{ "cells": [ { "cell_type": "markdown", "id": "b5cbe1ce-7a91-47ae-a99f-48bdbc9c779f", "metadata": {}, "source": [ "**Example 6.1.** Two forces, which we will call red (R) and blue (B), are engaged\n", "in battle. In this conventional battle, attrition is due to direct fire (infantry) and\n", "area fire (artillery). The attrition rate due to direct fire is assumed proportional\n", "to the number of enemy infantry. The attrition rate due to artillery depends\n", "on both the amount of enemy artillery and the density of friendly troops. Red\n", "has amassed five divisions to attack a blue force of two divisions. Blue has the\n", "advantage of defense, and superior weapon effectiveness besides. How much\n", "more effective does blue have to be in order to prevail in battle?" ] }, { "cell_type": "code", "execution_count": 1, "id": "20a2ca10-575d-46a2-a4eb-a1e2c1cd6e8e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.005" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lambda=1.0\n", "a2=0.05\n", "b2=0.005\n", "a1=lambda*a2\n", "b1=lambda*b2" ] }, { "cell_type": "code", "execution_count": 2, "id": "375b2ace-a8e9-42d9-9b06-6ba44913d899", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R0=5.0\n", "B0=2.0" ] }, { "cell_type": "code", "execution_count": 3, "id": "103d3190-fef7-457a-b843-9bcde0f9ad0f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dB (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dR(R,B)=-a1*B-b1*R*B\n", "dB(R,B)=-a2*R-b2*R*B" ] }, { "cell_type": "code", "execution_count": 4, "id": "f6b9952d-53a7-4514-87f2-974c9be4f8ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=2 R=4.85 B=1.709\n", "n=3 R=4.7231067499999995 B=1.43248571532125\n", "n=4 R=4.617653549477375 B=1.1685294241077373\n", "n=5 R=4.53224775805749 B=0.9154367118916803\n", "n=6 R=4.465730992537333 B=0.6717096917848079\n", "n=7 R=4.417147134005137 B=0.43601713238479733\n", "n=8 R=4.385716518252444 B=0.20717006877346977\n", "n=9 R=4.370815068850234 B=-0.015898194961091072\n", "n=10 R=4.371957418948806 B=-0.23414853475149122\n" ] } ], "source": [ "Rn=R0\n", "Bn=B0\n", "for n=2:10\n", " Rn=Rn+dR(Rn,Bn)\n", " Bn=Bn+dB(Rn,Bn)\n", " println(\"n=$n R=$Rn B=$Bn\")\n", "end" ] }, { "cell_type": "markdown", "id": "765c6f35-758d-42f0-b544-7862dcb05dca", "metadata": {}, "source": [ "Good to visualize what is happening when modeling a problem" ] }, { "cell_type": "code", "execution_count": 5, "id": "cf15581a-6ea3-473c-bd7f-6ef528eb1534", "metadata": {}, "outputs": [], "source": [ "Rn=R0; Rs=[R0]\n", "Bn=B0; Bs=[B0]\n", "for n=2:10\n", " Rn=Rn+dR(Rn,Bn); push!(Rs,Rn)\n", " Bn=Bn+dB(Rn,Bn); push!(Bs,Bn)\n", "end" ] }, { "cell_type": "code", "execution_count": 6, "id": "cceced29-bed7-41ab-a8a3-3a4f11b7405f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10×2 Matrix{Float64}:\n", " 5.0 2.0\n", " 4.85 1.709\n", " 4.72311 1.43249\n", " 4.61765 1.16853\n", " 4.53225 0.915437\n", " 4.46573 0.67171\n", " 4.41715 0.436017\n", " 4.38572 0.20717\n", " 4.37082 -0.0158982\n", " 4.37196 -0.234149" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[Rs Bs]" ] }, { "cell_type": "code", "execution_count": 7, "id": "954b7e12-7aa2-47cb-a4ce-b36b3aa8e8f6", "metadata": {}, "outputs": [], "source": [ "using Plots" ] }, { "cell_type": "code", "execution_count": 8, "id": "cf458809-f625-4056-a353-5b5efd7bc4de", "metadata": {}, "outputs": [ { "data": { 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push!(Rs,Rn)\n", " Bn=Bn+dB(Rn,Bn); push!(Bs,Bn)\n", " end\n", " display(scatter(Rs,Bs,xlabel=\"R\",ylabel=\"B\"))\n", "end" ] }, { "cell_type": "code", "execution_count": 10, "id": "ae49b668-31cd-4001-977b-e552381a3392", "metadata": {}, "outputs": [ { "data": { "image/png": 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MBuHmK4TIEyKvx8RnJ0Se2r+rXr16stPhYWOPEIByNm/ektNuiKkFb3Gtn9NhROz3G+SFgjQUIQDlJKVdLPQIKDdY7BV4JiVdSh7IRRECUI5/44aONy+UG7TPSgls2khGHEhGEQJQTmRkP7fEr4Qu439D+VnuCWsGDxwgLxSk4WIZAMrx8PBYu+SD0S/0z247uKh+G8eMM+7H1q9Y/K6Xl5fsaJCAIgSgoj69ws7G/7R58+ajp8882qN55PKfXF1dZYeCHBQhAEW5uLgMGzZsmOwYkI5zhAAApVGEAAClUYQAAKVRhAAApVGEAAClUYQAAKVRhAAApVGEAAClVXxD/fHjx48cOeLn59e1a1cHB4dKznv9+vVDhw6lp6cPGDCgQYMGd67w3//+Nz391oPeXV1do6OjTa/z8/NXrlx55cqVnj17RkREVPKfAwCgasoX4ZIlSz777LPc3Nynn3563rx5M2fOXLBggdFoFEK0bt06Li6uks/ia9asWbt27Y4cORIUFHTXIly8eHFxcXFgYKAQwjynwWDo1atX/fr1n3jiiXHjxr3xxhsTJ058oJ8PAID7+k0RxsbGTp48OSAgoFGjRgsXLiwoKFi6dOnrr7/esWPHQ4cO/eMf/1iwYMF7771XmXlzc3Pt7Oy8vb3vs87YsWNHjBhx+8i2bduuXbu2Z88erVYbHBw8bty48ePHazSaKvxgAABUxm+KcPny5aGhoXv27LG3t//yyy+HDx/+wgsvvPPOO0KIp59+WqfTbdy4sZJFaGdX8UHXuLi469evBwUFRURE2NjYCCF++OGH3r17a7VaIUSvXr2uXbt2/vz5Vq1aVeUnAwCgEn5TVykpKUOHDrW3txdCDBw40Gg0hoaGmr/auXPnZcuWWeofbtasmdFoTE1N/fDDDwMDA7ds2aLRaK5cudKwYcNbyezsPD09L1++fNcizM3NTU1NHTdunGnRxsZm+PDhXbt2tVQ8KYqKikx/BCiO7WBSVFRUmT8oa72ioiKNRqPX62UHkUyv15eUlJj2GRT3u94itFpthYcVf/NrlpeXV7duXdNrJycne3t7Z2dn81ednZ0LCwt/T9r7+fjjj00v5syZ07p169jY2KioKDs7O4PBYF6nrKzsXj+tg4ODs7Nzx44dzSPe3t41/SCqRqOp6T+CRbAdTNgOJppfyQ4iH9vB5Hdth8r86SD/701XV9f27dsnJSUJIRo2bJiSkmIaLywszM7ONu8gluPg4ODt7T1p0qSHF9T6tFote0KC7fArtoOJXq/XaDRsCltbW6PRyHYQVvjVKF+EX3/99enTp02vy8rKli5dun37dtOiuaKqLD09XafTBQUFmY5ymCo9MzMzPj5+woQJQojIyMiBAwfqdDpXV9cNGza0bNkyICDgAf9RAADuo3wR7t+/f//+/eZFcwv+XuPGjUtNTc3Jyfnzn//s7u6+atWqRo0arVixYu/evdu2bcvKymrfvn2PHj3s7e23bt3aq1ev/v37CyG6dOnSo0ePHj16PPbYY99++60FT0kCAHBXNqZ7BC1u//79+fn55sVu3bo5OzunpaXl5ua2bdvWaDSeOHHi+PHjBoOhbdu2ISEh5jUNBsPu3bvT09O7d+9uusvwrhISEiZNmhQfH2+N8LKYdoVlp5CP7WCSl5fn4uIiO4V8potlOCRouljGyclJdhD5LP4WYa1zhHe9gNPPz8/0wsbGJjg4ODg4+M51bG1te/fubaVUAACUw7NGAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKowgBWEVpaWlqamppaansIEAFKEIAFpaVlTX0uZhGwV0eGzGtUXCXIaPHZ2Zmyg4F3JOd7AAAahWDwdAz8ulTHSbrX/nINBKbGHuq3+Bj+3ZrNBq52YC7Yo8QgCVt3779ovsj+vaDzSP6kEGXPEO2bt0qMRVwHxQhAEuKTzx+069bucGcZt0PHD4mJQ9QIYoQgCW5ODnaFueVG7Qt0rnWcZKSB6gQRQjAkvpG9Kl37GthNP5vyGisd/Q/kU+GywsF3A9FCMCSWrduPeLJbh4ro8XlU0JfKq6c9lg1IrpP56CgINnRgLvjqlEAFrZw3uwBu3a/s2heauqFpk2bvf7WxD59essOBdwTRQjA8nr1CuvVK0x2CqBSODQKAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFAaRQgAUBpFCABQGkUIAFCanewAACxDp9P98MMPFy9dbtWyRc+ePTUajexEQM3AHiFQG3y/aUurzk8MX3XwhQNiyHvftA7tcfr0admhgJqBPUKgxktNTR336ps3Jm8VTm5CiGwhsi+f+uPQUeeO7Lez43ccqAB7hECNt3zNuqzuU0wteEvDNrmNQ/fu3SsvFFBjUIRAjXfmQrqhfvNyg7p6LdLS0qTkAWoWihCo8fwbNbDJSi83WCcn1dfXV0oeoGahCIEab+yIYfXiFonSov8NZV2sk/xTjx495IUCagwrnkjPzc09f/68r6/vXf8sNRgMR44cSU5O9vHxefzxx82Xeh89erSsrMz02sPDIyAgwHoJgdqhZcuW81+d/Nf5YVmdRpd5+DldPup5csM3n3/q4OAgOxpQA1irCJ999tnvvvvOzs7u9ddfnzlz5p0rhIWF3bhxIzg4+JdfftFqtbt373ZzcxNC9O7d29fX1/QLHB4ePm/ePCslBGqTcWNG9n+yz4aNm86mJoY+3mbAgNecnJxkhwJqBmsV4Zw5c1auXDlq1Kh7rbBkyZKgoCAhhF6v79Sp08qVK6dOnWr60rffftuiRQsrBQNqqwYNGsSMHyc7BVDzWKsIK2wyUwsKITQaTaNGjQoKCsxfOnbs2PXr1x955BF3d3crxQMAwET+zbYJCQl79uxZuHChadHV1XXRokUlJSW//PLLRx99dK99ypKSkoyMjE8++cQ80rNnz5YtWz6MxFaj1+v1er3sFPKxHUzYDiamjWBrq/qVffpfyQ4i3+/aDra2tjY2NvdfR3IRXrhwISoqauHChYGBgaaRM2fO2NvbCyE2b948ZMiQvn37ent73/mNRUVFBQUFCQkJ5pGAgAB/f/+HE9tKSktLS0tLZaeQj+1gwnYwKS0tNRgMslPIp9frS0tLeVSQ+J2/GlqttsLn7srcphcvXuzTp88rr7zy3HPPmQdNLSiEiIyMdHFxOXnyZM+ePe/83rp16zZt2nTZsmUPJ+rDUVpa6ujoKDuFfGwHk7KyMraDiUaj0Wq1slNIptfrbW1t+S8hrPAW8VCPNhgMBvO5wGvXrkVERIwfP/6ll16668rp6enZ2dkNGzZ8iAEBAMqx1h5hbGzsgQMHTpw4cf369by8vKioqNDQ0Li4uPDw8JKSEiHEwIEDCwsLs7OzZ8yYIYQIDQ2NiorauXPnihUrQkNDCwoKli9fHh0dzeWjAACrslYRenl5BQQETJs2zbTo6uoqhGjRooX5opgpU6bk5eWZ1zedCAwJCenevfu5c+ecnJwWLlzYv39/K8UDAMDExmg0ys5QFQkJCZMmTYqPj5cdxJJ0Op3pLwbFsR1M8vLyXFxcZKeQr6ioiHOEQgi9Xl9SUsJzEoQV3iJUvyIZAKA4ihAAoDSKEACgNIoQAKA0ihAAoDSKEACgNIoQAKA0ihAAoDSKEACgNIoQAKA0ihAAoDSKEACgNIoQAKA0ihAAoDRrfR4hoKYdO3Yu//K7qxk3OgW3eeWliT4+PrITAagARQhYhtFofOZPE3al5Gd1myia149LTVjd849ffPx+715hsqMBuB+KELCM2O83bL9kzBm1yrSo9w643uqJ0S/0Tz0eb2fHLxpQfXGOELCMVV9vyOky7jdDrvVLmnRITEyUlAhApVCEgGVk3cwRLp7lBsucvW7evCklD4BKoggBy2j/SCubtCPlBrXph1u1aiUlD4BKoggBy/jLCzFeO+eJrHTziHb/5yF+nk2aNJGYCkCFOIcPWEbTpk1jV348evIInatfWd0GmtSEsNDg5WuWyc4FoAIUIWAx3bp2OZOwJzk5+erVq0FBb3p6lj9lCKAaoggBS9JoNC1atGjRooXsIAAqi3OEAAClUYQAAKVRhAAApVGEAAClUYQAAKVRhAAApVGEAAClUYQAAKVRhAAApVGEAAClUYQAAKVRhAAApVGEAAClUYQAAKXxMUyo5TIyMt55f9H+Q0fd6taNHtj3uVEjbGxsZIcCUI2wR4ja7OeDB4N7RHyYE3TwyQ+3t58xdf3RLr37lZSUyM4FoBqhCFGbDY+Zcm3sN/qOQ4S7r2jQKnfA3BPe3T/46BPZuQBUIxQhaq309PQ8Ry9Rr8ntgwVdnvvyu02yIgGohihC1Fo6nU44e5QfdXLPy8uTEQdANUURotZq1qyZ8fIvwmj8zWjKweC2j0hKBKA6oghRazk7Ow/pF+G8+S1h0N8aunnZa9Prs197WWouANULt0+gNlv83jsuf39n1T+6CL8Q26JcZ92lFR+/17ZtW9m5AFQjFCFqM41G8+6cN+fMnH727Nm6des2bdpUdiIA1Q5FiNrPwcEhODhYdgoA1RTnCAEASqMIAQBKowgBAEqjCAEASqMIAQBKq/1XjSYkJGz4vx0Z2TlPdG4fFfW0nV3t/5EBAJVXm/cIjUbjyAkv9X1xzpxL/p8Y//D8F0fahPZIT0+XnQsAUI3U5t2j5avWbEgTunHrTYv5QX2SkvZHjZlwcNcWucFglpub+8FHn8bFJ3q41Y0e2PfpQQNlJwKgnNq8R/jpmv/owqbdPmJs3jU1uyArK0tWJNzu2LFjrR974p1zdXd2/Ov6RqOf/+T/noh8urS0VHYuAGqpzUWYmXlDeDQsP+reKCMjQ0YclPfM8y9cGbm2tNtY4dNCNOt0c8iieIe2H366THYuAGqpzUXo5+cnrp4tP5qR1KhRIxlx8BtXrlzJtqkjfFrcPljw+Pg167+XFQmAmmpzEb7xUozHxjdEWYl5xP7nNd3aBbm4uEhMBZOcnBxRx7P8qItnTk6OjDgA1FWbL5aJiAh/83zKvH/1LGzTt8TBrW7KTx0aua75fKnsXBBCCD8/P+OV08JoFDY2/xtNO9KmVSt5oQCoqDYXoRBi6uSYUcOiDhw4kJub2779e61bt5adCLc4Ozv37/2HL7e/Wxj+2q0uzLvhuWH67M8XyY4GQC21vAiFEJ6enpGRkbJT4C4+Xfiuw2szv/mgu8G/s6ZI53D1l4/em9OhQwedTic7GgCF1P4iRLWl1WqXfLBg3s2bJ0+edHNza9mypVarlR0KgHIowt+noKDg4MGDmZmZQUFBbdq0kR2nNnB3d+/WrZvsFADURRH+Dt98v3HKjL8XBv6h2NmrTvraVm7G79Ys8/Lykp0LAFB1FGFl/fLLLxP+Oi9z8lbh5CaEKBAi68R/+z875sCOzbKjWZfBYPjo02Ufr/y3Lr/A08Ptzb+8GDV4kOxQAGAxFGFlvf/x8szwmaYWNNG3/WPKgaUXLlxo1qyZvFxWFzFo2M+2gXmjvhVOdS/lXH1+0cxde37+6P15snMBgGXU5hvqLet0UopoGFRusKRBUFJSkpQ8D8eOHTsOF7jm9Z8tnOoKIYRbg5zhn32180BKSorsaABgGRRhZfl4e4mbl8sNanMue3t7S8nzcGzc8WN20IDfDNnY5Dzy1E9xcZISAYCFySxCg8Fw5syZGzdulBvPzs4+ffp0WVmZlFT3MnHkUPcf/yWMxv8NZSTXyTwbHBxc5ZEULMwAAAxBSURBVDmNRuPOnTvf++Bf69atu3r1qgVSWlpJaZnQ2JcbNNhqS0v4jAgAtYS1ijAyMtLHx8fGxmbPnj13XSE5OblNmzZRUVGtW7eePn26eXzBggXNmzcfNmxYYGDgsWPHrBSvCp58MmLU4y29Pn1KHI4VSfsddn7QaHX0d6uX2tz+hLDfIy0t7ZHHeg59b/30E25/+j6tXa+nliz//AFDnj17ts+gZxs/0smvbejQ5yZcuXLlASfs0y3U9fyucoMe53c+9ljnB5wZAKoJaxXhiBEjfvrpJ0/PO56q/KsZM2b88Y9/PHHixPHjx1esWBEfHy+ESEpKevvttw8ePHj06NGYmJipU6daKV7VLFowZ8fyd//a4NyI7G8W9qp39tCekJCQKs8W+czo0+HzsocsMnYdUdxn2vUpP8z/PPbnn3+u8oR79+1/fOCInY9MufTn/ekv7/3WvX+HsH7JyclVnlAIMWjQwKYZ8doDa27tCutLnbbO79zY5UH2gwGgWrHWVaPDhw8XQtxrb6mgoCA2Nvb48eNCCF9f30GDBq1bty40NPSrr77q1atXYGCgEGLChAmzZs26cuWKr6+vlUJWQbt27dq1a/fg85w7d+66xsPof9t+lZ19dsRfP/hs9ZePPVa1OWOmvX7juS+Fp58QQtjYGNr2vWZf56XX/775P6urnFOj0ezdtvEvM2dv/Edno4OLXWnB8yOHzXx1RZUnBIDqRs7tE5cvXy4rK2vevLlpsXnz5gkJCUKICxcutGhx6wPqPD093dzc0tLS7lqERqOxoKDg0KFD5pHAwEA3N7c716yeLl26VOrpX37Uu3nK4fSqTVhaWpqRW3CrBX9lbNkjcdOrVZvQrG7dup8t+ocQorCw0MnJ6QFnA4DqRk4R5uXl2dnZ2dnd+tednZ1zc3OFEPn5+bc/qMXZ2flez1/OzMxMTU0dP368eeTll1+OioqyZmpLcnd3t8u8UH70RkojX5+8vLwqTFhSUmIUd9n/NhgMVZvwriw41X3k5+dX+cxrbZKfny87QrVQVFSk0Wh4Dq1ery8pKdHr9bKDyPe73iIcHR3NXXMvcorQx8entLQ0Ly/P9Bm5WVlZDRo0MI1nZ2ebV8vOzvbx8bnrDF5eXm3atDGdWayJQkJCvEpvZKQdEX7tbw0Zyjy2z/3L4r9V+XOD3Rxsb+iuC9f6/xtKS2wV2LzGfRCx0WiscZmthO0ghLCzs6MIxa9FyFEZYYW3CDm3T/j4+DRs2HD//v2mxf3797dv314IERIScuDAAdPg0aNH7ezszIdPa5/N//m85eY/u8W+JhK+0f64pP6/wv487MnHH+Dx0wvn/q3eqhEiM/XWcvox768nLZ73N8vEBYBaylp7hF9//XV2dnZRUdGGDRtOnjw5bNgwNze3Dz/88NChQytXrrS1tX3xxRdfffXVDz/88PDhw/Hx8V988YUQYsiQIdOnT589e3Z4ePj06dPHjRvn7OxspYTS+fv7nzz409atW+OPnmjs4913/jd169Z9kAn7/7FvrKvL5Ndirufk2RiNAU0afrb+80ceecRSgQGgVrJWEZ48efLy5cvDhw/Pyck5dOjQoEGDhBBNmzYtKSkxrfDaa69ptdo333zT29t7586dphstnJycdu/ePWfOnN27d/fp02fGjBlWildNaDSafv369evXTwhhMBi+++67BzzN2aN79+P7dun1eltb25p7mm3r1q1RUVE1N7+l7N27t2vXrg/451Et8Msvv9StW9d8GZ2yrly5kpaWxmeWFRYW7t69e8CAARWvWmk2xtsflVJzJCQkTJo0qeaeI7zTlStXOnTo8OC3wNcC3t7eJ0+erN3PrquMsLCwmTNn9u7dW3YQyV5++eUmTZq88sorsoNItnLlyt27d69eXfW7oWqHw4cPjx07NjEx0YJz8qxRANVdDf173bLYCNZDEQIAlEYRAgCUVlPPEe7YsWPIkCGhoaGyg1hMSUnJzz//3KNHD9lB5Pvpp5+6du3KfWOHDh0KCAjw8PCQHUSys2fPOjo6+vn5VbxqrXb58uXs7GyuA9fpdCdPnnys0o+iHDx48OTJk++/Tk0twqKionXr1jVp0kR2EEtKSUnx97/juWvqYTuYXLx40cfHhz8IMjMztVotV88WFBTodLp7PWNEHXq9/uLFi02bNq3k+v7+/hXej15TixAAAIvgHCEAQGkUIQBAaRQhAEBpFCEAQGlyPoYJd4qLizt//nxoaGjbtm1lZ5EpJSUlKSmpY8eOKt82UFJSsnfv3vT09CZNmvTs2dPWVtE/WLOzsw8ePHj58uX69euHhYXV4kfwV1JycnJycnJYWJhGo5GdRYLCwsK9e/eaFwMDA5s1a2aRmblqtFp48cUXt23b1qtXr9jY2Llz544dO1Z2Ijm8vb3Lysry8vJ27NjRs2dP2XGk8ff3b9iwYcuWLX/++WdPT8/t27c7OjrKDiXBxIkTL1y40KRJk7NnzyYlJe3Zs8dSb3w1UV5eXocOHc6dO5efn6/m3wQXLlxo0aLFE088YVocN27csGHDLDIzRShfUlLSo48+mpSU1KBBg127do0cOTI1NVXNu8eSkpKaN2/u4+Pz1VdfqVyEpu0ghCgqKmrVqtX8+fOjo6Nlh5KsX79+nTp1mj17tuwg0rz00kt16tRZsGCBykXYrl27nJwci8+s6CGXamXLli3dunVr0KCBECIsLKykpCQhIUF2KDlq8ecw/y7m7eDo6Ojh4WH+8DJlGY3GgoICLy8v2UGk2b9//5EjR2JiYmQHkcxgMOzatWvPnj15eXkWnJYilO/SpUuNGzc2vbaxsfH19b106ZLcSKgmvv/++6tXrz711FOyg0izadOm8PDwli1bBgYGTpw4UXYcOYqLiydNmrR06VJlzxabeXp6Lly48OWXX27evPmPP/5oqWm5WEY+vV5/+4fQ2tnZlZWVScyDauLQoUMxMTFr166tV6+e7CzShISEvPbaa6dOnZo3b94PP/wQEREhO5EEM2fOjIqKCgoKunDhguwsMvn5+aWkpJjeLRcsWPD888+fP3/eIjOr/vdFdeDr63v9+nXz4rVr1xo2bCgxD6qDY8eO9e/f/9NPPw0PD5edRabGjRuHh4dPmTJl6tSp//znP2XHkaC0tPRf//pXcnLyhAkT3njjDSHESy+9dPLkSdm5JLC1tTXvM0RHRyclJeXm5lpkZvYI5XviiSdmz55dUFDg7Ox87Nix/Pz8Dh06yA4Fmc6cOdOvX78PPvhg0KBBsrNUFzdu3FDzudsajebf//636XVGRsa6devCwsI8PT3lppLu8OHD7u7urq6uFpmNq0arhcjIyMLCwgEDBixdunTo0KFvvfWW7ERyzJ49+9KlS2vWrOnTp4+vr+9bb71luoZINY0aNXJxcTFfJt6/f381TxOGh4eHhobWq1fv+PHj33333fbt2yv/4Tu10oULF/z9/ZW9anTRokVHjx5t1arV1atXV6xYMXfu3Ao/X6mSKMJqobi4ePXq1cnJyZ07dx48eLDsONKsX78+KyvLvPjMM8+4u7tLzCPLsmXLDAaDebFjx44dO3aUmEeWffv2xcXF3bx5s1GjRlFRUb6+vrITSabT6datWzd27Fg7OxUP5qWmpm7evDk9Pd3DwyM8PLx9+/aWmpkiBAAojYtlAABKowgBAEqjCAEASqMIAQBKowgBAEqjCAEASqMIAQBKU/GuTKDW+Prrr2fMmGF67ejo6OfnFxYWNmXKFDU/yBeoGooQqMF0Ol1ycvLkyZP9/PyKi4v37Nkzffr0uLi4jRs3yo4G1BgUIVDjjRw5smvXrqbXgwcPjo2NvXjxovlDLgHcH+cIgVqlR48eQghLfU4boAKKEKhVEhMTbWxs/Pz8ZAcBagwOjQI13q5duy5evFhYWPjjjz+uXbt2zJgxAQEBskMBNQZFCNR4M2fONL+OjIxctmyZxDBAjcOhUaDG27dvn9FozM3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The duration of battle is defined to be the number of hours of actual\n", "combat (there are 12 hours of fighting per day) until one of the variables x1 or x2\n", "becomes zero or negative. If both sides survive 168 hours of combat, we call it\n", "a draw." ] }, { "cell_type": "code", "execution_count": 13, "id": "80342e96-889c-428e-bec6-49c485af8b65", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "winred (generic function with 1 method)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function winred(lambda,nmax)\n", " global a1=lambda*a2\n", " global b1=lambda*b2\n", " Rn=R0; Rs=[R0]\n", " Bn=B0; Bs=[B0]\n", " for n=2:nmax\n", " Rn=Rn+dR(Rn,Bn); push!(Rs,Rn)\n", " Bn=Bn+dB(Rn,Bn); push!(Bs,Bn)\n", " if Bn<=0\n", " return true\n", " end\n", " if Rn<=0\n", " return false\n", " end\n", " end\n", " return false\n", "end" ] }, { "cell_type": "code", "execution_count": 14, "id": "f3c8d301-9958-43e0-8d26-fdb2254f3550", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "winblue (generic function with 1 method)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function winblue(lambda,nmax)\n", " global a1=lambda*a2\n", " global b1=lambda*b2\n", " Rn=R0; Rs=[R0]\n", " Bn=B0; Bs=[B0]\n", " for n=2:nmax\n", " Rn=Rn+dR(Rn,Bn); push!(Rs,Rn)\n", " Bn=Bn+dB(Rn,Bn); push!(Bs,Bn)\n", " if Rn<=0\n", " return true\n", " end\n", " if Bn<=0\n", " return false\n", " end\n", " end\n", " return false\n", "end" ] }, { "cell_type": "code", "execution_count": 15, "id": "e9ad01a2-f02e-4378-8cf0-bdafb245b887", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winblue(6.0,168)" ] }, { "cell_type": "code", "execution_count": 16, "id": "abdf4a2a-a0de-4fdb-89ad-f15afdf335e1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "false" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winred(6.0,168)" ] }, { "cell_type": "code", "execution_count": 17, "id": "7ff49ff0-cb05-4029-b44c-c34eb451aae9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "false" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winblue(3.0,168)" ] }, { "cell_type": "code", "execution_count": 18, "id": "3726e62e-352e-4dcc-b965-7969c8d97481", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winred(3.0,168)" ] }, { "cell_type": "code", "execution_count": 19, "id": "7e915d88-556f-4602-a611-3a70a8adeb43", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "false" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "c=(a+b)/2\n", "winred(c,168)\n", "a=c\n", "c=(a+b)/2\n", "winred(c,168)" ] }, { "cell_type": "code", "execution_count": 20, "id": "9121a909-2f21-48b4-854d-ee9c24620180", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.25" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c" ] }, { "cell_type": "code", "execution_count": 21, "id": "d369ea7a-bdec-43a8-9bc9-54310530ae9e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winblue(c,168)" ] }, { "cell_type": "code", "execution_count": 22, "id": "57d5019e-5777-4160-8ff7-1a6243f0b145", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "checking [3.0,6.0] at c=4.5...\n", "lambda=4.5 then red wins\n", "checking [4.5,6.0] at c=5.25...\n", "lambda=5.25 then red does not win\n", "checking [4.5,5.25] at c=4.875...\n", "lambda=4.875 then red does not win\n", "checking [4.5,4.875] at c=4.6875...\n", "lambda=4.6875 then red does not win\n", "checking [4.5,4.6875] at c=4.59375...\n", "lambda=4.59375 then red wins\n", "checking [4.59375,4.6875] at c=4.640625...\n", "lambda=4.640625 then red does not win\n", "checking [4.59375,4.640625] at c=4.6171875...\n", "lambda=4.6171875 then red wins\n", "checking [4.6171875,4.640625] at c=4.62890625...\n", "lambda=4.62890625 then red wins\n", "checking [4.62890625,4.640625] at c=4.634765625...\n", "lambda=4.634765625 then red wins\n", "checking [4.634765625,4.640625] at c=4.6376953125...\n", "lambda=4.6376953125 then red wins\n" ] }, { "data": { "text/plain": [ "4.63916015625" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "for l=1:10\n", " c=(a+b)/2\n", " println(\"checking [$a,$b] at c=$c...\")\n", " if winred(c,168)\n", " println(\"lambda=\",c,\" then red wins\")\n", " a=c\n", " else\n", " println(\"lambda=\",c,\" then red does not win\")\n", " b=c\n", " end\n", "end\n", "c=(a+b)/2" ] }, { "cell_type": "code", "execution_count": 23, "id": "562f8abb-2962-44de-83fd-fd1822037452", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.639637090131519" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "for l=1:100\n", " c=(a+b)/2\n", " if winred(c,168)\n", " a=c\n", " else\n", " b=c\n", " end\n", "end\n", "c=(a+b)/2" ] }, { "cell_type": "code", "execution_count": 24, "id": "f99f5db4-06e8-4ce8-a093-77c71362167a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.639637090131524" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "for l=1:100\n", " c=(a+b)/2\n", " if winblue(c,168)\n", " b=c\n", " else\n", " a=c\n", " end\n", "end\n", "c=(a+b)/2" ] }, { "cell_type": "code", "execution_count": 25, "id": "39f0fecc-1f94-4c79-b6f2-cd0d8b8d328f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winblue(6,12)" ] }, { "cell_type": "code", "execution_count": 26, "id": "c07883f2-935b-4957-8819-f0b78c09e940", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "winred(3,12)" ] }, { "cell_type": "code", "execution_count": 27, "id": "bbe95fd3-f927-4a5d-9d47-fb61c2fd19a3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.1851982913899617" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "for l=1:100\n", " c=(a+b)/2\n", " if winred(c,12)\n", " a=c\n", " else\n", " b=c\n", " end\n", "end\n", "c=(a+b)/2" ] }, { "cell_type": "code", "execution_count": 28, "id": "4ae8ebca-4460-4baa-85d0-46e7952bca9d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.708719030676319" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a=3.0\n", "b=6.0\n", "for l=1:100\n", " c=(a+b)/2\n", " if winblue(c,12)\n", " b=c\n", " else\n", " a=c\n", " end\n", "end\n", "c=(a+b)/2" ] }, { "cell_type": "code", "execution_count": null, "id": "ba5245ae-df6f-4180-8eb9-1766d2f84118", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.10", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.10" } }, "nbformat": 4, "nbformat_minor": 5 }