz7eo8fXcOOe91+PPXQk9f0vjU5gvA65PvOoGUakW6HruvpFU7c8O4LG7J3TOHMfvgC+QDa/H1ei/Sctqv+RmHR1G7qK//WOhfSV+rNclwFKMt2jlLaYynyzzcLwFzCfDPNbwFst5ixvChAgiIpIAG0rv7nbjwvbosD06dv+YvH2jyIXiSukEFoVlsEPCLsFfah4XD5qRbHhsJDcZT+8guyo8P6rz3QLra8JzoHeQjT93Rc2PdNUkyglV6uOcvJTGgQZOZ2RPd4yI0cbqnq+fhtISvpaKz9RkjMZC3y0XfiFG9/vZmNrwryf6WmtU2BfdNxLf93sYvftgJcXwU5W/FW7fxLEAeJUsr+B4hS5eVQu2iDQHayfXspu/jMGH3Og2Wh8T7o+2q9H6240PwIvDEgXid/pfd8uqUJ+Ur+nGgZZGdlnRwL6gqnWcxjiMMaxhDPP335L5+x/M6nX2Jtv2XlqXtdG+BIYsgral0L4ERs1axqhZq2lZOQoK9Of2H/AmhMXL/+jXitHBXIxXcfiRRqzn9lWuZm4FX7GIyABZC7AuvktDodtiAXks1btYfSX+q/+l5KZQXxr2RYE4fpu3TyFY6oNakWtDei3QNc+GA4fgx5k+Aj+5SdyTjH3uYo7c72Ha3lkHmICxARnW71knrPtxoIdRulU4XiHLv8jwKN08wmoe4/pcfxMRkfLZMPzvponA+HA7gcLheD0q821dJOqKsAgfeKMAHF9fHNu3jN7BOOx3nWsdWcRrqBboSgToWuziUc7FedWsXwG6JObw02l/Av+exafTfgn4EfDzPvuHncQGtLEFxhbA5hhb4NgC2ALYkP7/3bPA88AjwKMYj7KUJzUEnojk2LrAxsBG+GA8KdxuEJZoX6HRHcrVRa5FN79lt6/9UfDV3x6pNAVoSgukCtClU4AeMBsDnA6cTbybBrwJ/AS4csBfBZ7FEJazGS0hYBtbkGELjF3wFzUWswZ4CuNR4BGyPMom/Jvz17oARaSB2AT8z8Vm5C78zQBXgHs6xcIqzNrx4XhjchM4Resb49+PwXaXWAS8HZZ3+rld6NedvhmTWtf0AbrewnOkFlvGIwrQZbNhwMnAl4DNY3csAi4FfgburUGf5lTG08keZHg/WfbAsQf+K9XCHEsx7sDxSyZxN+fTNegaRKrGHL47QX5A3ix2W6w7VCfwv35xdfrNjA0B3gNsB+wQ1qOwvAHl/R1Zgv+AvyDczg/rc8PtvLAsUDcIaVAK0LHnFgqlVuZxK00BuqFZK3A8cC7w3tgdK4AZwAXgXkv0lB1sDrwf2CPc7goFJ66Zj/EbHNcxg8cSrUFk0KwN2B7//zdadqLw/+W+LMG3vEaj+jwNTAZXw//nbRg+JEdBeVv874/NGdhF9vOBOWF5DT/76WvAG/QEZKcRf6TZKUDTf2CuxRCtAN0UzOEvNvxvYO/YHZ3Ar/BB+pmKnPpYWhjH9nSzB45DgSNZ+6vcfwHXY/ySmcyuSB0iRdkQ/CRPu+KvJ9g1bBcaySbfO8AsfDicHdZn5fa5xWC7AFcDO4fndOGvTfh2+gHSJgAH4WdW2z4sm9H/jHVZ4NWwzCEXjqOw/Fr6r02kLihAU58BupYpQFeEHYAP0h8i9//RgLuBC/ytq9yMmpMZhePjOD4NHEzvP9QG/BXHL+nkBq5lccXqkCZlLfgg+wFyLcvbQ964772tAJ4CHgf+Te+AXOI1BdaG/7n7Orlxg/+Fb41+aGCvYTBsLHAA/mfvEPxr7+vvUhfwCn4SrH/Fbv8NbmUfz2su0xhOS4EPXJ2MoLvAONFttJMd4LcZ8TkHeu9fNKDjFD72UDJFux+1kO11cTq4glN5t+EKTNVtjMCKjJWdoQXLO3Zv8anAy7k/biR9/5yXetzVOL7IdO4q8Vj9UYDOe25/29I/BeiKsp3xf9CPgTD5i/cMcCHwq4rP7HQqG9LJJ3GcCLwv795VGHfiuI4l3KURPaQ8lsH/3zoQ39K6P37832KWAk/gw/LjYf3f4BKawdPei2+N3iPs6AYuAr4BbkXRp5V/vuHAvvjAfDD+A0NLgQd2Ai8Cz8WWKChX9mfvREYwknZWMgTHcNppoTuEKtczQ98osqH7iGN0z2twsVAUD2qOYfgQ5MOe9Qp7ufu8MeQ+yLfAWoEudz5/vP5CnzS+XzKDExM6lgJ03vOLteApQJdOAboqbAv8qB2ToVfrwTzgYvzIHW9XvIwO3gd8GvgUfui8uHnAuczgOsobPUaahjl8v92D8aH5APyYwdC6HIYshvbF0LIShi5cRvuyFxk6/2XG/fMNxj3zKuMfXkym24er3i1+Y8iSwbEMxxsYC3DMxTGficwf2Ogy1gp8ATifXJB7EegA98AgX387sCe5wLwXhWfKWwM8BNwD/AV4uM+L9M5hGMsZS5axOMZhjMUYi2Nkz/uUZVyYdXUEvq94O36K6vawPTKsRx9g4sFVmkeh6cAj8am6y7kfek/xXYrFlPp3xViMYw0tXMSVvDiAc/Sl6QM0FG91Huxxm5UCdFXZWPx7fha9A+wK4Frgp+CS+oVR3HlkeJ2DgE/jOJr414TGgzjOYAYNPByY9GsK6+CYgGM8xgYs3HU73t18ZzpHbIu1bErr8qE9Qbl9sZ+ts30xZCo2iEM30YgRjrkYCzDeIBNGkzDeoIsnuZa8PsG2LTCT3HUJWeAy4Cv9jz9srfiL+rYnd8HfdmG7UNeAbnyL+l+Ae/ngh15koz+tS0sYas4YHwLxWIxxOMbiw280Y9/QAsesRQa9un7Fw9EaYHnsvuVhXyTeFSKaQCVuFZYXzBxLceR/O7EMKzjC0NrP7135EloSHeZzONki/fgd3bg+Jr8y3sV/K9FbhuV05n0bOIR3cXmPXchSbljrfZHCFKAlcQrQqbA24Dh8C9kusTuywG3AT8D9tSqlnMMw3uU4jO+QC/VdGJfSwnlctdYfOKlXJzKCYWxMN+PJsAEwgSzjyTAJYzy5menWp7SL+yqhm8LdH0qxBh9gH8L4G46/M4PXQxeTzwHfJXdx7avAVHB/ARuKHwXjPeTCcrRduF9p63IYOdsY+/xs1n/4ZTZ4cCHrPZ6lZeUEjI1xbExlAnEUXn0roWMZxhpgCY7VWM++LmAJRpZMT1Dz4dLf5/uVZ0KgdSwjSxfQSXf4W9BGFy3hcd1k9btA6pgCtCROATp1djA+SH+Y3j8XjwLfAXdbVcqYzCgynIcPGtFFIPOA/2IG16NuHbVvMqNoZTO62YwMm5ENYye7nvGTi48fXqruIUb38NWYW0zrqjfJrJiHCzPLORZjLMKxmCyLe8IZrMDwff0dy+gKLYdDw/2r6eJqchcKnsMwFjORDBNxTMCYBEzAsWFoEZ9Ebla9/sL2HAhh+qXj5vDAz8+me8j+4T7Dj2yx8VrHaV0Bo16FkbP87ahZMOb5VYx+sZORc9poXVFOOO4CFoWvqBfjwjrhfcuwiGy4Lxvex1YW0c1K2lhON+9yVYEWSxHpT9MF6HL/YCucl04BumbYdsA5wIn0brn6GfClqk1wMJUdMC7B922NPECGM7mKygzDJ6U7jXF0sguOHfBTwm9GboKRdco4YjddI95lxcQMS7cawcoJGVZOgBUTYdX6sHLCGrpG/I2u9j/SPeyPLN7hiQRfzeCcR4bZjCfDBBzbAHvhekb+KNaCvpJ3N36DVz+xCfP2a6drWC4gR4F59MvdDF040FbwLH6SktnAHBxzsDD0XIY5dDKHaxj8xEoiUg4F6ASPLZ4CdM2x8fipws8E1g07HwA+AW5+1cqYwqdw/AiYFPZ04biYFXyL6/vo1yfJOZktaGFnHDuRDbd9T+2ebxW5cZOjMZRf4/UPtvCv03Zk4W77sXyj3cHlX2S2GLgTuAX4Q/99hWvMWQxhFbsBe2Hsgx9Ob+Igj7oKeBVjFo5ZwGs45uCYTTdzaGGuWodFalbTBWipPAXommUbAzeRG4rrdeAYcA9XrYQTGM1QzsPxOXKzo72J8SVm8mvUrSMZZzGE1exANzvj2Bk/G99O+BEU+rKSXDj2t45ZdDObVmZxFW/mHmrjgan4vvc7FjjWXHz/+98B9zbclM5T2BTYB8de+AsKd6L3jH9r8JOTxEPyq2SZtfZ7KSJ1RgFaEqcAXdNsKH7EgJPDjtXAmeBmVLWMKbwXx6X48X0j9+E4k+k8W9VaGsUpbE03RwNH4S8k7WvygSzGyziehJ7laX+BXH9sF/wQisezdreGF/CB+RbgEXBJjk5Q26YxHNiVLI5uZrEJbwxsmDwRqSNNH6BLbe1SOC+dAnRdsNOAn5IbEeBK4HMVn3yhN0cHJ+CnR94g7OsEvsUM/reKddSvqexAlqPD0IH5k9pEVgL/BJ7A8RTwJG08zWUD+fm0VuA/8ReE7pd351PAb4FbwD03wFcgIlKPFKAreOxmpQBdN2xv4EZyfTkfAz4O7rWqluG7dXwbxxnkvgK/mBmcjbp0rG0qO4fQfAx+aLR8z+K4C+NxunmKd3m+/LFdbQxwEv5i1Hhf6Szwe+AicH8u79giInWr6QN0XzSNd3kUoOuKrY9vPTww7HgLOA7cvVUvZTI74bgFx2YAOK5jEpM5v+DkBs3EMYU9yHA0xtHAlgUe8wRwExlu4ir+PfhT2jbAGcAUek/wsQT4OX5c8dmDP4+ISF1SgO6HQvTAKUDXHWsFvgOcG3Z0AV8H94Oql3IqG9LNnzC2D3tupYvj154NrglMYVMcnwc+DmySd69hPILjJrq5iWt4ZfAntAx+GumzgY/Q+/feC/i+8zPALS/wZBGRZqIA3Q8F6IFTgK5bNgW4lNyFYdcAp4Orbnj9DOvSzl1Eo4U47qWbI3tNjNHoTmZ7WrgHP5NfJBtmw4tC85zkTmjHA/8DbNXrfHAHftzwe8CpO42IiKcA3Q8F6IFTgK5r9n78UHcbhR3/wPeLTjCslWAyo2jhVoyDwp5HyfBhrmJhVetIg5945i9E4dlxL3Ajjt8lP/SZbYZvWT48tnMpcDVwCbiXkz2fiEhDaKgAXQ4rcZHSnYJ/z0amXYiUyyaA3Q9mYVkA9oGql3EWQ5jCjXRgYXmOjp5g35imsS0dzI295q9V5kTWCvZFsHdj/87zwc4CG1WZc4qINIx2fNbZO+1CkpA/81VS1PosTcbNBw7Ff3UPsD5wC1h1w+vFrGYpx+G4OuzZDniQU9i6qnVUyzS2Jcu95EZF+Roz+G7yJ7LdgIeBH+MvEDR8i/N24C4G1zxdZURERGqEWqAbip0aa6H8G1h7/89JnGMKF8RaZecxlZ1TqKNyfMvzm7HX+NXkT2IjwH4C1hX7N30e7MDkzyUi0tDUAi0ifXFXAJeHjQ/gWy2rzZjJF3H8d9iegHEvU9gnhVqS18F2oeXZTyZjfDX5iWTsw8Cz+PGcW/AT1vwA2AncfcmeS0REmon6PSdDLdANx9rA/i/WavmZ1Erp4Aw66A6ttMuZwmGp1ZKEDrbr1fI8ha8kewKbAPaL2L+dhX/LHZI9j4hIU1ELNMUDs4K0CACuEzgeekbAuCy1ADaDS3F8Bt+COhzHrUzlE6nUMlgdvA94gHjL80y+l8zBzYUPOs8CJ4adS4DPA/uBezaZ84iISL0rJ0DHA7LLWwo9RqRJuTn4EN2Nv/DsZrDRqZQynevDjHyrgHaMXzGVqanUUi4fnv8CrBf2fCXB8LwVcDd+xsB1w847gPeCuwhcNpnziIhIIxhMH+hCI21o9A2RXtxfgG+HjW2A6amVMpPb8bPlLQNaMK5kCmemVs9ATGYn4uHZ+AIz+H4yB7f9gKeAQ8KOOcDHwH0U3OvJnENERBqJLiIUqbzvAHeF9U+AfT61SmZwD8ahwNuAw/EzpnBKavWUYjI7keHP+PBswDnM5MJkDm7bAbcAw/HfFPwM2AHc7ckcX0REGpECtEjFuSzwaWBW2PFDsPRGw5jJI2Q5hFyIvrxmQ3R+eHacwwx+mszBbRL+g806+GB+ErizNaaziIj0p5wAHXXTKHYRYfwxIgKAewc4ClgJtAE3hgCXjqt5CuM/gHfwIfoypvRcOFcbprLzWuF5Ohclc3Abhe/jvGnY8RVwv0zm2CIi0ugGexFhsWHsNLW3yFrck/gxhcGPInG9nx46JTN5AvgIjqVABsc1TOX41OqJm8JWWK9uG59PMDyHDzDsEnZcCe4HyRxbRESagbpwiFSVuxK4JmwciO8fnZ4ZPITjI8C7+AsLr6ODY1KtCcBxOX40DMNxNjN6pkgfJHP4Czk/GHbcAZyRzLFFRESkmjSRSlOxoWCPhQk6smBHp10RHRxIB8vD5CRr6ODIFGv5ZGySlEuTPbh9LzY5ysN+qm4REakCTaQiIoPhVgHHAYvx1wtcA7ZtqiXN4D4cR5Lro/1bpvDRqtdxAqPJTX0+n26+ltzBbRr0TG3+EvBRcMuTO76IiDSLwQZo9XMWKYt7CfgM/udmFPBbsOGpljSdPwNHEk224riRKXykqjUM57uAv7jS8UWuZXEyB7YjoKc1+y3gcHALkjm2iIg0G03lLZIadzvww7CxI2lOshKZwd0YRwGr8SH6Bqb0TDBSWR3shnFa2HqA6fwqmQPb+4HfAK34SWQOCx9gREREyqKpvEXS9TX8FNIAnwJLfzzmmfwB43igExiG4zYmc1BFz3keGeASoAVYA5xKIr9HbEvgdvxU6p3AJ8A9PvjjiohIM9NU3iKpct3AicDcsOMisG1SLMibyS3A8UAXMJwMdzCVAyp2vrmcCuwVtn7EDP41+IPaBOBPwHh8GD8F3B8Gf1wREWl2uohQJHVuPv6iwiwwBEhvqu+4GdyM8SmiEA23MY09Ez9PBxOwnuH8ZrOa7w3+oDYSuBPYIuw4D9w1fTxBRESkZArQIjXBPYifVhrgs2DrpFlNj5ncAEwBshijyfIHOtgt4bP8GBgHgHEG1zHIkTGsDbgBeuqcAe5/BndMERGRnMEE6L6m8haRgYsmCxkOnJxmIb3M4BfANPzP91jgz0xhn0SO7ftWnxC2fsdM7hzcAc0BVwCHhR13Qs+FiSIiIokoJ0DnXyxYaBg79YUWGbi7oafv7xlgLWkW08sMZuI4nShEO/7EVA4f1DGPpZ0Ml+J/X7xLN2cnUOmXgclh/RHgOHBdCRxXRESkR7kt0PmjbvS3X0T65Qy4OGxsDilMZNKX6VyB40T8aBbDMW5jCp8t+3hj+BKwHQDG+VzDnMEVaC3Al8LGS8ARmihFREQqYbB9oIsNYyci5fkF9Ewe8rk0CyloOtfj+Dh+xsJWHNfQUcZFj9PYBPhq2HqWFi5KoLo9gfXC+v+CeyuBY4qIiKyl2S8izO+Coj7ckjK3HJgZNg4Ce1+a1RQ0nTswDgOW4D84X8gUvj+gY2S5BD82swFnchWdCVQWzZqYJXdBpoiISOKaZSrvQvUVq7eWX4c0h4uB7rB+VpqFFDWTB8hwMOCnw3acy1QuDhOi9G0qRxF1T3FcwwzuS6iqKEA/Bm5eQscUERFZS7NO5V1sNsVC94tUmZuNnz0P4ASwddOspqireJxuPgC8AoBxJm/wc6bRVvQ50xhOlp+ErXfo4r+TKcYmAVFr/SBH8hAREelbs0/lnd9vW/24pVZEQ9oNA6amWUifruEVMuwLPBP2fJosN3MOwwo+Psu3cGwWtr7MNSTVT/kIcj+/CtAiIlJRmspbpCa5e4GnwsaZYXKQ2nQVb2IcCDwU9hzBMu7iBEb3etxUdiA3y+IjbEiSMwNG3TcWAI8neFwREZG1NPtFhCK17JJwuyHwn2kW0q+ZvMNqDsWPZQ1wAMO4h5NZP2w7jEuANqALxymcTzaZk9sQ4OCwcSe4hI4rIiJSWLMF6Pw+2vnr9dL1RJrD9cDbYb32hrTLdx3LGcZHgRvDnt1o4QGmsQkdnAQcGPZfxHSeTPDMBwIjw7q6b4iISMUNZibCvqbyrveuHPVevzQEtxKYHjb2Bds9zWpKcjGr2ZBPYlwb9mxLlgeBH4bt18lyfsJnjbpvdAJ/TvjYIiIiaxnsRYTFhrGrtfGV8y92LHThoyaEkVp0CfSMkXxmmoWU7Hy6mMlkrGe0jY2JJjhxfJ6rWZbwGaMpxf8KbknCxxYREVlLs3XhEKkz7g3glrBxPNiENKsZAGMmXwS+FttzF9O5KeHTbAtsFTbUfUNERKqi3C4c5SwiUp5oSLshwLQ0CxmwGfwvxgk4rqaFKRU4w0di6wrQIiJSFQq2a0uiH/d6wE+B9hIfvwWwGzAaEv96WxqCPQLsAbwJbAZuTbr11Aq7BzgIeAXclmlXIyIiRbUDq4F9gL+lXMugqQtHZXQC7wCLSlxWhOel3Vdcatel4XYicEyahdQOG43/RQxwR5qViIiISPWdgg/PI/t7oDQrGwI2D8zA/pF2NbXBjgnvh4F9MO1qRESkT+34rLN32oUkQS3QInXBrQauChu7ge2ZZjU14sPhdjnwQJqFiIhIc2nGAF1oiL1aGGpPpD+XA1Hf59qfWKWizAEfCht/BrcqzWpERKS5NFOALiUkK0hLDXNvkpvl71iwDdOsJmW7AZPCukbfEBGRqip3IpW+QmYthtB4PaUMtVdr9YtEoslJ2vB955tVNHyd/eVKZgAAErhJREFUAXelWYiIiDSfwbRA9zWVd63qb2g6DesnNc49BjwcNk4FG5pmNSmKAvRT4F5PtRIREWk65U6kEsmfvrvQY0QkWdHEKusDx6VZSDpsPL4LB6j7hoiIpKDcFuh4l4d4l41an3WwlD7QIrXuBiBqdT07zUJS8mFyv7sUoEVEpOqa5SLC/Fbz/kbhqOUPAdL0XCe5Ie12Ads3zWpSEHXfeAd4JM1CRESkOZUboIu1OtfiBYSRUlrHa70FXSRyBRAN3dZEQ9pZG3Bo2LgLXHea1YiISHMqdxSOiCuyXqshGkobhUOkxrm3gP8XNo4C2zjNaqpoX2BsWFf3DRERScVgunAUCpwKoSLVc1G4bQVOT7OQKoq6b3QDf0qzEBER+f/t3d2vLWddB/Dv9BwK0optgRL7pm0kqIE0QeWl2HKASFuqMfHlRg134F/gnTEx8da/QBMTL7xplJBAbQX6AlgCvoBQML0QE4u01FALxAKnL+PFnsmZrq619sx62TPPzOeTrMw856yz1lP2sPZ3P/s3v2e5du3CsS0oW82FM1F9Ocnnm8GHm9355q7dvvsLSfXdUWcCwGIt5SZCmKu/aY7XJbl1zIkcX31zkl9oBso3ABjNMQL0lG8khLn5ROf8QxufNQ+/3jkXoAEYzb5dOLa1ggOOrnoiydebwdwDdFv//ESSx8acCADLtm8Xjk2WUIsJU3Ffc3xXUr9+1JkcTX1Fkvc2g08mlR/WARjNobpwaAUH42kD9LkkHxxzIkf0gSSvac6VbwAwqn228u4eV//O6hCcnc8nebY5v3vMiRxRW77xoyQPjjkRANCFA4pXvZDk083g7qQ+N+ZsjuSu5vhQUj036kwAWLx9biLcNLb6DGfv75vjG5L8ypgTObz61iQ3NQPlGwCMbp8V6HUhWniGcdyXS///m1sZxz2d8/tHmwUANHbdiXDbeNOfAUdTPZXky81gbu3s2gD9jaT6j1FnAgDZ7ybCTV04hGcYR1ve8EtJ/dOjzuRg6muSvLMZKN8AYBLcRAjz0dZBV0nuHHMiB3R3TtrzJQI0ABPRJ0Bv23XQjoQwHV9M8nRzPpcyjrZ843tJHh1zIgDQsgINs1G9lORTzeDOpH7VmLPZX93dGOaBpHp+zNkAQKtPgN5U17xa96wOGsbX7kr4uiS3jTmRA3h3knZrcuUbAEzGkBXo1WCsVAOm5/4kLzbnpbeza8tQXkrywJgTAYCuXdvYCdIwSdUzOamFTl7eP7lE7fz/Kam+M+pMAKBjnxpoQRqmqe3G8dak/plRZ7Kz+oYkb2sGyjcAmJRD3ES4WvcsSMO4uoGz1DKOD+TSZ8p9254IAGdNFw6Yn68k+e/mvNQAfXNzfCnJ18acCACsOkSAXu39rAsHjKqqc3IzYZJ8IKlfM+ZsdnRjc/xOUl0cdSYAsGKfAL1aqiE4w3S0ddBXJLljzIns6Ibm+MSoswCANXYJ0IIzTN+nkrQrtyXuStiuQH9r1FkAwBpDArTgDMWovp/kH5vBb4w5kx1ZgQZgsvoE6E1dNepTHsC42jKOW5L6zaPOZJD6p5L8ZDOwAg3A5OjCAfPVbWdXUhnHDZ1zARqAyekToKsdH8Coqm8k+WYzKKmd3Y2dcyUcAEyOFWiYt7ad3YWkvnLMiQxgBRqASROgYd7aOuhXJ3n/mBMZoA3QLyV5csyJAMA6AjTM22eS/LA5L6WMoy3heMomKgBMkQANs1b9MMkjzeCeMWcyQLsCrXwDgEkSoGH+7muONyb1W0edST/tCrQbCAGYpCF9oPV3hjJ9onNeQjs7K9AATNo+W3kL01CE6j+TPN4MJh6gbaICwPTt0ge6S5iGMrRlHO9J6qtGncl2ekADMHm7rED3CdMCNUxLG6DPJ/m1MSdyCj2gAZi8fW8itPMglOGzSX7QnE+5nV13BVqABmCSDtmFw1beMFnVxZz0hE6Se5J6qh14upuofHvMiQDAJlP9JgocXrsr4bVJ3j7mRLZoA/RTSfX8qDMBgA0EaFiO+3Lp/oSpduNoSziUbwAwWQI0LEb1rSRfawZTrYNuV6B14ABgsgRoWJZPNsd3JPW1o85kPZuoADB5AjQsS1sHfVmSD445kVeqr4pNVAAowK4BerXn87oHMD2PJnmmOZ9aHXS3B7QSDgAma9etvIEiVS8m+VQzuCupz485mxV6QANQhH1KOFb7PusDDWVodyW8Osk7x5zIius75wI0AJOlBhqW5/5c+k3SlOqgbaICQBEEaFic6ukkjzWDCyNOZNVNzdEmKgBM2i4Bui3PUAsN5XqoOb4rqV876kwu0QMagCLsexOhLhxQpoeb4+VJ3j3iPLrsQghAEZRwwDI9kpNa42Q6ZRztTYRWoAGYtF1LOPo8gMmqnkny1WbwvjFncsImKgCUwwo0LFdbB/2OpL5i1JnoAQ1AQfoE6NWa5j67EKqBhulrA/SrkrxnzInELoQAFMQKNCzXZ5O82JxfGHEeiRVoAArSJ0Cv1jSrgYZZqL6X5CvNYOw66PYGwheTPDnmRADgNFagYdnaMo5fTurXjTiPdgXaJioATN6QGuihD2D62gB9PuPWQbc10Mo3AJi8pa1A9wn4fgBgST6XpF3xHbOMo12BdgMhAJO3Sw306p+XUgO9GoqFZEj1gyT/2gwujDgRK9AAFGPICvRqMC5ppbad57r/Bli6h5vj25sNTc5YfVWSK5uBAA3A5O2zE2GrpCDdEqLhkrYO+lySXx3h/bst7JRwADB5+9RAlx6khWg48bkkF5vzMeqgu5uoWIEGYPIOcRPhat1zSUFaiIZUzyX552YwRoC2Ag1AUZbShaMb7jf93aa/hyVoyzhuTerXn/F7tyvQNlEBoAiHCNCrreGm2oVjm9LmC4f2cHO8LGdfB90G6KeS6oUzfm8AGGyfAL1aqjH14Hza/Kbehg+O6dEkP27Oz7qMQw9oAIqyS4AuLTgDp6qeS/KlZnDWAVoPaACKMiRAC84wb20d9NuS+g1n+L4CNABFOd/jOZturDvthrtSw3W3lntXNyS5P8lP9Hz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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "## A resonance diagram ##\n", "## New time sequence \n", "time <- seq(0, 6000, by = 1)\n", "## Sequence of values of T\n", "TT <- seq(1, 80, by = 2)\n", "## A matrix to store the results\n", "results <- matrix(ncol=4, nrow=length(TT),\n", " dimnames=list(NULL, c(\"R.min\",\"R.max\",\"C.min\",\"C.max\")))\n", "## Loop over all values in TT\n", "for(i in 1:length(TT)){\n", " parameters <- c(r0=1, alpha=0.1, T=TT[i], K=10, a=1, h=0.1, e=0.1, d=0.1)\n", " tmp1 <- ode(y = state, times = time, func = RM2, parms = parameters)\n", " results[i,1:2] <- range(tmp1[1001:nrow(tmp1), 2])\n", " results[i,3:4] <- range(tmp1[1001:nrow(tmp1), 3])\n", "}\n", "\n", "## Plot of resonance diagram\n", " plot(R.min ~ TT , data=results, type=\"l\", lwd=2, lty = 1,\n", " col=\"blue\", xlab = \"T\", ylab = \"Min / Max population size\",\n", " log=\"y\", ylim = range(results))\n", " lines(R.max ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"blue\"))\n", " lines(C.min ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"darkgreen\"))\n", " lines(C.max ~ TT, data=results, type=\"l\", lwd=2, lty = 1, col=c(\"darkgreen\")) \n", " legend(\"topright\", c(\"Resource\", \"Consumer\"), lty=1, lwd=2, col=c(\"blue\", \"darkgreen\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see a strong peak! (remember that this is a log scale). The frequency at which this peak occurs is the **resonant frequency** of the system, and is related to the natural frequency of the system (that exists even when it goes to a fixed point with constant parameters!). The external oscilation excites the natural frequency and drives large amplitude cycles, just like when we push a seesaw (ou gangorra, o balancín)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What if I really want to explore a 10-dimensional parameter space?\n", "\n", "First: good luck. Second, you will probably have to sample the space, rather than go through the whole thing. The recommended method to do it is using so-called [Latin Hypercube samples](http://en.wikipedia.org/wiki/Latin_hypercube_sampling), that uses a random sampling while ensuring a roughly regularly-spaced distribution. Notice, though, that this method is a way to sample the parameter space and do useful statistics with it, so the result will only make sense if you know how to properly interpret the outcomes. That said, there are implementations for both R and python:\n", "\n", "* [R-Cran pse: Parameter space exploration](http://cran.r-project.org/web/packages/pse/)\n", "* [PyDOE: design of experiments for Python](http://pythonhosted.org/pyDOE/randomized.html)" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "", "name": "r" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.2.3" } }, "nbformat": 4, "nbformat_minor": 0 }