{ "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", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= rR \\left( 1 - \\frac{R}{K} \\right) - \\frac{a \\frac{R}{C}}{1+ah\\frac{R}{C}} C \\\\\n", "\\frac{dC}{dt} &= C \\frac{e a \\frac{R}{C}}{1+ah\\frac{R}{C}} - d C\n", "\\end{aligned} $$" ] }, { "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": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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GnZUlq3liZNHNkaBHCLa9Wq1ZgxY+xjjnAli8WSlZUVGhrqLkcMmM1mg8GwaNGi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\n5PTbu01HjBgxZMiQPXv2qFun1QT6Bup0OhE5c6X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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/(1+a*h*R/C)\n", " dC = e*a*R/(1 + a*h*R/C) - 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=500, 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": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message in arrows(x0 = coords[, 1], y0 = coords[, 2], x1 = coords[, 1] + :\n", "“zero-length arrow is of indeterminate angle and so skipped”" ] }, { "data": { "image/png": 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vYuzUfT0id7f3//0twp3vXRtEGDBpp//yXYVagTJ07cfffdQog///yzUaNGapfj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q9Mwzz7Rv314IkZ2d7Xa7nU5nbm6uEKKg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\nxhuHDRsW6IIglPz6668mk4nTBtfEYrF8+OGHnTt3DnRBUFn0s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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Phase space flow and fixed points\n", "##first we need to calculate the coordinates for the vectors\n", "xs = seq(from=0.9, to=170, length.out=7)\n", "ys = seq(from=0.94, to=170, 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(0.9,170), ylim=c(0.94,170))\n", " ##and add the vector field\n", " arrows(x0=coords[,1], y0=coords[,2], x1=coords[,1]+dvs[,1]*0.05,\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": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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StXlIUUv/76a9l/ZTabN2zYkJube5tr9u3bV9Hi/k7Zx67QXGixWAwGg7o3BwAA\nlZZ+gl1hYeH+/fvL+6tTp04NHz48P/92b/dS3j9rsVjsL+7vlGAnIoWWQi+Dfv4JAACAtvST\nKgICArZs2VLeXzVq1OjcuXO3v2bevHkjR45UsbWmDMWKSEFhgfUzAABABeknVRiNxm7dumld\nRZncCHZMswMAAOpxv8UT58+fP3r0aEFBKZEoKysrIyPD+SWVl7IqVlgYCwAAVOVOwW7//v1t\n2rSpV69e8+bNQ0JCFi1aVOKCIUOG3HHHHZrUVi507AAAgCO4zVBsampqhw4dTCZT9+7dvb29\nt27dOnTo0Ozs7FGjRmldWrnRsQMAAI7gNh27t99+Oy8vb926dZs3b16/fn1aWlpYWNhrr712\n9OhRrUsrNzp2AADAEdwm2CUlJfXs2bN3797K1zp16qxfv95gMIwdO1bbwuxwo2NHsAMAAOpx\nm2B35syZEvPnwsPD33jjjbVr1+7YsUOrquzjaSjax46hWAAAoCK3CXbBwcG7du0qcXDcuHEh\nISHPPvvsn3/+qUlV9rF27ArNhdpWAgAA9MRtgl2/fv0OHz780ksvXb161XqwWrVqc+fO/eOP\nP4YOHXrlyhUNyysXo6dR+ZBfeLs3XgAAAJSL2wS7iRMnhoWFzZw5s0aNGt27d7ce79OnT0xM\nzJo1a0JCQvbu3athhWV345VidOwAAIB63CbY1apVKykpafz48eHh4WfPni1+avLkyQsWLGjQ\noEFWVpZW5ZULq2IBAIAjuE2wE5HAwMBp06YdOXLk0KFDJU4NHTr0yJEjJ06csON1sc7HqlgA\nAOAIbrNBsU0GgyE0NDQ0NFTrQmyzduyYYwcAAFTkTh073bgxFMt2JwAAQD0EOw0YvYpWxTIU\nCwAAVESw0wAdOwAA4AgEOw2wKhYAADgCwU4DN1bF0rEDAADqIdhpgI4dAABwBIKdBtjHDgAA\nOALBTgMsngAAAI5AsNMAHTsAAOAIBDsN0LEDAACOQLDTAIsnAACAIxDsNMB2JwAAwBEIdhqg\nYwcAAByBYKcBOnYAAMARCHYaoGMHAAAcgWCnAaOnUflAsAMAACoi2GnA08PTYDAIQ7EAAEBV\nBDtteBo8hY4dAABQFcFOG8poLB07AACgIoKdNpSFsXTsAACAigh22lAWxuYX5mtdCAAA0A+C\nnTaKOnYMxQIAAPUQ7LRRNMeOoVgAAKAegp02lKFYgh0AAFARwU4bDMUCAADVEQ+fuGwAACAA\nSURBVOy0weIJAACgOoKdNphjBwAAVEew0wZDsQAAQHUEO22weAIAAKiOYKcN5tgBAADVEey0\nwVAsAABQHcFOGyyeAAAAqiPYaaNojh0dOwAAoB6CnTaKhmLp2AEAAPUQ7LTB4gkAAKA6gp02\nlDl2BDsAAKAigp02GIoFAACqI9hpg8UTAABAdQQ7bbDdCQAAUB3BThvKUCxz7AAAgIoIdtoo\n6tgxFAsAANRDsNMG250AAADVEey0UbR4gjl2AABAPQQ7bRi9GIoFAAAqI9hpg6FYAACgOoKd\nNtjuBAAAqI5gpw1PD08RKTQXmi1mrWsBAAA6QbDThtKxE6bZAQAA9RDstKHMsRNGYwEAgHoI\ndtqgYwcAAFRHsNOG8koxYWEsAABQD8FOGzc6dgzFAgAAlRDstGGdY0fHDgAAqIVgpw1rx45g\nBwAA1EKw04Z1jh1DsQAAQC0EO22wKhYAAKiOYKcN5tgBAADVEey0wapYAACgOoKdNtjHDgAA\nqI5gpw1WxQIAANUR7LTB4gkAAKA6gp02WDwBAABUR7DTBosnAACA6gh22mDxBAAAUB3BThss\nngAAAKoj2GmDxRMAAEB1BDttsHgCAACojmCnDRZPAAAA1RHstMHiCQAAoDqCnTZYPAEAAFRH\nsNMGiycAAIDqCHbaoGMHAABUR7DTBqtiAQCA6gh22mBVLAAAUB3BThueHp4eBg+hYwcAANRT\njmCXk5Nz8ODB3bt3O66aSkXZ8YRgBwAA1FKmYHfq1KlHHnmkRo0arVu37tChg4hMmjRp8ODB\nZ86ccXB5eqaMxhLsAACAWmwHu7Nnzz7wwAOrVq2KjIzs2rWrcrB27drffPNNu3btzp496+AK\ndUtZP8F2JwAAQC22g93UqVPT09MXLVqUkJAwfPhw5eBLL720YcOGzMzM2NhYB1eoW3TsAACA\numwHu3Xr1nXt2nXIkCEljvfq1atv376bN292TGH6R7ADAADqsh3ssrKywsPDSz3VoEEDptnZ\njWAHAADUZTvYtWrV6tdffy31VFJSUvPmzdUuqbIg2AEAAHXZDnbR0dG//PJLbGys2Wwufnzq\n1Kn//e9/e/To4bDadI7tTgAAgLq8bF4xfvz4TZs2xcTELFy4sE6dOiIyevTopKSkffv2RURE\nTJo0yfFF6pPSsWNVLAAAUIvtjp2np+fmzZs//vhjk8mUmJgoIrNnzz558uTbb7+dkJDg6+vr\n+CL1iaFYAACgLtsdOxHx9vYeM2bMmDFjrl27lpaWFhQUFBgY6OjKdI9gBwAA1FW+d8X6+fm1\naNHCmuquXLmSmprqgKoqBYIdAABQl+1g17Rp06ioqD/++OPmU/Pnzw8LC3NAVZUCwQ4AAKjL\ndrA7fvz4jh072rZtu3btWicUVHkQ7AAAgLrKNBT75JNPBgYGPvzwwxMmTCgsLHR0TZVE0bti\nzayKBQAA6ihTsGvduvW+ffv69Okzbdq0hx566Pz5844uqzKgYwcAANRV1sUTNWrUWLt27eTJ\nk3/66ad77rln165dDi2rMlCCnanApHUhAABAJ8qxKtZgMMTExGzYsCE3N7dLly6ffvqpxWJx\nXGW6R8cOAACoq0z72BXXs2fPffv2DRo0aMyYMfXq1XNETZWE0YtgBwAA1GS7Y+fr6+vp6Vn8\nSGho6M8//zx8+PBz5845rDD9o2MHAADUZbtjl5ube/NBX1/fL7/8csCAAZmZmQ6oqlIg2AEA\nAHWVeyi2uL59+6pVRyVEsAMAAOoqfSjWYDAYDIaMjAzr59twbsH6QbADAADqKr1j179/fxHx\n9fUVkUGDBjm1okqDYAcAANRVerD77rvvrJ+XL1/urGIqF4IdAABQVzn2sbOyWCxpaWkmEzvr\nVogS7ArNhWaLWetaAACAHpQp2G3fvn348OEnT54UkYyMjNatWzds2DAgIGDixInsUWw3b09v\n5UNBIa+LBQAAKrAd7H744YcHH3zwq6++ys7OFpGxY8cmJyf36NEjIiJiypQpy5Ytc3yRpbt0\n6dLZs2fNZndtdykdO2E0FgAAqMR2sIuLi/P3909MTGzZsmVOTs7q1au7dOmyadOmhISEsLCw\n2bNnO6FKq+Tk5KFDh4aFhVWpUqVWrVr169f38fEJCQkZPHhwQkKCMyupOOXNE0KwAwAAKrEd\n7A4dOtS/f//27duLSGJiYm5u7pAhQ0TE29u7e/fuR48edXiN/+ell15q3br1okWLcnJy2rRp\n06dPnz59+tx7770iEh8f36lTp4EDB+bnu01IsnbsTIXMVgQAACqwvUFxYWGhNS395z//EZEH\nHnhA+VpQUKCMzzrB7NmzZ86c2bNnz2nTpt19990lzh46dEgZF/7ggw/efPNN55RUQdZgxxw7\nAACgCtsdu/Dw8J9++slkMuXn5y9ZsqRx48ZNmzYVkfz8/J9++qlhw4aOL1JEJD4+vlmzZuvW\nrbs51YlIy5Ytly5d2qlTpw0bNjinnopjjh0AAFCX7WA3evToM2fOtG7dOjw8PD09/ZlnnhGR\nzZs3R0ZGHj9+/PHHH3d4jSIikpyc3L59ey+vW7YYDQZD586dDx486Jx6Ko6hWAAAoC7bQ7FD\nhw7NyMiYMWPG5cuXBwwY8MYbb4jIjh07Dhw48PDDD7/22muOL1JEpFWrVklJSYWFhZ6enre6\nJjExsVWrVs6pp+JudOwK6NgBAAAVlGkfuwkTJly4cCE3N3fVqlVVqlQRkaFDh6ampq5evdrP\nz8/BFRZ56qmnfv/99+jo6FJ7cikpKYMHD962bVvv3r2dU0/FWfexYygWAACownbHzspoNFo/\nh4WFOaCY23nxxRcPHjw4d+7cjRs3hoSENGzYMDAw0GAwXL58OT09/cSJEyLSr1+/sWPHOrkw\nuzHHDgAAqKscwU5zc+bMGTFixPvvv79r165ffvlFeaeZp6dn3bp1n3zyyRdeeCEqKkrrGsuB\nOXYAAEBd7hTsROQf//hHfHy8iFgslgsXLpjN5rp163p42PPGW83RsQMAAOpys2BnZTAY6tat\nq3UVFeLtxRw7AACgJrfsdekDHTsAAKAud+3Y3ezKlStdu3YVkV9//bXsvyosLFy/fn1eXt5t\nrtm3b19FiyvNjTl2BcyxAwAAKtBPsCssLNy/f395f5Wenv7CCy8o6zBuRYl9FovF/uJKQ8cO\nAACoq0zBbuXKlStWrMjKyir17ObNm1UtyU4BAQFbtmwp769CQ0MzMzNvf828efNGjhxpMBjs\nLa10zLEDAADqsh3s5s+f/9xzz4mIn5+fr6+v40uyk9Fo7Natm9ZVlAMdOwAAoC7bwW7GjBkB\nAQEbNmy4//77nVCQTefPn798+XKTJk1ufm9sVlZWXl5egwYNNCmsvJhjBwAA1GVjVazFYjl2\n7NjQoUNdIdXt37+/TZs29erVa968eUhIyKJFi0pcMGTIkDvuuEOT2uzAUCwAAFCXjY6dyWQy\nmUw398acLzU1tUOHDiaTqXv37t7e3lu3bh06dGh2dvaoUaO0Ls1ODMUCAAB12ejY+fj4REVF\nrV69+s8//3ROQbfy9ttv5+XlrVu3bvPmzevXr09LSwsLC3vttdeOHj2qbWF2YygWAACoy/YG\nxYsWLfLz83vggQeWL1+empp68SZOqFJEkpKSevbs2bt3b+VrnTp11q9fbzAYxo4d65wCVOft\nyVAsAABQk+0x1jZt2uTn52dnZz/22GOlXqD6Bm+lOnPmTIlFr+Hh4W+88caUKVN27NjRuXNn\nJ9Sgrhsdu0I6dgAAQAW2g92gQYOcUIdNwcHBu3btKnFw3LhxCxYsePbZZ//73/9Wr15dk8Ls\nZjAYvDy8CswFdOwAAIAqbAe7L774wgl12NSvX79PP/30pZdeiouL8/f3Vw5Wq1Zt7ty5ffv2\nHTp06IIFCzQt0B7eXt4FJoIdAABQh+05dsXl5OSkpKRcvXrVQdXcxsSJE8PCwmbOnFmjRo3u\n3btbj/fp0ycmJmbNmjUhISF79+51fmEVoYzGsngCAACookzB7tq1a1OmTGnQoEG1atWaNWsW\nEBBQv379KVOmZGdnO7o+q1q1aiUlJY0fPz48PPzs2bPFT02ePHnBggUNGjS41UvPXJaylR0d\nOwAAoArbQ7G5ubkdOnRITk4OCgoaOHBgcHDwuXPnEhMTJ06cuHLlyqSkJB8fHycUKiKBgYHT\npk2bNm3azaeGDh369NNPnzp1KjU11TnFqIKOHQAAUJHtYDdp0qTk5OTx48e/88471gxnMpkm\nT548derUd999Ny4uzsFFlonBYAgNDQ0NDdW6kHJQdjyhYwcAAFRheyh2y5Ytbdu2nTZtWvHO\nnLe3d2xsbLt27TZt2uTI8nSuqGPHdicAAEANtoNdSkpK27ZtSz3Vtm1b933xgyswehmFjh0A\nAFCJ7WDXuHHjI0eOlHrq8OHDjRs3VrukSkQZimWOHQAAUIXtYNe5c+edO3d+8sknJd4wMWvW\nrO3bt7vjKx9chzIUS8cOAACowvbiibi4uI0bN77yyivz58+PiooKCgo6d+7c9u3bf/vtt0aN\nGsXGxjqhSr1StjuhYwcAAFRhO9gFBAQkJCRMnjz5yy+/PHjwoHLQaDSOGDFi0qRJbvciL5fC\nPnYAAEBFtoOdiAQFBc2ePfuTTz45depURkZG/fr1Q0NDjUajo4vTvaI5dqyKBQAAaihTsFMY\njcawsLCwsDDHVVPZsEExAABQUemLJwwGg8FgyMjIsH6+DecWrCvMsQMAACoqvWPXv39/EfH1\n9RWRQYMGObWiyoQ3TwAAABWVHuy+++476+fly5c7q5hKR9mgmDl2AABAFbb3sbt48WJeXl6p\np3Jyci5fvqx2SZUIGxQDAAAV2Q52tWvX/vbbb0s99eGHHzZt2lTtkioRtjsBAAAquuWq2NWr\nV2dnZyufd+3a5eVV8kqTyfT999/n5OQ4sDq9o2MHAABUdMtg9+qrr548eVL5/Pnnn3/++eel\nXhYdHe2IsioJ5tgBAAAV3TLYff7550o3rn///i+//PKDDz548zVVqlThXbEVQccOAACo6JbB\nrkePHsqH7t279+3b96GHHnJWSZWIskFxfmG+xWJhR0AAAFBBthdPbN68+Vapbv369S+88ILa\nJVUiyuIJYf0EAABQQ5leKXbmzJn//Oc/ly5dKn7QbDYvWLDg1KlTt5p+B5uUoVgRMRWarCEP\nAADAPraD3YEDB7p27Xqr/epGjx6tdkmViLJ4QpRpdj7a1gIAANye7aHYyZMnX716ddasWRs2\nbGjcuPHjjz++e/fuTZs2de7cuXv37jNnznRClXp1o2PH+gkAAFBhtjt2SUlJbdu2ffHFF0Vk\n8ODBO3bsuO+++0Skbdu24eHhixcvHjJkiMPL1Cnr8Cs7ngAAgIor0yvF7r77buVzx44d9+7d\nazabRSQwMPCRRx6ZP3++YwvUNTp2AABARbaDXWhoaFZWlvK5devW165d27Vrl/L1jjvu2L9/\nvwOr07sbHTuCHQAAqDDbwe7ee+9du3bthg0bzGZzcHBwnTp1rK+O3b17d/Xq1R1coZ4xFAsA\nAFRkO9jFxsYajca+ffsuXbpURLp37z579uxBgwZ17959w4YNffv2dXyRusVQLAAAUJHtxRMN\nGzZMSkqaO3duSEiIiMyYMeOPP/5YuXKliPTq1Wvq1KkOr1G/6NgBAAAVlWmD4hYtWnz66afK\n53r16u3evTs9Pb1atWqBgYGOrE3/mGMHAABUVHqwy8vLu/3P6tata73Mx4etde3EUCwAAFBR\n6cHO19e37LewWCwqFVPpMBQLAABUVHqwGzx4sJPrqJwYigUAACoqPdgtXrzYyXVUTgzFAgAA\nFdne7gSO42Msmp7IUCwAAKg426tibb4Klvae3ejYAQAAFdkOdkuWLLnVKX9//3r16qlaT+XC\nHDsAAKAi20Ox12+SlZW1ZcuW+++/v6Cg4JNPPnFClXp1o2PHUCwAAKgw2x27m7ep8/Hx6dat\nW4cOHe6+++6nn346MzPTy6tMGx2jBGvHLi/fxsaBAAAANtm/eKJq1aoPP/zwxYsXMzMzVSyo\nUvHxYvEEAABQTYVWxZpMJh8fn/r166tVTWVjMBiMnkYRyS/M17oWAADg9uwMdhaLZefOnQsW\nLGjWrJmHB3um2E8Zjc0rYCgWAABUlO25cf7+/jcfzM/PV14U+9prr6lfVGXi7emdLdmsigUA\nABVnO9h16dKl1OOBgYEDBgzo37+/yhVVMkrHjmAHAAAqznawW7t2rRPqqLSU9RMsngAAABVX\njm1KUlJSUlJS0tLSgoKCmjVr1rJlS8eVVXkUzbFjuxMAAFBhZQp2+/bt+9///d+tW7cWP9ip\nU6ePPvooMjLSMYVVFkVDsXTsAABAhdkOdqmpqT169Lh8+XLfvn179erVoEGDzMzMTZs2rVmz\npkePHvv27WvSpIkTCtUrZSiWjh0AAKg428HuzTffvHLlyrfffvv4449bD44aNWrlypWPPvro\nm2+++e9//9uRFeqc8lYxOnYAAKDibG9Bt3v37qioqOKpTvHII4907dp19+7djimssmBVLAAA\nUIuNYGcymdLT0xs2bFjq2dDQ0IKCAgdUVYkUDcWyQTEAAKgwG8HOy8urTp06O3fuvH79eolT\neXl5O3bsaN++vcNqqxR8jAQ7AACgDhvBzsPD4//9v//3xx9/DBw48NixY9bjx48fHzhw4KVL\nl95//30HV6hzRXPsGIoFAAAVZnvxRGJiYuPGjTdu3Pjjjz/eeeedQUFBmZmZaWlpZrP5jjvu\neO6556xXBgYGrly50pHV6hBDsQAAQC22g93q1atFpHbt2iJy7dq148ePi0hgYKCIXL9+PTk5\n2Xpl3bp1HVWmfrF4AgAAqMV2sLtw4YIT6qi06NgBAAC12N7upLicnJyUlJSrV686qJpKiI4d\nAABQS5mC3bVr16ZMmdKgQYNq1ao1a9YsICCgfv36U6ZMyc7OdnR9ukfHDgAAqMX2UGxubm6H\nDh2Sk5ODgoIGDhwYHBx87ty5xMTEiRMnrly5MikpycfHxwmF6hUdOwAAoBbbHbtJkyYlJyeP\nHz/+5MmTK1eunDlz5vLly//444+33nrrwIED7777rhOq1DGlY2cqNFksFq1rAQAA7s12sNuy\nZUvbtm2nTZtWvDPn7e0dGxvbrl27TZs2ObI8/VOCncVi4XWxAACggmwHu5SUlLZt25Z6qm3b\ntkePHlW7pMpFGYoVRmMBAECF2Q52jRs3PnLkSKmnDh8+3LhxY7VLqlyUjp2wfgIAAFSY7WDX\nuXPnnTt3fvLJJyUmgc2aNWv79u2dO3d2WG2VgvKuWCHYAQCACrO9KjYuLm7jxo2vvPLK/Pnz\no6KigoKCzp07t3379t9++61Ro0axsbFOqFLHrB07hmIBAEAF2Q52AQEBCQkJkydP/vLLLw8e\nPKgcNBqNI0aMmDRpUvXq1R1coc4xFAsAANRyu2B3/fr1lJSUjIyMsLCwzz777JNPPjl16lRG\nRkb9+vVDQ0ONRqPTqtQx6+KJvHyCHQAAqJBbBruvvvrqjTfeuHz5svK1devWS5YsiYiICAsL\nc1ZtlQIdOwAAoJbSg92WLVuGDx8uIp06dWrQoMGePXt+++23hx566OjRowEBAc6tUOcIdgAA\nQC2lr4qdNm2aiPz73//euXPnt99++/vvvw8aNCgzM3PRokXOLU//WBULAADUUnqwO3z48D33\n3PPoo48qX41G4+TJk0Xk0KFDziutcrjRsWOOHQAAqJjSg11mZmZ4eHjxI02bNhWRa9euOaOo\nyuTGdie8UgwAAFTMLTco9vLyus1XqMUa7K7nX9e2EgAA4O5sv3kCDsUcOwAAoBaCncaYYwcA\nANRyywHWHTt2WBdP3P7g8uXL1a+r0mC7EwAAoJZbBru0tLS0tLSyHERFEOwAAIBaSg92+/fv\nd3IdlZav0Vf5QLADAAAVVHqwa9OmjZPrqLQ8PTw9PTwLzYXqzrHbvVuWL5cmTWT4cPHxUfHG\nAADAdbGJifZ8vHxyTDkqduxWrpTHH5fCQhGRb76RzZulShW17g0AAFwXq2K1p0yzU2sfuytX\nZMSIolQnIgkJMnasKjcGAACujmCnPWUrO7U6dp9/Lhcvioh884107iwiMmeOHDyoyr0BAIBL\nI9hpz9fLV9QLdl9/LSLSqpX861/y+efi5SVms0yZosq9AQCASyPYaU9ZGKvKUOzhw/L77yIi\nTz8tItKsmTz1lIjIqlVy8mTFbw8AAFwawU57Kg7FbtxY9OHhh4s+vP66iEhhoXz+ecVvDwAA\nXBrBTnvK4glVtjvZtk1EJDRUwsOLjkREyP33i4gsXCgFBRV/AgAAcF0EO+0VDcUWVHQo1mKR\nXbtEpGjNhNXw4SIiZ87Ili0VfAIAAHBpBDvtqdWxS0mRy5dFRDp2/NvxQYOkalURkfj4Cj4B\nAAC4NIKd9tRaPLFvX9GHyMi/Hff3l379RERWr5bc3Ao+BAAAuC6CnfaKOnYVXjzx668iIj4+\n0qpVyVNPPCEicu2arF9fwYcAAADXRbDTnlodu99+ExFp3ly8vUue6tlTAgJERFasqOBDAACA\n6yLYaU+tjl1ysohIREQpp3x9JTpaRGT9ekZjAQDQLYKd9lTp2F25ImfOiIi0aFH6BY88IiJy\n7Zps2lSR5wAAANdFsNOeKh27o0eLPtwq2PXsKdWqiYisXFmR5wAAANdFsNOeKh07a7Br1qz0\nC6pWlV69RETWrZP8/Io8CgAAuCiCnfaUjl1+YX6hudDum6SkiIh4ekrjxre8ZuBAEZHLl4te\nUAEAAHSGYKc9pWMnFRuNPX5cRKRhw1KWxFr17Vt0dtUqu58DAABcF8FOe9ZgV5HR2NRUEZEm\nTW53TfXq0r27iMiaNWI22/0oAADgogh22lOGYqViwe7ECRFbwU7+b21sZqYkJNj9KAAA4KII\ndtqreMfuzz/l4kURkUaNbFzZr594eYmwUzEAAHpEsNNexYPdyZNFH0JDbVxZu7Z06SIisnIl\no7EAAOgNwU57FV88cepU0YeGDW1fPGiQiEhGhiQm2vc0AADgogh22qt4x65cwW7gwKLR2GXL\n7HsaAABwUQQ77VU82KWni4j4+Ei9erYvrlNHHnxQRGT5cim0f+M8AADgctw72JnN5mPHjh0+\nfLigoEDrWux3I9gV2Bns0tJEREJCxGAo0/VPPCEikpkp//mPfQ8EAACuyG2CXUxMzFdffWX9\nWlBQ8N5771WvXj08PLxly5Z+fn4jR478888/NazQbr5eFe3YnT4tIhISUtbrBw4UX18Rkfh4\n+x4IAABckdsEu9jY2MWLF1u/vvrqq+PHjzcajYMGDRoxYsTdd989b968jh075uXZ//IGrVR8\nKFYJdnfcUdbrq1eXfv1ERFatkmvX7HsmAABwOW4T7Io7dOjQrFmz2rVrd+zYseXLl8+dOzcx\nMXH+/PmHDx+Oi4vTurpyswa7XFOuHT83m+XMGZHyBDsRefppEZFr12T5cjueCQAAXJFbBrtd\nu3ZZLJYZM2bUqlXLenDYsGEdO3b84YcfNCzMPhWcY3f+vOTni5Qz2PXsKfXri4jMn2/HMwEA\ngCtyy2B3+vRpEWndunWJ461btz5y5IgWFVVIFWMV5YN9Q7FKu06kKKiVkZeXPPusiEhCghw8\naMdjAQCAy3HLYNe0aVMROWXdve3/ZGZmhtp894LrqeAcu4yMog/lCnYi8txz4ukpIjJrlh2P\nBQAALsedgl1KSkpsbOyKFSuaNWtWp06d2NjY4mf37Nmzfv36yMhIrcqzm7eXt6eHp1S4Y9eg\nQfl+GBoqffuKiCxeXPSqWQAA4NbcJtiFhIScPXs2Jibm0Ucfbdeu3YULF7799ttt27YpZydM\nmBAVFeXh4fHKK69oW6d9fLx8xN5gd/asiIiHR5l2Jy5B+dvKyaFpBwCAHnhpXUBZpaWl5ebm\nHj9+PCUl5dixY8eOHUtJSfHyKqr/u+++q1279vz58yMiIrSt0z6+Rt8cU05Fgl2dOuJV/n/M\nrl3l3ntl71759FN59VXx97fj+QAAwFW4TbATkSpVqkRERJQa3VauXNm8eXMPD7dpQJagrJ/I\nzbdnuxMl2AUH2/noCRNk4EC5eFFmzJCJE+28CQAAcAXumoRKaNGihfumOvm/9RMV6dgFBdn5\n6P79pW1bEZEPPii6FQAAcFPu1LHTsSreVcTeDYozM0UqEOwMBnnvPeneXa5elbFjZckSO+9T\ngskkv/8uKSmSni4ZGXL5sly9+rcLfHykalWpXl38/KR6daleXQICJCBAatYUPz+pVk2qVZOA\ngKJ1uwAAoCz0E+yuXLnStWtXEfn111/L/qvCwsJ169aZTKbbXLNv376KFmeL0rGzYyjWYpHz\n50UqEOxEpFs3GThQVq2S+Hh5/HGJjrbzPnl5smOHbNokO3fKr7/Kbf9Sy6F6dfHwEC+vsk4B\nNJkkO9vGNdevS66tv2zluQAA3QgPl82bdT6hXD/BrrCwcP/+/eX9VXp6+siRI2//hlnlrMVi\nsb84W5Q5dnYMxV66VJSf7FgSW9ynn8pPP8mlSzJsmOzdKw0bluO3hYWyaZN88418/7389Vcp\nF1StKrVqFTXhFEquunZNcnJsv6z2zz+LPly4UI6qKs76XACAPiQlyYkTctP7DXRFP8EuICBg\ny5Yt5f1VaGjoWVszy+bNmzdy5EiDwWBvabYVDcWWv2N37lzRhwoGuwYNZPZseeIJycqSf/5T\nfvpJir2t7ZZOnZIvv5Svv76xSbKIeHnJvfdKx45yzz1y113SqJHUrHm7m5jN8uef8uefcuWK\n/PWX/PWXXLtW9P/5+XL5sojIX39JYWHR9VeuyM0Zu1o18fYu/f41aogj/+kAAG7jrrt0nupE\nT8HOaDR269ZN6yrs5OvlK3bNsVMr2InI44/Lnj3y4YeSnCydO8uaNRIWXpyMIwAAIABJREFU\nVvqV+fmyYYN8/rn88IOYzUUHq1SRfv1k4EDp2VOqVy/Hcz08pGZNG+EPAACUhX6CnVtTOnZ2\nDMWqGOxEZPp0OX9eFi+Ww4flH/+Q//1fee65G28qy86WhARZs0aWL//bqGiHDvLcczJokAQE\nqFADAACwG8HOJdi9eEJZOSEqBTsPD1mwQBo0kOnTJTtbJk2Sd96Rhg2lVi25dEnS0m6Mh4pI\n9eoyeLC88IL+29oAALgLgp1LKNqguPxDsUqw8/KSwEB1KvHwkGnTpFcvef112bdPLBY5eVJO\nnrxxgdEoDz4oTz0ljzwiVauq81AAAKAKgp1LKBqKLbBzKLZ2bZU35oiKkr17Zc8e2bRJjhwR\nk0mMRmnSRO69V6KiyjeFDgAAOI17BLuZM2fGxMSU8eLLykJKt2J3x06Z61a3ruoViYhERkpk\npEPuDAAAHME9gl2vXr2OHTs2b968vLw8f3//huXaZs0dKB27/ML8AnOBl0c5/lGUjp0qE+wA\nAIC7c49gFxYW9sknn/Tp06dXr15RUVFr167VuiKVKR07Eck15fr7lmNLbKVjV6eOI4oCAABu\nxp1emdSzZ8/w8HCtq3AIpWMn5V8YS7ADAABW7hTsRCQyMtJoNGpdhfqKd+zK/qu8vKJXeBHs\nAACAuMtQrNWSJUu0LsEh7OvYWXcJdtDiCQAA4F7crGOnV/Z17KzBrnZt1SsCAADuh2DnEm4E\nu/J07LKyij4Q7AAAgBDsXERVn6J3OOSYcsr+K2uwY44dAAAQgp2LsG8o1vqiWIIdAAAQgp2L\nsG8o9uJFERFPT6lZ0xFFAQAAN0OwcwkVGYqtWVPlF8UCAAA3RSJwCfYNxSodO1ZOAAAABcHO\nJVT1tqdjx2snAABAcW62QbFeWTcotmMotlwduys5V9YeWHv+6vk2IW0ebP6gh4FkDwCAfhDs\nXIKXh5e3l7epwGTH4olatcp6/Zr9a579+tnLOZeVry3qt5g/dH77xu3LVysAAHBVNGxchTLN\nLievHB27cgW7Hw/9OGjOIGuqE5HDZw5HvR/1TdI35aoTAAC4LIKdq1Cm2ZW9Y3f1quTliZRt\nKPZS9qWn5z9dYC6o6l11xagVZz84O23gNB8vH1OBacj8IUt/WWp/3QAAwGUQ7FyFEuzKPsdO\naddJ2Tp2setjz189LyLzhsx75J5HgqoHje89ftOrm/x9/c0W8zNfP7M9Zbt9ZQMAANdBsHMV\ndgc7mx27C1cvzP1proh0bd51cPvB1uOdwzt//z/fK327QXMGnbx4stxFAwAAV0KwcxV2B7vA\nQBtXfrHzC2WEd1L0pBKnujTr8uXQL0Uk61rWoDmDrudfL0fFAADAxRDsXIXy8gnVO3YWi+Xr\nhK9FpPUdraPCo26+YHD7wa/2eFVE9p3aN+bbMeWoGAAAuBiCnatw0By7PSf3HD9/XESGdRp2\nq2vee+S9TmGdROTzHZ8v2b2kjAUAAABXQ7BzFfYFO4NBatS43WUr/7tSRDwMHo/d+9itrjF6\nGr8d8W0d/zoiMmrJqMNnDpe1aAAA4EoIdq6iKNiVeR+7S5dERKpXF6/bbjL9/f7vRaRjk47B\n1YNvc1mDGg2WDF/iYfC4lndt0NxBV69fLWMZAADAdRDsXEV5O3ZleZ/YiawTv2f+LiJ9W/e1\necOHWj40MXqiiBw5e+SZr5+xWCxlrAQAALgIgp2rUIJdtim7jNcrHbvbL4ndfHiz8qFXq15l\nuWfMP2P6RPQRkVX/XfXO2nfKWAkAAHARBDtXUc2nmojkmnLL2Cory/vEtv6+VUTq+Ndpc0eb\nstzTw+AR/1x8s6BmIjJl3RRlOS0AAHAXBDtXoXTszBZzGd8qVpaO3Y6UHSISFR5lMBjKWEaN\nqjW+/5/va/nVslj+f3t3Hh1lef99/DuTyUr2yULCkgRCAkkw1A2RHEAEFUhVWn3sAR6wPkqx\nSH8VDkfFUrTY6qkeWyqW9tfjafWIHE499kehUilqKb+KiBTCTiABskKWSViyJzPPH1ccQtYJ\nmZn7nnver7/u3HMlfLluxA/XdjuWvrf0w4MfuviNAABAcwQ7vVDBTlxeZjdgsCuqLqq8XCki\n0zKmDaqSjMSM7c9sDwsKa7e3L/jDgg/2fzCobwcAAFoh2OnFsKBh6qKhZeBldh0dcvmySL9T\nsV+c/UJdTE2fOthipoydsu2ZbaGBoW0dbYveWbR+x3r2UgAAoH/9HpUBL1JvnhDXRuzq6sRu\nF+l3xO7L4i9FJCwo7JaRt9xEPbMmzNr5450Pv/1wfWP9T7f99F+F//r9//39mPgxN/Gjaq/V\nFl4qLKouOldzrqK+oqK+orahtq6x7krTlYaWhraOtmst17q2HxY8LCggSBUfHBgsIjFhMSIS\nbAlW45qWAEtESISzfWBAYHhwuCuVXG2+2m5vv4nfAgDAAHKSc9bmr3V9eZIvItjphXPEzpVg\np+Zhpd8RuwPnD4jIbSm3Wcw3+ZSnZ0z/93P/nv/b+YWXCnef3J29LnvptKXL71mekZjRz3c1\ntzUfrzheUFpwpOzI0fKjR8uPVl+tHtSv29DS0CANIlLXWHdzlQMA0NOf5c/5ufm3jr5V60I8\niGCnF2pXrLg2FesMdjExvTdobW89UnZERO5IvWMoVWUlZ339k69Xf7j6v//1381tzb/59De/\n+fQ3uaNy89LzModnJkYmmsTUbm+vvlpdWldaVFV0svLk2aqz/YyKJUQkJEYmxkfEW8OtMWEx\nIYEhoYGhvbZUqa61vVUdAXO56bLdbheR+qZ6NS/s/Mi9TGKKDuvzbR49xxcBAL7i1tG3Zidn\na12FZxHs9MK5ecKVsDLgi2KPVRxraW8RkdtSbhtiYREhEb9b9Lsnpj6xdtvaf5z4h8PhKCgt\nKCgtGPAbQwNDs0dk3zLylgnDJ2QOz0xPSE+LSwsJDBliPQAAoC8EO71wrhIb1IhdX2vsDpUc\nUhe3prhnwPnOtDs/+fEnpy+e3npg66enPj144WC3OoMtwWlxaeOTxk9ImpA7MveWkbdkJGYE\nmAPc8qsDAABXEOz04vqInTuC3eHSw+pnjksY55bylMzhmT/99k/Vm8cqL1faGmzNbc2RoZHR\nodHxEfFu/IUAAMBNINjpxfU1di5MxapgZzZLdB+LwdQCu4kjJnpuzCwpKikpKslDPxwAANwE\nzrHTi0FtnqirExGJihJzHw/waNlREbm5g04AAICPItjpRVhQmDpZx5Vg1/+LYsvqytSW0okj\nJ7qxQgAAoHMEO70wm8zq4A/Xp2L7WmB3rPyYushJznFXeQAAQP8IdjqiZmNd3zzRV7A7XnFc\nXeSMINgBAOBHCHY6ol6T5cr5t2qNXV+nE5+oPCEiceFx7FQFAMCvEOx0RL1VzPURu77W2J2s\nPCkiWclZbqwNAADoH8FOR8JDwsWFETu7XerrRfqeij1VeUpEJiRNcG95AABA5wh2OuLiiN3l\ny9LRIdLHVOylK5fUltjxw8e7vUIAAKBnBDsdUSN2V5uv9t+s/9dOnL54Wl1kDs90Y20AAED/\nCHY64uKIndo5IX2M2BVeKlQXmYkEOwAA/AvBTkdcXGPnHLHrdfOECnbBluAUa4p7ywMAADpH\nsNOR8ODBBbteR+zUVOzYhLGee0ssAADQJ4Kdjqhz7BpbGzvsHf0063+N3dnqsyKSHp/u9vIA\nAIDOEex0RI3YORyO/pfZqbNOpLcRO7vDXlxdLCLjEsd5okIAAKBnBDsdUa8Uk4FmY2trRUTC\nwyUoqPtHpbbS5rZmERmXQLADAMDvEOx0RE3FykDBTu2K7XUetqi6SF2MTRjr3toAAID+Eex0\nxBns+j/KTq2x632BXdVZdZGewBo7AAD8DsFOR9QaOxloxK6fYKdG7IIsQaNiRrm9PAAAoHME\nOx0Z1Ihdr2edqJ0TqdZUzjoBAMAPEex0ZOhTsSrYjYkf4/baAACA/hHsdMTFYNfP5onimmIR\nGRvPzgkAAPwRwU5HIoIH3hXb2CjNzSK9TcXaGmz1jfUikhaX5qEKAQCAnhHsdCQ8JNxkMonI\nlaYrfbXp57UT52rOqQumYgEA8E8EOx0xm8xhQWHS71RsP6+dUAvsRGRMHMEOAAB/RLDTl8iQ\nSBG50tzniJ167YT0NmJ3vva8ukiNS3V/ZQAAQPcIdvoSGRop/Y7YDTgVGzssNio0ykPlAQAA\nPSPY6YvaGDuUYMfOCQAA/BbBTl86p2L73jzRzxq78zXnRSTVmuqRygAAgO4R7PRFTcUOuMYu\nMFAiIm6473A4LtReEBbYAQDgxwh2+qKWxw04FdtzHvbSlUtNbU3CiB0AAH6MYKcvair2ctPl\nvhr09doJ5yF2jNgBAOC3CHb60jkVO9ABxf2ddcKIHQAA/opgpy9qxK7d3t7Y2thrAzVi13Pn\nhFpgJyIp1hTPlQcAAPSMYKcvasRO+h60U5snrNbu99WInTXcqg5MAQAAfohgpy/Os4X7WmbX\n11SsGrEbHTvac7UBAACdI9jpS//Brr1drl4V6XsqlgV2AAD4M4KdvkSHRauLXoNdXZ04HCK9\njdiV2EqEBXYAAPg3gp2+qM0TIlLfWN/zU7XATnoEu+qr1Q0tDUKwAwDAvxHs9MU5Ytfryyec\nwa7b5gnnllimYgEA8GcEO31xrrHrdcRO7ZyQHiN2F2ydwW60lc0TAAD4L4KdvoQHh1vMFhls\nsHMeYhfLVCwAAP6LYKcvJpMpKixK+t48oXTbFauCXXhwuDW8xwF3AADAbxDsdCc6NFpE6hrr\nen6k1thZLBIdfcN9tsQCAAAh2OmQ2j/Rz1RsTIyYTDfc53RiAAAgBDsd6ifYqRG7vl47wYgd\nAAB+jmCnO2oqtr6pl2Cn1th1C3ZXm6/aGmxCsAMAwO8R7HQnZliMiKis1k1NjUjfh9gR7AAA\n8HMEO92JCYsRkbqGPjdPdAt2aueEEOwAAPB7BDvdUcGuqa2ppb2l20dq80Rfh9ixeQIAAD9H\nsNMdNRUrPWZj29rk2jWRPqZigyxBydHJ3qkQAADoE8FOd2KHdY7IdZuNtdnE4RDp43TikTEj\nzSaeJgAAfo0ooDvOYGdrvGHETu2cEJG4uBvaqxfFssAOAAAQ7HTHGexqr9V2vV/7zVfdpmLP\n15wXkVRrqscrAwAA+kaw053rI3Y3rrHrNdi1tLdcunJJ2DkBAAAIdjoUG9Z7sLN981XXXbEl\nthK7wy4iqXGpXqkOAADoF8FOdyJDI4MsQSJS23DDVGyva+zUPKyIpMSyxg4AAH9HsNMj6zCr\niNRcrel6U03FhoZKWNj1m7x2AgAAOBHs9MgabpU+Rux6PcQuwBwwKnaU18oDAAD6RLDTIzVi\n121XrFpj131LbO15ERkRPSIwINBb1QEAAJ0i2OlRXHiciFRfq+56U43YdTvETq2xS4tL81Zp\nAABAvwh2ehQfES8i1VddCHa154VgBwAARIRgp09qxM7WYFNHmSg9g11re2tFfYWwcwIAAIgI\nwU6f1Ihdh73DeZSd3S719SI3HmJ3wXZBJT9G7AAAgBDs9CkhMkFdVF2pUhd1ddLRIXLjiN25\n6nPqgtOJAQCAEOz0KT48Xl1UXe0MdtXfLLe7IdjVdAa7MXFjvFYbAADQLYKdHl0fsfsm2Dlf\nOxEff72ZCnZBlqARMSO8WR4AANAngp0eJUYmqgvnVGyv7xMrrikWkZTYFLOJ5wgAAAh2uhQX\nHmcxW0Tk4pWL6o4z2HU9oLi4ulhExiaM9XJ5AABAnwh2emQ2mdXG2EtXLqk7zjV2XadiVbBj\nSywAAFAIdjqlZmMvXr5hxC48XEJDOxvUXquta6wTkbHxjNgBAAARgp1uJUcnS4+p2K7zsEXV\nReqCYAcAABSCnU4lRSWJiHqxhHwzFdt1HvZs1Vl1wRo7AACg+HCws9lslZWVdrt94KY+SAW7\nqitVHfYOEamqEhFJSLjeQAU7k8nEiB0AAFB8LNgdO3ZsyZIl6enpoaGhVqs1OTk5ODh41KhR\nixYt+ve//611de6kpmLb7e1q/0TPEbszVWdEZET0iLCgME0qBAAAemPRuoBBWLFixdtvv+1w\nOJKSknJzc61Wq4jYbLaysrLNmzdv3rx5/vz5W7duDQwM1LpSNxgZM1JdlNeXJ0cnqzV2XQ+x\nO3PpjIhkJGZoUBwAANAlnwl2v/3tbzdu3Hj//fe/+uqr3/rWt7p9evz48fXr12/duvWNN954\n4YUXNKnQvZwvkyirK8uKv6OxUaS3EbtxieM0KA4AAOiSz0zFbt68OTMzc8eOHT1TnYhkZ2dv\n2bIlLy/v448/9n5tnuAcsSu1lV7qPMxOEjtfSCHVV6ttDTYRyUzM1KA4AACgSz4T7I4dO3bX\nXXdZLH0OMZpMpmnTph09etSbVXlOfHh8aGCoiJTWlVZVfXPzmxG705dOqwumYgEAgJPPBLuc\nnJz9+/d3dHT002bfvn05OTleK8mjTCaTGrQrqS1xvk/MGexOVp5UF+OTxmtQHAAA0CWfCXYL\nFy48derUt7/97V7H5AoLCxctWvT555/PmTPH+7V5SGpcqoicrz1/sfOU4utTsSrYhQSGpFpT\ntSgNAADokc9snvjhD3949OjR3/3udzt37hw1alRKSkpsbKzJZKqrqystLT137pyIPPjgg6tX\nr9a6UrdRL4E9X3P+m5nY6+fYnag4ISKZwzMDzAGa1AYAAHTIZ4KdiGzatOkHP/jB66+//sUX\nX3z11Vetra0iEhAQkJCQsGDBgqVLl06fPl3rGt1JjcZVXa0qt18ViYiIuP6i2BOVJ0QkOzlb\nu+oAAIDu+FKwE5FJkyZt3rxZRBwOR3V1td1uT0hIMJt9ZkJ5UJzvCjtXUyyS6xyuq2+sL6sr\nE5GJIyZqVRsAANAhHwt2TiaTKaHrC7aMKD0hXV2UXjkjkutcYHek7IjD4RCRnBEG2SkCAADc\nwphjXcaQkZhhMplEpKqlULrsnDhcelhd5I7M1ag0AACgR746YtdTfX39PffcIyKHDh1y/bva\n29t37NjR1tbWT5uDBw8OtbhvXL0qM2eKiHz2mUREDNA4PDg8OSq5vL78ivmkdNk5cajkkIjE\nR8SPih3lrsIAAIABGCfYdXR0HD58eLDfVV5evnz58qampn7aqNgXEOCG/adHj8rXX4uIfPWV\n3HvvwO0nJE0ory9vDj0uXUbsDl44KCLfGt3LGzgAAIA/M06wi4yM3L1792C/KyUlpby8vP82\nX3zxxdSpU90S7GJiOi+cZw73L2dEz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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": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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w4ddu7cqfGAQoBiB3woR+yMjbnmAACtERQUdPHixa+++qpGjRozZ85MTU3lnUgT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\nIDU1tcKSrKysffv2NWrUqFWrVrJ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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": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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198cdeuXV+7affu3YsXL+7bt2+VbQMAoBKShF12dvbvfve7d999d+jQoUVFRfuP\nr1u3bujQoVu3br3nnnuqeCEAABWS/M0Ty5Yt69Chw/z585955pnvfve7LVq02LJly8aNG0tL\nS1u3bn3FFVfsv2ejRo0KCgqqci0AAN8qedjNnj07hNCkSZMQwo4dO9atWxdCaNSoUQhh165d\na9as2X/PZs2aVdVMAACSSR52H3/8cTXsAADgMCW/3AkAABlB2AEARELYAQBEQtgBAERC2AEA\nRELYAQBEInnYbdmy5SC3vv3226kbAwDAoUsedl26dJk+ffo3j+/Zs2fMmDEnnnhiFawCAKDS\nkoddq1athg8fft55533wwQf7Dy5durRHjx6jR48WdgAANUTysHvttdfGjRu3cOHCLl26PP74\n4//4xz+uueaaU089taSkZNKkScuWLauGlQAAJJX8I8VycnJuvfXWCy+8cMSIET/72c+OOuqo\nL774YtiwYRMnTmzVqlU1TAQAoCIq+q7YBg0atGjRIoTwxRdfHHHEEfn5+c2bN6/KYQAAVE6F\nwu5Pf/rT9773vRkzZtxwww1FRUWDBg268cYb+/Tp8/rrr1f1PgAAKih52A0YMODyyy9v1arV\nsmXL7rvvvo4dOz799NPTpk3bsGFD7969b7rppmpYCQBAUsnDbunSpbfffvtrr7120kkn7T94\nySWXvPXWW+edd97vf//7qpwHAEBFJX/zxGuvvdalS5dvHm/evPl//dd/Pfnkk1WwCgCASqvQ\nBYq/7aa5c+c+++yzKd0DAMAhSv6MXQjh/ffff/bZZ7du3XrgwdLS0kcffbS4uPihhx6qmm0A\nAFRC8rBbtWrVgAEDtm3bVu6t11xzTaonAQBwKJK/FDtmzJjPP/988uTJ8+bN69Chw0UXXbR8\n+fIFCxb069dv4MCBkyZNqoaVAAAklfwZuxUrVvTs2fPqq68OIQwfPnzx4sV9+vQJIfTs2TMv\nL+/xxx//6U9/WuUzAQBIJvkzdp9++mmPHj3Kvs7Pz3/llVdKS0tDCI0aNbrgggumTp1atQMB\nAKiY5GHXrl27Tz75pOzrbt267dixY+nSpWXftm7deuXKlVW4DgCACksedr169ZozZ868efNK\nS0tbtmzZtGnTGTNmlN20fPnyhg0bVvFCAAAqJHnYjR07NicnZ/DgwU888UQIYeDAgffff/+w\nYcMGDhw4b968wYMHV/1IAACSS/7mibZt265YseLBBx9s06ZNCGHChAnvvvtuQYAICEwAACAA\nSURBVEFBCGHQoEHjxo2r8o0AAFRAhS5QfPzxx//xj38s+7p58+bLly/ftGnTUUcd1ahRo6rc\nBgBAJVQo7L6p7Nk7AABqjvLDbsWKFRU/Rdll7QAASK/yw65v374VP0UikUjRGAAADt3BXopt\n0KDBOeec07p162pbAwDAISs/7G699dZZs2YVFhY++eSTffv2HTZs2NChQ9u1a1e92wAAqITy\nr2M3bty4tWvXrl69evTo0Tt27PjVr37Vvn37Xr16/e53vysqKqrmiQAAVMTBLlDctWvX0aNH\nv/HGG2vXrr3rrrtCCCNHjszLy+vWrduYMWPefPPN6hoJAEByyT95IoSQl5c3cuTIV1555b33\n3rv33nvr169/++23d+3a9bjjjvvtb39b1RMBAKiICoXdfm3btr3xxhuXLFmyadOmyy67bO3a\ntT55AgCghqj0BYpffvnlWbNmzZw5c8OGDVlZWZW6MAoAAFWnQmGXSCReeumlmTNnzpo1q7i4\nODs7Oz8///rrrx86dKiLoQAA1BAHC7tEIrFs2bKynispKcnOzu7Xr99NN900dOjQli1bVttE\nAAAqovywe/HFF2fNmjVr1qz333+/Vq1ap59++m233TZkyJDmzZtX8z4AACqo/LDr169fCKF+\n/foXX3zxkCFDmjZtGkJ455133nnnnW/euX///lU6EQCAijjYS7Gff/75n//85z//+c8HP4XP\nigUAqAnKD7vbb7+9emcAAHC4yg+70aNHV/MOAAAOU+UuUAwAQI0l7AAAIiHsAAAiIewAACIh\n7AAAIiHsAAAiIewAACJR/nXs2rRpU/FTbNq0KUVjAAA4dOWHXbt27Q78dtOmTcXFxSGEJk2a\ntGnTZtu2bRs3biwtLT3ttNO6dOlSDSsBAEiq/LB78cUX93+9YcOG/Pz800477d577+3du/f+\ng9dee+3ixYv/4z/+ozpmAgCQTPK/sbv55puPOOKIefPm7a+6EEL79u1nzZrVrFmzsWPHVuU8\nAAAqKnnYLV269PTTT69Xr97XjtepU6d///5LliypmmEAAFROhd4VW1JSUu7x4uLiI444IqV7\nAAA4RMnDrk+fPs8///zTTz/9teN//etfn3vuuZNOOqlqhgEAUDnlv3niQHfdddfChQuHDh36\n4x//+Oyzz27ZsuUHH3zwzDPPzJw5s169euPGjauGlQAAJJU87Dp37vzMM89cd911Tz755JNP\nPrn/eN++fe+7775OnTpV5TwAACoqediFEE4++eSXXnrp1VdfXbt27ZYtW9q0adOpU6cePXpU\n9TgAACquQmEXQsjKyurVq1evXr2qdA0AAIesQmFXUFAwa9asTz75pNxbFy5cmNJJAAAciuRh\nN3Xq1CuuuCKEUK9evTp16lT9JAAADkXysJswYUKDBg3mzZt3yimnVMMgAAAOTZLr2CUSiaKi\noksvvVTVAQDUcEnCbs+ePXv27Kldu6LvsQAAIF2ShF1ubm7//v1nz5792WefVc8gAAAOTfKP\nFHvsscfq1at32mmnzZw5c/369Z9+QzWsBAAgqeSvsXbv3n3v3r1ffPHFhRdeWO4dEolEqlcB\nAFBpycNu2LBh1bADAIDDlDzsHn744WrYAQDAYUr+N3YHMXfu3CuvvDJVUwAAOBwVuo7J+++/\n/+yzz27duvXAg6WlpY8++mhxcfFDDz1UNdsAAKiE5GG3atWqAQMGbNu2rdxbr7nmmlRPAgDg\nUCR/KXbMmDGff/755MmT582b16FDh4suumj58uULFizo16/fwIEDJ02aVA0rAQBIKvkzditW\nrOjZs+fVV18dQhg+fPjixYv79OkTQujZs2deXt7jjz/+05/+tMpnAgCQTPJn7D799NMePXqU\nfZ2fn//KK6+UlpaGEBo1anTBBRdMnTq1agcCAFAxycOuXbt2n3zySdnX3bp127Fjx9KlS8u+\nbd269cqVK6twHQAAFZY87Hr16jVnzpx58+aVlpa2bNmyadOmM2bMKLtp+fLlDRs2rOKFAABU\nSPKwGzt2bE5OzuDBg5944okQwsCBA++///5hw4YNHDhw3rx5gwcPrvqRAAAkl/zNE23btl2x\nYsWDDz7Ypk2bEMKECRPefffdgoKCEMKgQYPGjRtX5RsBAKiACl2g+Pjjj//jH/9Y9nXz5s2X\nL1++adOmo446qlGjRlW5DQCASqhQ2H1T2bN3AADUHIf1WbHptXXr1g8++KDs2isAAGRY2K1Z\ns+bSSy/t2LFj3bp1Gzdu3KpVq9zc3DZt2gwfPnzJkiXpXgcAkE6H+FJsWlx77bWTJ09OJBIt\nW7bs3r1748aNQwhbt24tKSmZPn369OnThwwZ8uSTT+bk5KR7KQBAGmRM2N1///2TJk06++yz\nx48fv/+TMPZ7880377zzzieffPL3v//9yJEj07IQACC9Mual2OnTp3fu3Pm///u/v1l1IYQu\nXbo88cQTp5566rx586p/GwBATZAxYbdmzZq+ffvWrv2tTzFmZWX169dv9erV1bkKAKDmqNBL\nsQUFBbNmzdr/ibFfs3DhwpROKl/Xrl1XrFjx1Vdf1apV69vus2zZsq5du1bDGACAGih52E2d\nOvWKK64IIdSrV69OnTpVP6l8l1xyyTXXXHPuuefefffdJ5xwwtduLSwsHDNmzHPPPTd27Ni0\nzAMASLvkYTdhwoQGDRrMmzfvlFNOqYZB3+bqq69evXr1gw8+OH/+/DZt2rRt27ZRo0ZZWVnb\ntm3btGnThg0bQgjnnXfeTTfdlMaRAABplCTsEolEUVHRiBEj0lt1ZR544IERI0bcc889S5cu\nfemll/bs2RNCqFWrVrNmzS6++OIrr7yyf//+6d4IAJA2ScJuz549e/bsOchbFqrZiSeeOH36\n9BBCIpH4+OOPS0tLmzVrlp2dMW8BAQCoOkmSKDc3t3///rNnz/7ss8+qZ1AFZWVlNWvWrEWL\nFtnZ2VOnTvWxEwAAyZ/reuyxx+rVq3faaafNnDlz/fr1n35DNaw8uCuuuGLatGnpXgEAkGbJ\nX2Pt3r373r17v/jiiwsvvLDcOyQSiVSv+rqSkpJVq1Yd5A7FxcVz584t+3rw4MFVvQcAoAZK\nHnbDhg2rhh0H9+yzz/785z8/yB3mz58/f/78sq+rITQBAGqg5GH38MMPV8OOgxs6dOjzzz//\n6KOP1qtX77rrrmvQoMGBt95yyy19+vQZMmRIuuYBANQENeXtrgdXv379P/3pT4MHDx4xYsQT\nTzzx2GOPnXrqqftvveWWW3r06HHzzTencSEAQNqV/+aJrKysrKyszZs37//6IKpt67Bhw1at\nWtW+ffv+/fvfeuute/furbYfDQBQ85X/jN35558fQij7ALGa8Dd2+7Vu3XrRokX33nvvbbfd\nNn/+/GnTpnXp0iXdowAAaoTyw+6pp57a//XMmTOra0yFZGVl/frXvx44cODFF1/cq1ev8ePH\nH87ZNm3adNZZZ5V9iMW3+cc//hG8JwMAqPEy42/svunEE0989dVXb7rpphtuuOFwztOiRYuR\nI0fu2rXrIPdZvHjx9OnTq/NFZwCAQ1B+2K1YsaLip+jTp0+KxlR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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": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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3PhknLlMGAA3NxgYqKq68Ykxiw4vsD7uvfrpNcfjhvpG3Wy77S4x+I6lqrvU0FE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UmYmIiIjMBoudnHz9NbRaAAgOxskLJwG0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\nqKgYe53yvn37pk2blsn42SYs/6rH8PBw0oOklICc5QTktFuzZ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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", " # strictly speaking, we should start each simulation with\n", " # the state obtained in the last iteration;\n", " # y0 = out3[nrow(out3),]\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": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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GcVgefYEfZPAAAAABEh2FnF/BZbebALBMyOBgAAAA6QHKfcz549e/LkyRq/+cyZ\nM3GdjBBYigUAAADhkiPYDR06dM+ePfPmzfN4PDk5Oe3atbN6RmYJvI4dIdgBAAAAESVLsCss\nLHzppZeGDRs2dOjQ/v37FxcXWz0js8yfYydffsU5dgAAAEDJdY7d9ddf36VLF6tnIYb569jh\nHDsAAABQSKZgR0RFRUVut9vqWQggtmOHpVgAAACgZFmK5RYsWGD1FMRAxw4AAACES7KOnWOI\n3TyBYAcAAACEYGcVsR07LMUCAAAAIdhZxXzHTt6lQ8cOAAAACMHOKtg8AQAAAMIh2FkDmycA\nAABAOAQ7a2ApFgAAAIRDsLOG+aVYdOwAAABAAcHOGuaXYnGOHQAAACgg2FkDS7EAAAAgHIKd\nNcx37OQjINgBAAAAIdjZgYFz7BRJDkuxAAAAQAh2VjHZsVMEO3TsAAAAgBDsrGIy2CladMb2\n1QIAAIDDINhZw+TlTtCxAwAAgHAIdtYwuSsWwQ4AAADCIdhZA+fYAQAAgHAIdtbDrlgAAAAQ\nAsHOGmI7dtg8AQAAAIRgZxUsxQIAAIBwCHbWwOYJAAAAEA7BzhomL3ei+BEEOwAAACAEO6tg\nKRYAAACEQ7CzBpZiAQAAQDgEO2sg2AEAAIBwCHbWEHuOHa5jBwAAAIRgZxVcxw4AAACEQ7Cz\nBpZiAQAAQDgEO2uIDXbo2AEAAAAh2FnF5Dl2uFcsAAAAhEOwswbOsQMAAADhEOysYXIpFnee\nAAAAgHAIdtYQuxSLYAcAAACEYGcVLMUCAACAcAh21sBSLAAAAAiHYGcNXMcOAAAAhEOws4bY\npVgEOwAAACAEO6uIXYrFOXYAAABACHZWwa5YAAAAEA7Bzhoml2KxeQIAAADCIdhZD8EOAAAA\nhECws4aoXbEu1zl/BAAAgIYMwc4CoZCwYOd2E2HzBAAAABARgp0lFEnOzOYJBDsAAADgEOws\noAh2Zs6xY8EOS7EAAABACHaWUDTYsBQLAAAAQiDYWQAdOwAAAIgHBDsL8CTH9rQa6Lch2AEA\nAEA4BDsL8GCXknLOH7VTLMUi2AEAAAAh2FmC99tSU4lwjh0AAAAIgmBnAeEdOwQ7AAAAIAQ7\nS5gPdjjHDgAAAMIh2FlAsRRrZvNEejoRgh0AAAAQEYKdJXiLjgU7A7AUCwAAAOEQ7CygWIol\n/auxWIoFAACAcAh2FjAf7NCxAwAAgHAIdhYIX4rVm8z4COjYAQAAAIdgZwHF5h3qymUAACAA\nSURBVAnS37Hz+6UHaWnnDAgAAAANGYKdBUSdY5eSIkVDdOwAAACAEOwsITzYoWMHAAAAhGBn\nCfPn2LHvT00V37Hbvp3WrRM2GgAAACQSgp0FeIwzuSs2JUUaQVSwO32a+valIUNoxQoxAwIA\nAEAiIdhZQFTHTvhSbEkJVVUREa1dK2ZAAAAASCQEOwuIuo5daqrgjt3hw9KDQ4eMD7J7N732\nGp0+LWRGAAAAoEOa1RNoiGy7eeLECemBmVh200303//Sp5/S0qVCJgUAAABaoWNnAfPXseOb\nJ8R27M6cUT7Q6+hR+u9/ibCYCwAAYAUEOwuIWooV3rHjee7XXw2OUFpaPwLv/wEAAEBiINhZ\nQODmCbEdu8pK5QO9jh6tf8zP2AMAAIDEQLCzgKhz7Ph17ER17HieY3tjDSgvr398/LjZ+QAA\nAIAuCHYWsO117Hiw8/vJ4zEygnzXxcmTAqYEAAAA2iHYWSB8KdYmHbvq6vrHtbVGRqioqH98\n6pTZ+QAAAIAuCHYWCO/Y6RWnjp18BdZ8sDO8tRYAAACMQbCzkt3uPFFTE/mxdvJdFwh2AAAA\nCYZgZ4Hwjp2xYCf8OnbyMGesY/fLL5EfAwAAQAIg2Fkg/Bw7veJ0HTv5OXZ1dUZGkC/mypdl\nAQAAIAEQ7CwQfrkTO1zHLhAgr7f+jwh2AAAASQfBzgLCr2NHIpp2irVXY5c7kQc7w7evUKir\no1WrTN2+FgAAoIFAsLOA+XvFKnbFkoimnWK3hLGOnXwQUcHujjtoxAi6+mphpxICAAA4FYKd\nBUR17Pg5diSiY6dIcsaCnfwsPcP3JZM7fZqWLyci2rmTvvlGwICiVFbS7bfT6NHn3GwDAADA\nWgh2FhB4gWKBHTshS7HCO3bffVefWb//XsCAosyaRYsW0fLlNHWqmAFFNTj9fnroIRo5kn7+\nWcBoZ87QxIn0f/+vgKGIaM0aeugh2rdPwFB1dfTUU/TMM+T3Cxht+3b6n/+hr74SMBQR/fvf\nNHGimHNMjx+n//N/aOFCAUMR0ccf0/jxtHevgKE8Hpo2jZ59Vkz9t22jCRNo/XoBQxHR668L\nrv+CBQKGItRfP9vW3+5CEMvcuXOJqLKyUtSAP/wQIgoRhUaNkh7s26dvhBtuCBGFrrgi9M9/\nSiMYm53fHzpxQjkr9r+33tI9mtcr/WxWlvTA4zEyK7kXXqif0oQJpoYKBEJvvx1auDAUDJqd\nVSgU6tNHmlX79gJGe+SRkMsVGjEiFAiYHeqtt6SJjRghYGK33iqN9tlnZoc6cCCUnh4iCl10\nkYB/gqeekib27LNmh/L7Q+3ahYhC2dmhY8fMjrZqlTSx224zO1QoFLrpJmm0Tz81O1RZmVT/\nrl0FvMymTpUm9txzZoeS1//oUbOjffgh6q8P6m+Mx+Mhog0bNggYSzR07Cxg/l6xil2xZKhj\nFwpR//7UqhW99RaRiI4db9e1bCk9ML8aK/90deCAqaFmz6a77qI//pHefNPkpCgYpC1bpMf7\n95tdjT12jF58kUIhKi6mNWvMzu2DD6QHH398zsq4ATU1tHKl9Pjdd00NRUQrVkjbrnfuFNB8\n5U3E994zO1RJifTSqqmR1v3N4BNbvtzgVb65qipavVp6bP5pLl8u1X/XLtq82exo/Gma7ybK\n679ihdnRFi+WHqD+GjXA+u/YYXY0m0Ows4Dwe8WSoXPsDh6kDRsoFKJly4jCTqozEOx4NOTB\nTr5J1hj5euKhQ6aG4v38efNMjUNEZWXn5OCffjI12uef1+fyjz4yNRRR/XuG10vffWdqqC1b\n6l8G5pcpS0rqH3/5pamhKitp507p8fbtZlex5edumn+afDSPh7791tRQ339PPp/0WODESET9\n+Wt+2zbUXxPUX6841b9jR2rb1uxoNodgZwHzmyeE7IrlDbD9+4nCOnbya9ppFB7szHfsysrq\nHx87Znwcr7e+x7Z5s9nbnSnOEtuzx9Ro8vaVPP0YUF1NBw/W/3HbNlOj/fhj/eO9e83GdPlo\nW7eaGuq//63/JBMMinyaJifm9Z7TYzY5mvwDw+7dZvsfSVF//ktqDOpvQIOq//XXU2kpNWtm\naij7Q7CzgKiOncldsXwBkQWmeHTszAc7eZfu5Enj45SW1n/4CwbNbrCVx00is9sU/vvf+sc7\nduh+Mcjt23fOj8tHNqC0tP5xMEi7dgkbjffbjFGc/izwae7ebeps9P37z/lxgU8zGKTdu02N\nFr/6C3xh7NmD+seG+hvAnmaXLqYGSRbJF+xOnDixa9cuf6RXX3l5+eHDhxM/Jb0EXqDYTMeO\nX/L3zBkKBpXBzkzH7rzzpAcmezxVVdINZ9mAHo/x+88qstcPP5ia2JEjREQuF7VqRWT65D/W\n/3O5iMJabnrxmaSnE4W9AejFWrlpadIfzTQmy8ulF4PbbXYokj1NNjeBT9PrVaZ2A0OR0Kcp\npP6nTkmfsoRMjD9NNjcho6H+2qH+evH6d+hgakrJIpmC3ZYtW3r27NmqVasLL7ywbdu277zz\njuIb7rzzzvPPP9+SuekSvnlCb79Nca9YAyOQrJ0WCNCvvwpYiuXRsEUL5X/CGJafiKhHD+nB\nqVMGh+JpKTOTiGj7djPzkibWrBl17kxk+uQ/diS9+GLpj2ZiCv9cc/nlRKZbiaxol10m/dHM\naHxibLTTp01dDYEVPC9POkybuX5KKCTNjT9NM6PxVwIbzeSFXdho8ZhYRYWpsxFYxVB/vUMR\n6q9/NLETc/zZdUzSBLvS0tI+ffrs2LFj8ODBw4YNq6ioGDNmzJw5c6yelxECl2LNdOzkqaui\nQkDHjo8gqmN39Kj0oFs36YHhG4uxKJaSQn37EpleIzh+nIioVStq06Z+cGN+/VX6h+jXT/oK\n/9RrAKtYSgpdcQURUVmZqYVdNlqXLlJSN9OY5P+UffpID8yMxgreujW1a2d2qPJy6aXOXhgm\nR2NP0+WSnuahQ6auHM6e5kUXSacEof4x2bb+/PxgIU8T9deL1791a+ODJJGkCXZPPPGEx+NZ\ntWrV2rVrP/zww7KyssLCwocffniXyfMLrGCTe8Uq7uvKYxlbxRMS7Ex27PhvI+9mGQ52bKgW\nLaSMuHu3qcRz4gQRUcuW0mHCTLDjP3vFFdLrwcxSCHuazZtTx45ERB6PqRMT2WE6P1/6mGtm\njZj/U7LEKWS0/Hy64AIicx1TPrHLL5fqb2ZirGJNm0qn8vh8xnf8hEJxeZqov0Zi68+DdVGR\n9AD1Vxen+rOTZxwvaYJdSUnJ9ddff8MNN7A/nnfeeR9++KHL5Xr00UetnZgBAm8pZqZjp7hL\nBI9lublE5s6x40uxJjt2rDFGRBdeKD0wvH7H8k2rVtIRp7q6/lfdALbv5LzzpMNEVZXxZ8oP\nfG3bUn4+kbkDK0ucvJVIsjVQvX75RXpJtGpF7AQHM+ev8n9KvrBifrSWLaWJHT9u/IxvVjEi\nOv98adOPmYkJrH9FhfQ7yJ+m+YkR6q8Z6m94NDvXH8HOXo4cOaI4f65Lly6PPPJIcXHxelF3\nQkkU80uxQs6xkwe7ykrpXTw1lRo1IjIU7PhG2rw8aWImgx37bUxLo8JC6SuGT0xhwa5FC+rU\nSfqKmTM2WLBr0UKKYiQLLnrJjzjmj188cfIVB8P5lW+aFtKYZPXPzqZOnaTXhpnR2Nz4xAIB\n440B3tEU+DTjVH8zLww2sawsKiwUUH82mrz+hl//qL/h0VB/vRPLyqLGjY0PkkSSJtgVFBR8\n/fXXii9OnDixbdu2d9999y+Gd0taQdSdJ0zuipUHu6oqKdhlZgpYis3MlH5/TC7FstDTokX9\nZYcM/zuzXRctWkhrlGQi2IVC0opw8+b1F3bh+UwvfmDlR0PzrUR54jQ8Gp8YH628vP6SMYYn\nlpYmNXQNT8zjka7IKuRp8vePFi2ooMDUUCQL1mLrzyZ28qTxxgyfWGqqdKaEmfqz32vU38DE\nUH+N4lT/BiJpgt2NN974008//e1vf6uUhYVGjRrNnTt33759Y8aMqRByz+GECO/Y6e23CbmO\nnXwbbHiwM/AWHh7shHTsWrak7Gxp/7zhYMdafXl5dMEF0oVFDJ+K++uv0vElL68+2Bk+lY0l\nTpeLmjeXjoZmDqwscebl1R9YDbey+AZk/v4RChnPrzxYE0mjGZ4YP8+yeXPpiE8mOqZsYikp\n9UUzcx1sNlrz5tSqlfQyE/I02cSCQbP1b96cSFz95cHC5MsM9TcwMdTfwMQaiKQJdk8++WRh\nYeHs2bObNm06ePBg/vVhw4ZNnjx55cqVbdu2/c7kHZQSxSZ3npBvg5UHOxahTHbscnKITHfs\neGOfzp75ZzjY8cSTlSWlMcN7FPhycF5e/dmEJoNdkyaUliad/3HqlPEPpryVmJlJTZoQmWgl\n8gOrPCYazk+8/nT2NBeTUYzO7ZianFiTJpSaKk3s5EnjW/n403S7pScr5GnyE4NM/mvK62/y\nPZKNxieG+mucGKH+2sSv/g1B0gS75s2bl5SUTJo0qUuXLkfP7WlMnTr17bffbtOmTbnJm7En\nik12xcqDXXW1MtgZ6Njxc+wyMuwV7GpqpJzatCkRSXusDO9R4MGuWbP63r7hlx6PYnT2iB8M\nGoyJVVXSvxpbuWahR0iwM7/izDumZPqNTR6sxR7x2dP0+w2eyllTI/0KyEcznPjlT9N8/cOf\npq3qL3/Fiqq/wJcZ6q9FstS/IUiaYEdEeXl5zzzzzM6dO3+U39yOiIjGjBmzc+fOn3/+ed26\ndZbMTRcewqy9jl20YGfyHLuUFEpPF7MUGx7sjN3umq/Ss2DH9igY3jwvHy07m7KyiEwEO3b8\nkh9YyejxS544yXSwYE8zJYWaNKnPryZjCpsYG8184mnatP5saJOjsReGyacZsf4m39hSUig3\nV0D92b+mkBeG/Gmar798YmLrL+RlhvobmxjZuP4NQTIFO3Uul6t9+/aDBg2yeiKxxWMp1kDH\nTn432Opq6ZQ78x27jAwiEtCx8/mk/hxb7mTBztiAvM/HVidNXlVYERPZ9AzfEiM88ZDRmBhx\nYiYPrLm59ad7G54Yn5s8P1VXG7yrN3+a8qKZnFj83thMTqxJE0pJERys2QvDfP3l/5pCPtig\n/tonRqi//rkh2EEcxWMpVlTHLivL+OYJscHu1CmpLOw4aGZA3udj6ZCdcX/mjMEDqyImsva+\n4SsnyxOPyTP2FBMzeWBlo7GJNWkixX1jo9XVSa8uxdMUmF+FPE2T+VVRf4ETa9ZMumOmsc8P\nHo9Uf/nEDM8tfvU3ObH41b9pU9Rf61Bk+/o3BM4JdhUVFZdeeumll16q66dKS0vT0tJcqsaO\nHSt2qgJ3xYrq2NXUCNs8wW7GambllJHvyiRzwU5xxOFbKY3t2FKMxk6PExvsjB2/Ik7McCuR\nf2ImIpdLyq9CJibkabpc0mvM5PuH/GnyTXMCn+bp0wbvcRKx/gKjANmv/mJf/wLrzzaNEuqv\nYWJk+/o3BGlWT0CYQCCwZcsWvT/VqVOnzZs3+1V3IS5btmzGjBkmpqYkcCnWTMdOHt3k59ix\nz0aWd+zkF1gyOSDPl2wQ+TUC+GXttFMcWE127OQfTPPyyOWiUMjsgZVNjMUUj4eqqoxclpON\nxj/jNm9Ox48bnBg/sMp7nGS0aGy07GzphSokv8orZng0Rf3Z0/T76ZdfjLyjyN/Y2NxOnBD5\nwiBz9W/UCPU3ODHUX/vE4lH/hsA5wS43N9fYzomePXuqf4Pwq6iIukCx2I4dP8eOjWky2LFf\nobo68nqltV295NvdyVyw4z/FBjG5R4EdJho1klI1O2/D2DHa76fqaqKz5UpLoyZNqKLC4PFL\nseIsP0wbCHZsNPmBlYw+zWgTMzMan5iZYB0InFN/thWmtlbw+/epU0be2NjT5G9FZuof8R2X\njL5/KyaG+uudGOqvRfzq3xA4ZynW7XYPGjQouTZPmNwVa/IcO3nHji/FZmWJ2TzBf4UMr8Yq\ngh2LJtXVRhr7imBn8hoBbDQ2FJ0NdsYuEBB+xDFzmI5HfhIysWhvbAIn9ssvRn4FKiull5Mi\nJhr711TUPx5PU8gLA/XXPhrqr3diZPv6NwTOCXZJxJ67YkVdxy6uwS4YNLLjQRHsTO6xUhxx\nWLDj+wMMDEVhxy8zB9bUVMrOrp8YmUtjivxqbChe//gd8UMhI0WLVn8zT5PfbZk/TTP/moqX\nmdhgIWRiqL/GoQj11z+3eNS/IUCws4A9O3ZsKVZUx45/BDQc7NjvcFaWdKE4vpho4Np47EfS\n06VF4YwM6Tfc2Km4ETt2ZOj4pTj5j8z1//jE2M18hBxY+cTMJE5FsM7IkKKnyafJmKm/YmJk\nrv6sYo0bS/U3MzEKe5pC6s9e9g2t/mZiCuqvXbLUvyFAsLOAqMudmLlXrM93zn80fsHO/E3A\nGPPBTn6emZlrvCmOOPz0EQM3Kw4/4ggJdvKhjI3m80kNSMXTrKoycrszsflVkTjt88bGRlP8\nUxobzetV1p+NVllppP7xeP9Oovob+MVE/Q1Iovo7HoKdBcI3T+iNZebvFau4mklVlRTLzFzu\nJOmCnbFzhOMR7MR27ORDGRstWuIMhYw8Tf5PJuRpstHCn6aT6h9eMfYyC4WM/ELZ9v07fGLs\naaL+MUdD/fVOjBpSsEuOXbGzZ8+ePHmyxm8+Y+xVmUCilmJNduyYjAzyeKiiQppDVpa0T8pA\nx45lQbbcaSbuMNGCHZueLuxH2JkfjJlrBMQ12LHRjBVNkV+zsyk9nbxeU1GMjyZ/mvx6Vxqx\np5mWJq2qk7mnmSz1z8iQ9hgKTJxEdOZM/bYYXRMTVX/F04zHBxvUP+ZoqL/eicnr73jJEeyG\nDh26Z8+eefPmeTyenJycdu3aWT0jUwTeeULRsfvoI5o6lSZOpJEjY4zAG3JNm9Lx4/W5UNRS\nLD/cGI7Z8tvGkyyWGejYhQc7M+cIK45fvDcpMD+xrRjsUs96R5N/Km3alE6cEJl4yMTTlHdM\nbfLGFq3+lZUUDNb/cmmkSJxsNGNvbOrBWi82MdTf/MQI9Y8uierveMkR7AoLC1966aVhw4YN\nHTq0f//+xcXFVs/IFAPBbvNm+v57GjNG6oeFX6CYJbPnnqNNm+jRR3UHOy47Wwp2Bk5lUCzF\npqRQMGg82LHUxT+o8VgmpGNn5lTcaAdWIWsE8iVsvcEu4vuHsWAn9sAaMXGSoYpFO/nPzMQo\nLKYHg/Trr7ovvhUxvx49Kv6FoVe0YN1A6i/kgw3qr3G0pKi/4yXTOXbXX399ly5drJ6FAHqX\nYgMBGjKE/vIXmjdP+kr4BYpZ1CsrIyI6cCB2UuQNOcVvb1aWdEHzYNDgeXsseqamSr+Khm/J\noLhts9ilWL7iYOBmbux6K+EdO8NHnIijGTgahj9Nw+8fKhMzPJp8Ymw0w89RPhr/KCLkaYpt\nTAp8mnabmGLFn2xcfwMTQ/2dXX/HS6ZgR0RFRUVudhRPZnrvPHHkiJRyfvjhnBHCL3fCvs3n\ni32HBt6x48mJ4W+TpH81Vt6xI3PnsXm90u+2kI4di2LhwY59MNWFXyGZHyaysqQDq4ELu7Dn\nwq/DQuYuExPX9w+bdCzC34rMj5aSIl1+gsw9TZsHa7H1D4/pqL/6aKi/3olR3OrveEkW7BYs\nWLBs2TKrZ2FWeMdOvW/Er8rBQ1K0pVie52LGApWOneFgJ+/Ykbm7U/MsInAplh+8yMSOrfDE\nQ6YPrOHHaBIa7IS8f4g9sLI9fT6f7stNRwx2JhsDjRpJV94i+9VfyBtb+Dsu6q9lKEL99c8t\nKerveEkW7JxB7zl2PEywX7ZQSPp+xVJsbW19FIt5vIgW7Bo1EtaxM3OtOB7s+PR4LBPSsTPc\n2I/HJ+bwxGNgtFAowtMUeGDNyZFebEIOrIYP0+FrNHS2aEKCtfn6x2kpykz9o73jGhgtYv0F\nfrBB/fVOjFD/WNCxU1NTU7N9+/ZNmzbFbzYNBO/PaTzHjr/Lsoac/MflHTt5mNMe7AQuxbKO\nHQ927Jas8p0Z2oUHu7Q0aTOB4WAn79gZPpUtYseOHQ0NL8XKD6z8ZGG9x6/aWumFEX7ENzwx\n+WgpKdJTFtixMDCa2GAncGIR68/+NYW8saWkSI9tWH+TTzN+r3/UX+/EGkj9HU9TsDtw4MDN\nN9/ctGnTHj169OnTh4imTJlyxx13HDlyJM7TcybDHTt2cwi+pyG8Y8cJ6djp2hjr80m/2Hwp\nNj+fiOjECSO3OwsPdnQ2mekNdqGQVBl5sDO8lZX/1+WjseOXkO0Ohu+xq5J42MULRI0mJL8a\nfmPjL+x4BzuB9a+u1r3HPGH1F/g0xbZyUX+9E0P91UdDsDvH0aNHr7nmmmXLlhUVFQ0cOJB9\nsUWLFu+9994VV1xx9OjROM/QgfQGO7bESWeDnXzvhbxjJw928scRRevYNWok7YolnR07vhuD\nB7s2bYiI/H46cULHOAwPSfxAQ2d/M/UGu7o6qWLyq1PGYynQtkf8UCj2ZpqIo6Wnk3yrks2f\npm0nZng0Rf1N9l/jF6zjMTHUPyLUH8FOi9jBbvr06QcPHnznnXc2bNhw7733si/+7W9/W716\n9bFjx6ZNmxbnGTqQ3sud8GDHrmAkX4qN1rHjPxIN/wjFrwDMNG5scCmW/xf5Uuz550sPDhzQ\nMQ7Dj3fyjh37zdR7ujH//ohLsQI7RkKOOG63FED1RjGViZHRp6k4FBp+muGj8YkZS5x07r+m\nwIllZ0sfbAy/sYVPjIw+zWSpP+tYo/7RoP52q7/jxQ52q1atGjhw4J133qn4+tChQ4cPH752\n7dr4TMzJ9F7uRBHs5Eux8sudsL9lYt7plYc2lWCnq38e3rFr31568PPPOsZheBAx37HjeTf8\nUEiClmLFHnGMjaZ+YDU2mnwoMvr+wV+ZQiamkl/1vnlQlKdpsv5COhYRXxgNpP7Gnibqj/pH\nFLH+jhc72JWXl0e7LHCbNm1wmp0BKpc7+eEHevNNZassWsdOsRQr79LF7Njx/0STJvVrr5mZ\n5HabXYrlHbtOnaTkunu3jnEY9tublqb8NEn6gx0/FMqXYnljTOypbHqpHFgNd+wi5ldjTzNi\n4jTcYxC74hP+Nun1nvPZRvtoQt4/ItZfbLA2Vv+IUcDkC4ME1V/lg43YjjXqrzK3Blh/x4sd\n7C655JIf+IVxz1VSUnLhhReKnpLzRTvHLhikwYPp3nvr7zDB8JTGHkRbijUW7Nzu+q4Ye2By\nKZZ37LKzid3Ud/t2HeMwrJGWm1t/gSUyuhQbsWNHRhszKodpjyd22SOOFjFYiD2wGhtN7MQi\nJk47jBa//Cp2YiZbKULWyNRjirGiie0Yxe+FgfrHHIqSpP6OFzvYjRgx4ptvvpk2bVrw3J11\n06dP//7774cMGRK3uTlWtGBXVSXdgGvjxnO+n8eFYJD8/shLsXo7dnyZ1e2uP49NEexMLsUS\n0aWXEhF9/72OcRj228sPf4yxjh0PdvKOHZl+/xZ4mE5Ax07gxIRE4fR0qbNrbGIZGfV9ZYrP\n07Rh/U12LOSjma8/P/KQif5TPDpGqL/e0Rpg/R0vdrCbNGlSv379Jk+e3LVr11dffZWIxo0b\nd/nllz/xxBPdu3efMmVK/CfpNNGuY8d/LfmF6xh558zrPWcpNlrHTvs5dmlpymAnalcsEV1+\nORHRzz/rvkwx79jJmdw8oQh2Zt6/09LqV5zJ6PGLX9LThkuxKhNTvDiNTYzMxcSIQ4kdzYZv\nbAInZnK0iO+4okaz+esf9VcZipKn/s4WO9ilpqauXbt21qxZXq9348aNRPTaa6/t37//iSee\n2LBhQya7aCzoEa1jx1+yiuwiD1geT33HTnGvWF3BTt6xY7eIoLN3dxW1K5aIioqkB5s36xiK\nzgY7flxgjHXs+HknEYOd2GCh66DDr8Mi5PiVsFai368vW6u/sRmLidHqr2s0/iuTXMEuEBBZ\nf4GLd3pHS2T9Bb7MUP+Ikq7+zqbpAsXp6ekTJkw4cOBAZWXljz/+eOrUqfLy8qeffjpH8cYL\n2kS73AmPICrBTtGxi7YUGzOTyTt2LVtKj887j0joUuxll0kPtm7VMRSdPaxEXIo1fI5dxGAn\nNljoionRTv4zdmCNOBq/PYbAYEE6i5aAjoWxN7Z4TIziGeyM/WtGO3lcYP35xCx/YRDqr39i\nDbP+zqbvXrGNGze++OKL885eIaOioqK0tDQOs3K48I4dy2o8GykuLxwt2Ck2T8i7dDGDnbxj\nd8EF0uO2bYmELsXm5VFBARHRTz/pGIrOJiTFBweTmycELsXGNfGw45eQFU9+Ko/Y/GrswJqA\n+guZmLH6RwzWbrd0Hzw7vMyE1D/8Ji6E+msYilB/PRJQf2eLHew6d+7cv3//ffv2hf/VG2+8\nUVhYGIdZOVy0c+x4NlIspCqCXbTr2Cm+TZ28Y9e9u/SYPRC4FEtEnTsTEenN/yodO8UV+2JK\nZLATmHiqq2Nc3TDiaGlp51yrncw9zYhHfNJ5YFVvTBpLnNEmZnnHLj39nF0dZC6mR3xh6J1b\ntPrbdmKov7UTayD1d7bYwW7v3r3r16/v1atXcXFxAibUEEQ7x45nI0Wikv+R35KV/bjLJQ0S\nDBrv2I0aRRMm0F//SqNGEck6duaXYunsZYrLynQMRWd/dSOeY0c6m3b8F1txOqhtjzhsYsGg\nvrMJI36UJ3Ofv+O64sNGE9uxEJI42cT8fn2fHyK+MEhoY8Zk/eP3wSYeLwzUX2U01F/vxCLO\nzcE0LcXefvvteXl5N91002OPPRYwcEd3OFe0YKelYycPdqxdx/5fsRSrq2OXnk6zZtErr0jN\nNmMdu2jBjt1Y7NgxHfeh55km4lIs6Qx20TZPsMNEdbWOiVF8OnYCj19CDqzBYORrtYs9sJoJ\n1gl4xyVDMV1IsBZbf7Edo4QlHrJB/ePasUb9o0lM/Z1NU7Dr0aPH5s2bBT24QQAAIABJREFU\nhw0b9swzz1x33XUnDNzUHWRiLsWqd+zkS7H8/82cY6cgcPMEkXSOnc+n44onNTVSifhvMsN/\nMw20sihKx45fc0T73Ej0O67A45eQA2tdnfSCtOFSLBtNMTFjpxKqv+PqHU09WFtYf7GncqrX\nX2DHWu/c4lH/BDTGUP9wiam/s2ndPNG0adPi4uKpU6d+/vnnl1122ddffx3XaTmb3o6dPGBp\n7NjFzGT8G+QXumQEbp4golatpAfaPw7ww5OQpVj24S8jo77ajMD8ZOzAqt7KIkP5VciBNeZH\neYH5VcjJf2TobTIewVrIxGK+MAQ+TSGnIhgbzbYfbFB/xtn1dzYdu2JdLtfkyZNXr15dW1s7\nYMCAl19+OaTr7G44K1qw42FLkajkKU2xeYLOJrNgUNnYU8e+IS3tnHt2McY6dtE2T7BLqBBR\nebnWofjvraJjZ2wpVv0dlwR9MDVzYFUcDfnTFDgxIR/lzUwsJUX5wmAT8/n03Yct2vsHm5vl\n7x9CJhaPd9xo9fd6Y5+2ET6abd+/w1//qH80Dbz+zpYW+1vOdf3112/evPmWW26ZMGFCK96N\nAT3Cr2PHmnBagp1i8wTJlmLl54pp7NilRfr3F9uxYxc9JhHBzkzHLvxC2mYaYxEPrKdOWX/8\nsu1HefVgrf2YK7AxKXYpKh71j+samXy0sxew0jq3pHuatp0Yof4WTczZYnfsMjMzU89drmvf\nvv1XX3117733Hj9+PG4TczJFMiM9HTuVpVhdHTuVYCd28wQPdmfOaB2KJ624BjuxjTEzwSIB\nSyHGzkpUTCwrS3qxCWxlGZubDRsDCVgjE1v/eDRmhLzM7BOsUX/zE7Nt/Z0tdseuVnG1XCIi\nyszMfP3110eNGnXs2LE4zMrhot15ggc4Rb9NEeyiLcXKv01Ix07I5gl+I1rtwY7/3iquFW6f\njp3YFU/FaLZNPC4XNWpEv/5qZDSV+msfze+XPmwkpjEp8IUh6qwgVn8DE0P9zU+MUP9YoyVR\n/Z1N91Ks3PDhw0XNo0GJdo4d75AFgxQM1v+tIrEpGn626tilpCjHzM6mjAzyeKiiQutQMTt2\nQn6xDeQnvkNFyDkuifzEXFtLgUCEjTK6JkYmDqxCznFUmZjA+htr5caj/hHTgLFgHS3xk57X\nP+qP+quPlkT1d7bIS7Eul8vlch0+fJg/VpHYCTtBzI4dEckvF6i+FMvPsZPnMI0du/BrnZC5\nzRMRT5Zq0oRIz31U+ZFOYMdO5cBqbbAIP6vXTMdOSGNA/cCqayhK1BubbZeiDDzNaFde5HOz\nYbBG/fVODPWPJjH1d7bIHbuRI0cSUWZmJhHdcsstCZ1RAxDzHDv2OGLA8vsjL8UaC3YRO3ap\nqeRyUShkpGOnWIdlcnPpxAn65RetQ0VbijVzgWIhHbt4BLvwobKzpfoLXIoloupqKWHHpHJg\nNfz+YduOXXq6spHQqJGR+kf7/CBf2FLcIk99YhFHM7ywrj4xXUOpjIb6RxsN9bdb/Z0tcrBb\nvnw5f7xkyZJETaahiLYrNloyM3AdOzNLsUTkdpPXa+Qcu2jBjkhHsIvWscvMpNRUCgSMHHFU\ngp32mBiPT8zhE0tJoexsqq4WfGC1Kj/F7Jha27GLWP+sLKqpERyshXRMDTzNxHSsUf9oUH/G\nbvV3Nh3XseNCoVBZWZlX1+V3QCbmdezUH2u5jl3MTMavYxcR+7qojp3eu1qx31uXK8KpbOwr\nxi5QHHEosu4Ts8oRR+AHU5vkJ7Edi2hrxKKO+NbWP+ZSlOUvDNTfkomh/gLr72yagt0XX3xx\n77337t+/n4gOHz7co0ePdu3a5ebmPvnkk7hGsQHRgl208+oMXO4kZrBj/y2Vjh0ZCnYRz7HT\n+9vIrxyREvbyZGlMSMcuLU2arcBgx2+Gpn00lQOr9on5fNK/uJDNv2LfP2JuXtH+woi5RhwI\n1E9e48SE1N/jkf7dxdY/ro0ZAxND/QXWX2ziQf3VR2tou2JjB7v//Oc/11577ZtvvlldXU1E\njz766I4dO4YMGdK9e/enn3568eLF8Z+k00S7V6w82EV7rHKOnajLnfCvG9g8IbBjp1iHZQx3\n7CL+YrP/hJClWHb80nXnWYETi3nEJ0H5yXCwTkwr0cBoKvUX+I5L1q24of6M3eofj8RjYLQG\nW39nix3sZsyYkZOTs3Hjxm7dutXU1KxYsWLAgAFr1qzZsGFDYWHha6+9loBZOozepVh5sNO4\nK1b+IxHFPMeOxC3F6u3Ysd/biJeU1Jt46GzijHj80htTtBxY9R6/hHxijscRn4R27MInlpEh\nvfyETMxw/yNi/fU+zYTVX+BSOK+/wJOfdM0N9Uf91UeLa/2dLXaw+/HHH0eOHNm7d28i2rhx\nY21t7Z133klE6enpgwcP3rVrV9zn6DjRLneiZSlW7K7YaBcWMtCxUwl2en8bWW5T6dgJWYql\nOHTsdM0t5sQMfGIWeMQP3y5nYGIUn6cp8P1DSLBG/VF/9dFQfxvW38FiB7tAIOA7Gxk++eQT\nIrrmmmvYH/1+f7WuGgMRRbrcCfuKxqVYIefYJb5jpzfYierYqfxi27ZjF4+JCTziW3UqYTw6\nFkLecRM8sdpa1N/KiaH+1k5MVP0dLHaw69Kly+eff+71en0+34IFCzp27Ni5c2ci8vl8n3/+\nebt27eI/SafRsnnCwDl2woOdqAsUs99Gv7/+g526mMFO+zEiFFLb1aH3jD3bHljj8YlZZWKh\nkI5ztBPcsdD7r5mMrRQ7n8qJ+kecG+pvw/o7WOxgN27cuCNHjvTo0aNLly4HDx686667iGjt\n2rVFRUV79+79/e9/H/c5Og6LcSkpaufYqSzLJqBjJ/ZyJ3rvGKES7PS2sjweqbYqHTuxB1aB\nJy+LSpzs7jACD6zaR1PZLkdC86uBi9fEvNyDbTsW2kfj9Y/3ipvY+hvuWKP+qL+cev0dLHaw\nGzNmzPTp00+dOnXw4MFRo0Y98sgjRLR+/fqtW7fedNNNDz/8cPwn6TQsarhcxO/HZrddsWKX\nYvV+mhS4FKtyKDQwmtgVT4HBQiVxpqRIz13IgVXv+4fKxMjqPSIC1+hVnmZqqvSfENhK0T43\nLa9/G9Zf4Osf9VefW0Ouv4Npuo7dY489dvLkydra2mXLlmVlZRHRmDFjSktLV6xY0Vhxn3bQ\ngH2GMBzsFKfoGbtAsZbr2BnYPKGy4kmafxv5deyiDaWrY8ck11Ks4WAhcMUnYW9sQmK64aWo\neLdSDI8mpGOqPjGBLzObLAWi/qi/9ok5mI47T7hld4wvLCzs2LFjHObTIPClWB7sWFbTuBTL\n/0plKdbk5U4MLMWqXMeOBzuNJ2axbxNyjp2WA6veYOFyibzcq8qh0OOJ/e/IqCROMtoYsO0b\nm9sdYbuc4aUolYppv6tePJ6merDW+KIV+8KIR/1VXmaof8SJof4kqP4OZuSWYmCSmaVY+XXs\n4r0UK+pyJ/zYIWoptq5Oa+LhRxwhHTu+Dz/8lhjx6NhpH019xdMOB1aBjTEhrUSxo2l5/xbS\nMY3HUrglrVyxo2l5maH+8RstSevvYAh2FhC1FGu+Y6d+HTvhmyc0duxUlmL1Bgu+FCukYyew\nlRUMql05We/TjMdSiNgDq8BzHKNNjP022fD9w8L8KraVon6BHjvUP96vf9RfZahoo9m2/g6G\nYGcB3rETe7kTazdPqFzuhB+JtAS7QEDKiCrNJxL0i83+E9pXPFWOOHrvPKslcWofLfHn2AlJ\nnMZaiRFfGHr3iPh80j+6DZ+mls8Pdkv8qL+BiaH+ESWs/g6GYGeB8HPsjAU7ecfO79fXsYvT\n5gnzS7E8/KksxZL+/KS+q0PXwmK0rr6uw7SWI772iSXsHBfbJk69o2mpGNnvadp2YnpHQ/3J\n6KkgqL+oiTkYgp0Foi3Fyq+mnZg7TwhfilXv2PFfMxVaTtcg0cFO4xqxlgOrwCO+qNFs3rHz\n++v/mQxPjHTmVy1nxZH9gjXqrzKxaKPZtv5sNNQ/4mgJmJiDIdhZIHzzhMotxRS9t0BA01Ks\nyV2xepdi+Q0e1Dt2WvKTJcFOV8cukcFO1/ErJUXtadq2Y0c6n6ZtOxapqSS7coDBiRHqj/rr\nnxih/tGHijaag0V5Yz/X+++/v3Tp0vLy8oh/u3btWqFTcj5dS7GKiBbesWPhzOutbwSGQlqX\nYqN17PQGO5bqyH7BTss5dqTzaBhtKVZXforHET9iqiP9B9aYexS039JH+/tHs2ZaRxPSsUjk\nO67AYJ2VRSkpFAwKrn9NDeqvaTTUP94TUx9NbP0dLHawe+ONN/785z8TUePGjTMbWnniQ9eu\n2PBgF7Fjx1/B6enk8ST6cifqjTH7d+xsuxRrtwOry0VZWVRTY8enaaxjIXCPjnr9hXQsWP2r\nq61szKD+qL+uidm2/g4WO9i9+OKLubm5q1evvuqqqxIwoYYg2q7YiOfYqQQ7+Tl28lcwSzOB\nQNSGHMXaPKH3HDv1jl1GhvQxS9c5dhF/FfVeBzjxwcLCc+zUJ1ZbS6FQ/WeJaPjJmiqj1dSI\nPMeIrMivYtfoBb7jBoPSb5PK06yuTvrGDOpPqH8kiay/g8U4xy4UCu3Zs2fMmDFIdQJpWYrl\nIS/mUmx4sOPfqULsOXbqhwk+Ky2NMfWPkmI7drpaiaTtHDu9F9hLwIGVjRYManqa6tdhIZ2f\nvxOZXwVOLB7vuIGApg82Md+KLD+VCvXXO7Foo6H+eidGQuvvYDGCndfr9Xq9adHe/8GQc5Zi\nc0up5/9f6T9G5pZi+fsxDyvqp9mp74rVuxSr3rGjs79XAnfFVlVpmlg88pNtz7FTP7BqHC3m\noVDg07TDUmzC3nE1zo1PLNpnpHgEawvrL+Tu0qg/of6qoyHYnSMjI6N///4rVqz45ZdfEjOh\nhuCcXbED7qSi/+8/Zx6lc5di9Xbswhst6rFMy3XshHfszC/FxmnzhIXn2EVrJeq6jryWiWkc\nLR6fmF2uyE8zHvlVSMc0M1P61GTD+hsI1nauf8TRUH+V0VB/ElR/B4t9uZN33nmncePG11xz\nzZIlS0pLS0+FScAsHYYvxYYoSC2+JaJj3m0UpWMnT3sUqWPHwhkbk2RvVOY7dgKDHYtQ5pdi\n3W6DN3hQv9dZ4j8xqx9Y+XXkbdux07tdN+K5fcYaA+of5YUkfpfLyNOMWX8tc4vHUnjM+gvZ\nfI36R5sY6s/Yrf4OFnuNtWfPnj6fr7q6+tZbb434DSGeKUAbvhRbUXOGUvxEVB04SZrPsYu4\neYLjvw/qwS6Rmyf4rESdY+Hx6FuKTU+v36ciJ7Zjx484WvYoaMlPtbX2DXYCo5jGidHZf83E\nnHyTnU1VVSLfcTXOLR4dUyHvuIT6ExHqH320pKu/g8UOdrfccksC5tGg8KXYitoK9pW60BnS\ntis2EIi8FMtpCXaBgDSHmJc70ZJRSEPHjn3d/Dl2RNSoEZ0+re9QqN5HJKEdO7ZHgR/L1IdS\nGS07m06dEvM0LezYqb8VxWOPSCBAHk/slRex+VXg04xTx9T8xCj5669rxQD1J6fX38FiB7t/\n//vfCZhHg8KXYqvqpL6TP1Tn8XsCgfoXYMyOHb8MniKcaQl2/PQ79aXYUIj8/sgXE1fQeI6d\nljvnxPzFZlc80dixUz8UslPZQiFNRxy/X6qbllNJYga7mBWLx1KIVScvCzn5hl+CW8vTjHko\nt6T+iX9jE5g4HVD/xHesUX+ycf0dTN8txWpqanbv3l1ZWRmn2TQQvGNX7a1/edZ4a3TdeYJn\nMkU447+oKpsn+JjqHTvSvBqbyKVYXcFOvZXF78El8B2XtB104vHBVMiBNeY5LgKXQtgFDjWO\n1tDqL/BUqmgT03WOPOovfGKof7hE1t/BNAW7qqqqp59+uk2bNo0aNeratWtubm7r1q2ffvrp\nau0XswcZfo5dtae+gFV1VRF3xUbbPMHzXPw6dqQ52AncFcu+Jy0taujUtflUPdjR2dVYgSd/\niBrN5p+YhUxM1znaGo/4GkezZMXNbu+4dq6/gc8PqD+D+itGa4DBLvZSbG1tbZ8+fXbs2JGf\nnz969OiCgoLjx49v3LjxySeffP/990tKSjIa4Aq2ObxjV+ur7xRp79ixr/DdAAaCnfCOnfBg\np/KrKLBjR0TZ2XTmjAUdOzYxtzvyrg6KT7Cw6hw79fprPEdbe/21jxbttuVkaI9zYoK12JPH\nbVt/q1acUX/5aI6vv1PF7thNmTJlx44dkyZN2r9///vvvz979uwlS5bs27fv8ccf37p161NP\nPZWAWToMP8eu1lsfKGp9terXsWOrnIGAsmNnYPNE4jt27Ovaz7ETFexijmbgOiwCj1/qR3yN\nQ5HmA6uuyw2ox0S/X8y/pvaFRbH115I4NQ5FsZ6m2HMc2SuWnSMfk8CnifozqH+0uSVj/Z0q\ndrBbt25dr169nnnmGXlnLj09fdq0aVdcccWaNWviOT1n4kuxHn/9a7POV6d+HTsW7MLPsXNY\nx079tl0kumMXj6VY7THFzgdWu71/2DlYJ/4cR42jxSNYC2wMo/6ov0KC6+9UsYPd7t27e/Xq\nFfGvevXqtWvXLtFTcj6+FFvnq086db469cud8GCnsWOnsnnCzh27mPuYWLATe45d4jt2MZ+m\n9hWHUCjGaPwc7aRuTMZ8jcXjHVfLUPy25So9Bu33EbFtsLYk8aD+iqFUJob6h0PHLqqOHTvu\n3Lkz4l/99NNPHTt2FD0l5+NLsSrBLnzzBHt1xjzHTsudJ+zcsUv8OXYkKPFYdWD1eqVXVMyn\nKXApVuPcBD7NmPXXdVVCgR3TmO+4LpeRxjDqr3Eo1J9B/aONho5dBP369fvyyy9feuklxR0m\nXn311S+++KJfv35xm5tj8aVYr9/Lv1jrq1W/80Qiz7HjVy2x4Tl2LD8FAprSmCUdO+35KTFr\nlGJHM3BgtWHHImbH1Kr6a7ylkq652XBiqL+1E0P9nS32rtgZM2Z89NFH//M///PGG2/0798/\nPz//+PHjX3zxxbZt2zp06DBt2rQEzNJh+FKs/Bw7r99rbCnWPufYuVwxrmPn8cS+lUXMKMA6\ndkRUVRX17hSKiSXmHDuxRxw2MY+HAoGo+VvjxMjQYVrIJ+Z4vH8kspXC9oioL+XE/FRDRI0a\nUXm5HZeiBNY/Hh1rUfV3wB4F1F8+lMbRGuxSbOxgl5ubu2HDhqlTp77++uvbt29nX3S73fff\nf/+UKVOaNGkS5xk6EF+K9QXqc5PH7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QPnbB7U6gOFLMn6PUpGIdpNGcBuA/Xsxv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\npJvpE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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": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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MLV2Lw8bN0qdhQiIio9LHZE7+7ffxEeDgDjxqFSJbHTFEfz5nB2Bng1lohIWljs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\nVhdcIqJXYrEj7XbkCPr3x5MnADB8OGbOFDtQOdp7ce+UbVOqVq4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J24tdUlJS9+7dX/mSra3tX3/9VdqRSNOpVNi9G19+WfAv7+7d8cMP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\ncsmIESIBDLumJjlzR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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": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }