{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HANDY model\n", "\"Human And Nature DYnamics\" is a rather simple model that can be used to study the behaviour of societies or civilizations. It extends upon the well-known predator-prey model by introducing the concepts of accumulated wealth and social stratification. \n", "\n", "Essentially, HANDY describes the competition between humans and nature. Humans can accumulate wealth (essentially 'store food') that will enable them to prosper for some time even if nature is depleted beyond recovery. The population is split in commoners and elites. Commoners do the most fundamental work, i.e. deplete nature to get food for themselves and the elites). Elites could be thought of as managers, elderly, scientists, etc; they do not directly affect nature, but thrive on the wealth accumulated by commoners. Within the model, inequality can be introduced by having elites earn more money (i.e. consume more) than the workers. In that case, if nature is depleted, famine starts to affect the commoners before it reaches the elites.\n", "\n", "The model was introduced in a very [well-written paper](http://www.sciencedirect.com/science/article/pii/S0921800914000615) that also received a lot of attention. Journalists claimed that it predicted the collapse of the current society and critical reviews ([like this one](https://www.wsws.org/en/articles/2014/11/01/hand-n01.html)) accused it of oversimplifying reality. The authors' response to this critisim can be found [here](https://www.elsevier.com/connect/q-and-a-when-a-theoretical-article-is-misinterpreted). \n", "\n", "Regardless of the societal impact of the publication, this model is a very nice toy model and implementing it is a nice exercise. Here I present my implementation of the model in Python and try to reproduce the results of the paper. First, I used scipy's `odeint` solver for the numerical integration. Interestingly, scipy used the lotka-volterra model as [an example](http://scipy-cookbook.readthedocs.io/items/LoktaVolterraTutorial.html) to use this solver. However, this algorithm became unstable for several simulations, probably due to nature becoming negative etc. Using scipy's `ode` instead works fine, regardsless of the solver. However, to reproduce the collapses in the paper, I needed to downgrade to a simple euler scheme.\n", "\n", "Without further due, I will now present the code and proceed with the solutions. I will not bother to describe the model in detail, since this is already very-well explained in the original paper." ] }, { "cell_type": "code", "execution_count": 337, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def handy(\n", " # Prognostic variables & time\n", " x_C = 100., # Commoner population\n", " x_E = 25., # Elite population\n", " y = 100., # Nature\n", " w = 0., # Accumulated wealth\n", " # Model constants\n", " alpha_m = 0.01, # Normal (minimum) death rate\n", " alpha_M = 0.07, # Famine (maximum) death rate\n", " beta_C = 0.03, # Commoner birth rate\n", " beta_E = 0.03, # Elite birth rate\n", " s = 0.0005, # Subsistence salary per capita\n", " rho = 0.005, # Threshold wealth per capita\n", " gamma = 0.01, # Regeneration rate of nature\n", " labda = 100., # Nature carrying capacity (lambda not possible)\n", " kappa = 10., # Inequality factor (1,10,100)\n", " delta = 0.00000833, # Depletion (production) factor\n", " # Extra options\n", " verbose = True, # Print diagnostic output of the simulation\n", " ):\n", " ''' Integrate a society to the next era '''\n", " \n", " from scipy.integrate import ode\n", " import numpy as np\n", "\n", " def tendency(time,society):\n", " ''' Compute the overall tendency for each prognostic variable '''\n", " # Parse input for readability and to prevent negative values sneeking in\n", " x_C = society[0]\n", " x_E = society[1]\n", " y = society[2]\n", " w = society[3] \n", "\n", " # Compute diagnostic (time-dependent) variables:\n", " w_th = rho*(x_C+kappa*x_E) # Threshold wealth\n", " omega = w/w_th if not w_th==0 else 0 # Normalized wealth\n", " c_C = min(1,omega)*s*x_C # Commoner consumption\n", " c_E = min(1,omega)*s*x_E*kappa # Elite consumption\n", " alpha_C = alpha_m+max(0,1-c_C/(s*x_C))*(alpha_M-alpha_m) if not x_C==0 else alpha_M\n", " alpha_E = alpha_m+max(0,1-c_E/(s*x_E))*(alpha_M-alpha_m) if not x_E==0 else alpha_M\n", "\n", " return [\n", " beta_C*x_C - alpha_C*x_C, # Commoners tendency\n", " beta_E*x_E - alpha_E*x_E, # Elites tendency\n", " max(-y,gamma*y*(labda-y)-delta*x_C*y), # Nature tendency, prevent from becoming negative\n", " delta*x_C*y-c_C-c_E # Wealth tendency\n", " ]\n", "\n", " # Do the actual time stepping\n", " society = np.asarray([x_C,x_E,y,w]) # Scipy prefers the state of my society as a list\n", "\n", " # Using SCIPY ode-solver\n", " solv = ode(tendency)\n", " solv.set_integrator('vode',method='bdf')\n", " solv.set_integrator('lsoda')\n", " solv.set_initial_value(society,0.)\n", " ys = []\n", " while solv.successful() and solv.t<1500.:\n", " solv.integrate(solv.t+1.)\n", " ys.append(solv.y)\n", " solution = np.vstack(ys).T\n", " \n", " # Euler forward integration reproduces the collapse mechanism!!!\n", "# ys = []\n", "# for t in range(1000):\n", "# society = society + np.asarray(tendency(t,society))\n", "# ys.append(society)\n", "# solution = np.vstack(ys).T\n", "\n", "\n", " if verbose:\n", " #####################################################\n", " # Some additional output for better interpretation ##\n", " # Determine the type of society\n", " if x_E==0:\n", " soc_type = 'egalitarian'\n", " soc_descr = 'no elites, only workers around'\n", " elif kappa==1:\n", " soc_type = 'equitable'\n", " soc_descr = \"no inequality, but elites don't work\"\n", " else:\n", " soc_type = 'unequal'\n", " soc_descr = 'elites present and richer than workers'\n", " print \"This is an %s society (%s)\"%(soc_type,soc_descr)\n", "\n", " # Determine the ratio of elites/workers\n", " if not soc_type=='unequal':\n", " psi = x_E/x_C\n", " else:\n", " psi = solution[1,-1]/solution[0,-1]\n", "\n", " # Determine whether an equilibrium is possible\n", " eta = (alpha_M-beta_C)/(alpha_M-alpha_m) # Helpful dimensionless parameter\n", " condition3 = abs((alpha_M-beta_E)/(kappa*(alpha_M-alpha_m))-eta) < 0.0001\n", " if not alpha_m<=beta_E<=beta_C<=alpha_M:\n", " print \"No equilibrium is possible for this society\"\n", " elif soc_type=='unequal' and not condition3:\n", " print \"No equilibrium is possible for this society\"\n", " else: # equilibrium possible\n", " workers = gamma/delta*(labda-eta*s/delta*(1+kappa*psi))\n", " elites = psi*workers\n", " nature = eta*s/delta*(1+kappa*psi)\n", " wealth = eta*rho*(1+kappa*psi)*workers\n", " chi = workers+elites\n", " delta_opt = 2*eta*s/labda*(1+kappa*psi)\n", " chi_M = gamma/(eta*s)*(labda/2.)**2*(1+psi)/(1+kappa*psi)\n", "\n", " print \"A theoretical equilibrium for this society is:\"\n", " print \" Commoners: %.f\"%workers\n", " print \" Elites: %.f\"%elites\n", " print \" Nature: %.f\"%nature\n", " print \" Wealth: %.f\"%wealth\n", " print \"Its carrying capacity is %.f\"%chi\n", " print \"Maximum carrying capacity would be %.f\"%chi_M\n", " print \"... attained at depletion rate %.3e\"%delta_opt\n", "\n", " return solution" ] }, { "cell_type": "code", "execution_count": 314, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "def visualize(solution):\n", " \n", " from mpl_toolkits.axes_grid1 import host_subplot\n", " import mpl_toolkits.axisartist as AA\n", " import matplotlib.pyplot as plt\n", "\n", " ax1 = host_subplot(111,axes_class=AA.Axes)\n", " ax2 = ax1.twinx(); ax2.axis[\"right\"].set_visible(False)\n", " ax3 = ax1.twinx() # this one we do want on the default right side\n", " ax4 = ax1.twinx(); ax2.axis[\"right\"].set_visible(False)\n", " \n", "# par.axis[\"side\"].label.set_visible(True)\n", "# par.axis[\"side\"].set_label(PYlabel)\n", " \n", " new_fixed_axis = ax2.get_grid_helper().new_fixed_axis\n", " ax2.axis[\"left\"] = new_fixed_axis(loc=\"left\",axes=ax2,offset=(-60,0))\n", " ax2.axis[\"left\"].toggle(all=True)\n", " new_fixed_axis = ax4.get_grid_helper().new_fixed_axis\n", " ax4.axis[\"right\"] = new_fixed_axis(loc=\"right\",axes=ax4,offset=(60,0))\n", " ax4.axis[\"right\"].toggle(all=True)\n", " \n", " p1, = ax1.plot(solution[0],label='Commoners',color='#1f77b4')\n", " p2, = ax2.plot(solution[1],label='Elites',color='#ff7f0e')\n", " p3, = ax3.plot(solution[2],label='Nature',color='#2ca02c')\n", " p4, = ax4.plot(solution[3],label='Wealth',color='#d62728')\n", "\n", " ax1.set_ylabel('Commoners')\n", " ax2.set_ylabel('Elites')\n", " ax3.set_ylabel('Nature')\n", " ax4.set_ylabel('Wealth')\n", " \n", " ax1.axis[\"left\"].label.set_color(p1.get_color())\n", " ax2.axis[\"left\"].label.set_color(p2.get_color())\n", " ax3.axis[\"right\"].label.set_color(p3.get_color())\n", " ax4.axis[\"right\"].label.set_color(p4.get_color())\n", " \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I will name the figures after their respective section is the original manuscript\n", "\n", "# 5.1 Egalitarian societies (no elites)\n", "## 5.1.1 Optimal depletion rate: soft landing to optimal equilibrium" ] }, { "cell_type": "code", "execution_count": 315, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an egalitarian society (no elites, only workers around)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 75000\n", " Elites: 0\n", " Nature: 50\n", " Wealth: 250\n", "Its carrying capacity is 75000\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 6.667e-06\n" ] }, { "data": { "image/png": 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XUIuPgjzrDjLGmFhhXULD9XsqNv4XzqqyV7pllthNQwUZBXTu7yJuzmwS5849\nWd7Z3UdTm58lNn7FGGNihn0RD3czcCnwE29V+fOeio2XAn+OckwmAgoyCyg6pPQuH7wk/54WZ4aQ\ntbAYM7OJyGdFZLuIbBORB0UkRURyReQpEalzn3OiHWe4iMjPROSwiGwLKKsUkf3BNhkWkTtEpF5E\ndorIeyIdn7WwBPBUbEwE/tNbVX5yeVhvVfnzwPPRi8pESn5cHv5mOF6YN6i8sdmZIWRjWIyZuURk\nEfBpYKWqdorIIzjrYq0EnlHVKhGpwNkj7otRDDWc7gP+G/j5kPLvq+r3AgtEZCXOz2MVzlYzT4vI\nclXti1Rw1sISwFtV3gPkeio22jfVDDB7XztxwL5FyYPKB1pYllgLizEzXQKQKiIJQBrOCuU3AOvd\n+vXA+6IUW9ip6l9x1gYLxQ3AQ6rqV9UGoB64IGLBYS0swRwFDnsqNr4E+AYKvVXlN0QvJBMJfTW7\nANg1d/AfBI3NHWSmJJCdZrs0GzNTqep+EfkesAfoBP6kqn8SkXmqetA97BAwL2pBTp5PichHgM3A\n51X1GLAIZzX3AfvcsoixFpbhGnH2AYoDMgIeZprp2r6D9qxE6uOODir3NvtYYt1Bxkx7a9asIT09\nnfT0dIBBf6G4Y1NuAApxujzSRWRN4DGTsaFtOInIBhHxiYgP575CcTfOvndnAweBf4tUfGOxFpYh\nvFXl7wbwVGzM81aVN491vJm6ump20OaZzb72fYPK97R0cMairChFZYyZLPfff//J1+6WJ4GuABpU\n9Yhb/2vgIqBJRBao6kF3/7jDkxXvRKnqLcAtACKyOcRzmgZei8hPgD+4b/czeOX1fLcsYqyFZQhP\nxcZ/9FRs9ANN7vsbPRUbt41xmplitLubbm8jfZ5FHO48TFdvFwC9ff3sP9aJx8avGDPT7QHeJiJp\n7ka0l+Ps7fYYsNY9Zi3wuyjFNykGNvV1vR8Y+D58DLhJRJJFpBAoBjZFMhZLWIb7Ps605m4Ab1X5\nL4FlUY3IhF13YyP09pJSXAzA/hPOHwYHjnfR268sybUuIWNmMlV9BfgVsAWoxvm+/DFQBVwpInU4\nrTBVUQsyzETkQeAlYIWI7BORW4HviEi1iLwJvAv4LICqbgceAXYATwDrIjlDCKxLKChvVfkmT8XG\nwKIp00dpQuOvrwcgp/QsqP8l+9r3sTR7KV53SrOtwWKMUdWvAl8dUuzHaW2ZdlT15iDF945y/J3A\nnZGLaDCNr83dAAAgAElEQVRLWIY77qnY+HEAT8XGVJwMcsr0UZrQ+OvqIS6ORasugHrY274XcDY9\nBJvSbIyZHGXrywT4MFBUvbb662XrywqA+dVrqyPavRItNSWlFwEeAvKP0tqaoeu+BGUJy3DvBp4E\nknGmNXuZptn0TOavrydxcT65WfNJS0hj3wln4O2eZh/JCXHMy0iJcoTGmBniLqAf57vn60A78Chw\nfjSDioSaktINwFJgKzDQfaQMX6guKEtYhvBWle8i9OleZory19eTvKwYEWFxxuKTM4UamzsoyE0j\nLk6iHKExZoa4sHpt9Tll68teB6heW32sbH3ZdF0E6jxgZWltzWkNs7CEZQhPxcYS4D+AAiB+oNxb\nVb48akGZsOrv7qa7sZGMK529LfMz8mlobQCcKc3WHWSMmUQ9ZevL4nHHSpatL5uD0+IyHW0D5uOs\n5zJuoSUslVk3Ak9Q2dpOZdaXgXOAb1LZuuV0PjTGbeLUqOfe8Z4sIolAK9CuqvNEpAh4FWfxuXbg\nXFX1usc+gdMMCFCpqt9yyz+MM9Apzo1ltaqqiGQA23H+wbuBq1X1hdO90Zmqu8ELfX0kL3Mmf+XP\nyueF/S/Q199HY3MHFy2dHd0AjTEzyX8CvwHmlq0vuxP4APDl6IYUXjUlpb/HScgygB01JaWbcAYv\nA1BaW/PeUK4TagvLv1DZ+ksqsy7Bmcb1XZzV7y4cV9RTQ6K3qvxtEzj/VziDdFPd9w8Cm1T1GhH5\nI/AQztz+64HLgDycFQT/LCLfVdUe4EfAOuBn7rW+DHwD+AlOIlQgIv8BPIDTEmTGwV9fB0DycmdK\nc35GPv4+PzuPHKCzpw/PbGthMcZMjuq11b8oW1/2Gs5YSQHeV722uibKYYXb98Y+ZGyhJiwDg2PK\ngR9T2bqRyqxvhiOAGLTZU7HxK96q8q+P90QROQ9nDZdvcmr3ztWcGjxVgdPaAk5C8pyqtgPPi0gr\n8FER2QQkquq97jUfAm7GSViuAO5wz/8Czv4O4i4PbULkr6+H+HiSCp2hSosznMUaXz/oTHUuyLWE\nxRgTeW5X0PbqtdUlQG2044mU0tqa5wBqSkq/XVpbM2hn65qS0m8Dz4VynVAXjttPZdaPgL8HHqcy\nK3kc5041lwBf81Rs1MBHiOf+FvgUg/sfE1X1Dff1m0Ci+3ohsDvguGZgBXAmcCKgvBanFQZgFvA6\ngKr6cRLJ4hBjM67u+nqSCgqIS3LGteVn5ANQc9QLYPsIGWMmRfXa6j5gpzuVeSa4MkjZNaGeHGoL\nyweBq4HvUdl6nMqsBcD/C/VDphJvVflpTQ8Rka8Bx1X1FyJye7Bj3HEoEW0N6ezsxFlF2uHxeGho\naIjkR045/rp6kotP5XkL0xcSJ3F4W/cSJ3NZlJ06ytnGGBNWOcD2svVlm3CW0gCgem11SOM6poKa\nktJPAP8EFNWUlL4ZUJUBvBjqdUIcdNvaQWXWYZzWhzqcwah1IUc7xXgqNn4TeI/79nFvVfnQlQ6D\nuRIoEZFenH7IOBHZDfSIyFmq+oaInMWpgbwHcHbAHJAH7MRphZkVUF6C0/oCTsvLamCziCTjzGIa\n9O+QmpqKz+fDBNfv99O9Zw+Z155K6hPjE5mfNp9DHftZmH0JSQnTtfHQGBOD/iXaAUyCB4A/Av+K\nMzRiQHtpbU1LqBcJdZbQV3HmT68A/genW+N+4OJQP2gkInI1zjTieOCnqlo1pF7c+muBDuCjqrol\nlHNPh6di40s49/lbt+iTnoqNV3qryi8a7TxVPVnvtrDcoapF7piUKpxmryrcLh2cxYIedmf+nA1k\nAfepao+I9Lh7OPwMuAn4L/ecZ4DbcQbffgfYb+NXxqe7oQH6+0/OEBqQn5HPG22HKLHuIGPMJKpe\nWx3S+I0pLh5owxm7OUhNSWluqElLqF1C78f5y96ZxlzZeoDKrIwQzx2RiMQDP8RpndgHvCoij6nq\njoDDrsEZp1GMMyvpbuDCEM89HWcDs7xV5X0AnoqNiTg/6NP1IWCTu3V5O+4AXFV9TESeB1pwpnt9\n3Z0hBPAJnKTkHpzdQb/hln8c2OZeqxtnELQZB3+dM7A2KUjCsoka20PIGDOpytaXtXNqv7oknAYB\nX/Xa6szoRRV2r3HqHocOu1AG9zaMKNSEpZvKVqUyy/nAyqxw/Rl6AVCvqrvh5IyYG3DWHhlwA/Bz\ntyXhZRHJdre79oRw7ulawqkBsYvHe7Kq/gD4gfu6Hsgd4birRijfAGwIUt56OvGYU/z19ZCQQLLH\nM6h8TspCiG9nQbatcGuMmTzVa6tP/vHv7it0AzCRpTViTmltTVhWjw81YXnEnSWUTWXWPwL/APw0\nDJ+/CNgb8H4fw9d2CXbMohDPPR0/BXZ5KjZ63fdLcFpypre+Xji6K9pRRJx/+xaSFs1HjtUPKk9v\ndxq35uqb0GRjWIyZkhJTIDekP9ZjUvXaagV+W7a+7KsMHusxbdSUlObg9Jic3LCttLbmr6GcG+qg\n2+9RmXUlTtfICuArVLY+Nf5QY5+3qvxTnoqNPwVudIse9laVV0czpknRdRzufnu0o4g4/9a5pOT0\nDLvX85OSYNF8Zm/+HPy1M0rRGWMmZNF58I/PRDuKcSlbX/Z3AW/jcMaLdkUpnIiqKSn938BngHyc\nDRDfBrzEqRXfRxXqoNtvU9n6ReCpIGUTsZ/BXRz5blkoxySGcC5AoYgETpv5tareMkZcAwMcEoE1\nnoqNeKvKJ3qvsS05A25cH+0oIqrf30PPw18l69r3wI1XDKrbtc0LXffSsPrDsPDS6ARojJmY1Jxo\nR3A6rg943Qt4cbqFpqPP4IzjfLm0tuZdNSWlJcC3Qj051C6hKzm1cuuAa4KUjderQLGIFOIkGzfh\nDFIN9BjwSXeMyoVAq6oeFJEjIZwL0KCq54UakKdi4y6c7qaDnBokpEz8XmNbQjKsel+0o4io7h07\nQJXki66DVVcPqnul5k3oe5ADs7Km/c/BGBNTflq9tnrQWiRl68suxtmWZbrpKq2t6aopKaWmpDS5\ntLamtqakdEWoJ4+esFRmnVzshcqs017sZSSq2isinwSexJn29DNV3S4it7n19wCP40xprseZ1vyx\n0c6daEzAEm9VeXIYrmNijL/eGbcydEozgLfZR0riXPa075nssIwxM9t/4WwoPFbZdLCvpqQ0G2fZ\nkKdqSkqPAY2hnjxWC8uIi71Q2RryYi+jUdXHcZKSwLJ7Al4rQeZuj3RuGHg9FRuv91aV/z7M1zVR\n5q+rh8REkpYsGVa3p6WD7MUL2dNmqwIbYyKvbH3Z24GLgDll68s+F1CVifNH+LRTWlvzfvdlZU1J\n6bM46489Eer5YyUsSmWrl8qs4QlDZVZuuJKWGPND4DFPxcYenL16BFBvVbmt1z7F+evrSfYsQRIT\nB5V39fRxqK2Ld6Qt5vX2l/D3+UmOt0Y2Y0xEJeGsap6A02sxoA34QFQimgQ1JaWXAMWltTX/U1NS\nOgdnCEZIfymG0sJyHacWfQlcpCLkxV6mmO8Bd+J0NfWNcayZQvz19aScsWpY+b5jHahCUfYStrQr\n+9r3sTR7aRQiNMbMFO4Kt8+VrS+7r3ptdcjdIlNZTUnphFbNH2MMS+t17nNYFn2ZIvzeqvIvRzsI\nE179nZ307NtH1vuGD773Hu0AYOXcItgLjW2NlrAYYyZLR9n6su8CqwhYm6R6bXVIU32nmEGr5pfW\n1hyoKSkNedX8sQbdjj7op7J1S6gfNIU0uovG/R5nkC/A9J/WPM3539rtzBBaVjysrrHF+We+YNEK\neA32tNnAW2PMpPkF8DBOb8ZtwFrgSFQjipzu0toarSkpVYCaktJxrZo/VpfQv41Sp4S42MsUkwz0\nAIHzXqf/tOZpzl/vbGqdXDx8htCeZh8ZyQkUZOeRlZxlM4WMMZMpr3pt9b1l68s+E9BN9Gq0g4qQ\nR2pKSn8EZNeUlA6smv+TUE8eq0voXROLberxVpUP/xPcTHnd9fVIYiJJBQXD6hpbOijIS0NEWJKx\nxFpYjDGTaWDT24Nl68vKgQOMsP/cVFVTUno78DecPfbeRcCq+aW1NSGvmj9Wl9AXqGz9jvv6Ripb\nfxlQ9y0qW7807shjnKdi46U4P9T5BEwt81aVz49aUGbC/HX1JBUWIgnD/5NvbO6gdIHTjbo4czFb\nmqZjT6cxJkZ9s2x9WRbweZz1VzKBz0Y3pLDLx/leLQGqcdZx+xvOhJ6QjdUldBPwHff1HcAvA+qu\nBqZdwgL8CdiIM3LZZglNE/66OlLPPntYeV+/su9YB+9Z5eSjSzKW8Pjux21qszFmUlSvrf6D+7IV\np/Vh2imtrfm/ADUlpUk4s4QuwlkE9sc1JaXHS2trVoZynbESFhnhdbD300Wft6p82s6Bn4n6fT56\nDhwg+8bh/6wHjnfS06d48tIAKMgsQFH2tu1lWc7w8S7GGBMOZevLvjJKtVavrf7GpAUzeVJxWpCy\n3McBnBaXkIy9cFzw18HeTxf3eSo2/hl4EDi5aaK3qvyB6IVkJsL/1lsAJAVZkn+PO0OoYCBhyXDG\nuOxp32MJizEmknxBytKBW4E8YNokLDUlpT/GmbbdDryC0x3076W1NcfGc52xEpazqMxqw2lNSXVf\n475PGfm0Ke0c4AL3OXDzQ0tYpih/3ch7CDU2OwnLkjxndl1Bppuw2MBbY0wEVa+tPjkLt2x9WQbO\nTsYfAx5i9Bm6U1EBzgzcOpzNivcBx8d7kbFmCU3L/QzGcB6Q5a0qD5b9jkhEsnD+IeJxErqXVfWd\nIlKEsyt1Bk52ea6qet1znuDU1PBKVf2WW/5h4F4gDtgBrFZVFZEMYDvOgOBu4GpVfWEiNzsT+Ovr\nkaSk4DOEmn0kxccxP9PJv7OSs8hOzqaxfUYsPGmMGYWIrMBZI2VAEfAV4OduuQfwAh9U1XG1FgCU\nrS/LBT4HfBhYD5xTvbZ63NcJFxH5Gc56MIdV9Qy3LJcR7lVE7sBpEeoDPq2qTwa7bmltzdU1JaWC\n08pyEc4A4zNqSkpbgJdKa2u+Gkp8cad/a9NWMzB8d7yxtQFLVTUVyAHOE5FbcbqWNqlqErAJJ3tG\nRK4HLsNp+rsc+JqIDGxy8yOcDR+TcfZZGFh59ydAu3ute7FWn5D46+tJKipC4ofn343NHSzOTSU+\n7tSQrIKMAva27Z3MEI0xMUhVd6rq2ap6NnAuzmKiv8HZDPgZVS0GnmHw5sAhcVe3fRXnD9my6rXV\nldFMVlz3MXgNMhjhXkVkJc7EnFXuOXeJyIiNHKW1NVpaW7MNZ8PiP+LMFFqK07IUkrG6hGaiVGCb\np2JjC9A7UDjWtGZ3V+km920aTjKoOMsQn++WV+D8BwpOQvKcqrYDz4tIK/BREdkEJKrqvQAi8hBw\nM05/5hU4s7UAvgB8SkTE/WwzAn9dHWkXnB+0rrGl42R30ICCzAI2N22ejNCMMVPH5cBbqtooIjcA\n73TL1wN/YfyLi34e8OP8QfrPZevLBsoFZ9Bt5kQDHi9V/auIeIYUj3SvNwAPqaofaBCRepzhFC8N\nvW5NSemncVpWLsJZd+Zv7uNnhHHQ7Uw02sjtUbktJG0443teUdWfici9qvqGe8ibOJs9ASwEArtz\nmnEW0ukCTgSU1wIfdF/PAl4HUFW/iPQBxcCu0415uutra6P30CGSi4evB6iq7Gn2cWHh4DWaCjIL\n+MPuP9DV20VKwnQdqmWMGaebcFrMAeap6kH39SFg3ngvVr22eqr0cIx0r4uAlwOO2+eWBePBWRbl\ns6W1NQdHOGZMU+UHNmm8VeX/idPslec+nnbLxqSqPW6XkAdYISLvG1KvRHh2VWdnJyJy8lFYOJP2\nrRzOX+8OuA2SsBw90Y2vu48l7gyhAQMzhfa174t8gMaYqFmzZg3p6emkp6cDJI10nIgkAe9l8Fpk\nwOT8Xg8XEdkgIj4R8QHj/nI43Xstra35XGltzaMTSVbAEpZhPBUbvw+8gTMIag3whqdi4/fGcw1V\nbcTZjfJWoEdEzgJwnwe6mQ7gDOAakAfsxGmFmRVQXoLT+gJOy8tq91rJOAN86wI/OzU1FVU9+Who\naBhP6NOOf5fT+JQSJGHZ0+KMq/YM6RJakukMYbKBt8ZMb/fffz8+nw+fzwfORIaRXANsUdWBbv8m\nEVkA4D4fjmyk4aGqt6hquqqmA6F+OYx0r/uBxQHH5btlEWMJy3C3AWd6q8qXeavKlwJlOONNRiUi\nJSKyxH2dgzPbaAuwFahyD6vC7dIB7gIuE5EMEbkUZxGd+9zuox4RuVVEBKcZ8iH3nGeA293X3wH2\n2/iV0fl31RGXnk7CwoXD6gamNBcMaWFZnOH8P2gDb40xrps51R0E8BjOrsq4z7+b9Igmz0j3+hhw\nk4gki0ghzvCETZEMxMawDCfeqvIdAe/rCG1V31XABjfJEOBFVf2qiGwANolIN85o8PMBVPUxEXke\naMFpYvu6qg5sgvUJnBlB9wA1nFpA6OPANvda3UD5BO5zRvDX1ZFcXIzzzzJYY3MHIpCfkzqo3KY2\nG2MGiEg6cCXwfwKKq4BH3JmgjZwaZziliciDOANsZ4vIPuCrjHCvqrpdRB7BWXqjF1inqhHdzsYS\nluHe9FRsPAr81n1/A04ryahU9VHg0SDl9Yyw86aqXjVC+QZgQ5DyVgY3wZlRqCr+ujoyrrwyaP2e\nlg4WZqWSnDB8Jl5BZoEtHmeMQVV9OF32gWXNOLOGphVVvXmEqqD3qqp3AndGLqLBLGFxeSo2vhtY\n7q0qv8BTsfHbOFOIwRlT8s3oRWZOV++RI/QdPx50wC2At9lHQW5a0LqCDJvabIwxscQSllMexOmK\nwVtVfnI+vadi49+5daOuw2Jij7/OGY+cvHx50HrvUR/XlC0IWmdTm40xJrbYoNtTZnmryn89tNAt\ny45CPGaCTiUsw1tYjvm6OdbRQ+GQGUIDlmQ4M4VsarMxxsQGS1hOSRylzn5OU5C/ro74vDwScocP\nIWpodqY0F84OnrAMbIJoA2+NMSY22BfxKQc9FRt/PrTQU7HxPpzV/cwU499VN/L4laNuwjIneMIy\nMLXZBt4aY0xssDEsp1wLvOSp2HgcqHfLluEsznZR1KIyp0X7+vDX15N94weC1jcc9REnsDgn+KDb\nganNe9otYTHGmFhgCYvLW1W+Hcj0VGz8LKcSlAe8VeX/HsWwzGnq9nrRzk5SSlcGrd991Mfi3DSS\nEkZuZLSpzcYYEzssYRnCW1X+feD70Y7DTEzXjhoAUlYGT1i8R33DluQfypPp4eWDL496jDHGmMlh\nY1jMtNS1YweSlERy0fD9vVSVhqO+EQfcDijMKuRwx2F8Pb5IhWmMMSZElrCYaamrpobk5cuRxOGT\nvw63++no7hs7Ycl0kh1vqzcSIRpjjBkHS1jMtKOqdNXUkFJaGrT+rSMnACgaYYbQgMIsJ2HZ3bo7\nvAEaY4wZt6glLCKSKyJPiUid+5wzwnFXi8hOEakXkYqA8u+KSK2IvCkivxERW9zNANB74AD9ra2k\nrAyesOw61A7A8nkZo15nccZi4iWehtZQd2E3xhgTKdFsYakAnlHVYuAZ9/0gIhIP/BC4BlgJ3Cwi\nA6MonwLOUNUzgV3AHZMStYl5XTWjD7jddfgEmSkJzM1IHvU6ifGJLM5YjLfNG+4QjTHGjFM0E5Yb\ngPXu6/XA+4IccwFQr6q7VbUbeMg9D1X9k6r2use9DORHOF4zRXTtqIG4uBH3EKpramf5vAxEZMxr\nebI81sJijDExIJoJyzxVPei+PgTMC3LMImBvwPt9btlQ/wD8Mbzhmamqa8cOkooKiUtNHVanquxq\nOsHy+aN3Bw0ozCqksa2R3v7esQ82xhgTMRFdh0VEnib4Lsf/HPhGVVVE9DQ/45+BXuAXIxxSKCKB\n81J/raq3nM5nmamhq6aGtAsuCFp3uN1Pa2cPy+fOCulahZmF9PT3cODEgZP7CxljjJl8EU1YVPWK\nkepEpElEFqjqQRFZABwOcth+YHHA+3y3bOAaHwWuAy5X1ZESngZVPW/cwZspqaepid6mJlLLzgha\nv6sptAG3A4qyiwBnppAlLMYYEz3R7BJ6DFjrvl4L/C7IMa8CxSJSKCJJwE3ueYjI1cAXgPeqasck\nxGumgM433gAg9ayzgtbvanKmNIfaJeTJ9ADYOBZjjImyaCYsVcCVIlIHXOG+R0QWisjjAO6g2k8C\nTwI1wCOqut09/7+BDOApEdkqIvdM9g0EEpELROSYiPhFpEtEHnXLi0SkWUS63WdPwDlPuOXdIvKl\ngPIPu9fodu9N3PIMEdnjlp8QkUsm+z5jXdebbyKJiSSPsAbLrkPt5KYnMXvW6DOEBmQlZ5GXkmcJ\nizHGRFnUEhZVbVbVy1W1WFWvUNUWt/yAql4bcNzjqrpcVZeq6p0B5ctUdbGqnu0+bovGfQTwA+tU\nNRkoBK4XkeuBB4FNqpoEbMKZ6YRbdxmQB1wOfE1EBpZl/RGwDkjGGWT8Zbf8J0C7e617gQcm48am\nks433iS5tJS4pKSg9dsPtrJyQea4rlmYVWgJizHGRJmtdBsmqvqGqj7gvj4INOOsHbOaU2vMVADn\nuK/XAc+paruqPg+0Ah8VkbOARFW91x2X8xBws3vOFcAP3NdfAPIHWl8MaG8vndu2jdgd1N3bz65D\nJ1i1aPwJy+7W3Yw8TMoYY0ykWcISAW5XzRzgfpzk4w236k1goBVlIRC45nszsAI4EzgRUF6L0woD\nMAt4HUBV/UAfUByBW5iS/PX1aGcnqWeeGbS+7nA73X39nLEwa1zXLcwqpK27jWP+Y+EI0xhjzGmw\nhCXMRGQezpibf1PV/YF1botJRP9M7+zsREROPgoLh+9WPF11bh0YcBs8Ydm+vw2AVQvH38ICsPu4\n7SlkjDHRYglLGIlIKrAdeFpVv+gW97jdPLjPAyuQHQCKAk7PA3bitMIELhJSgtP6Ak7Ly2r3WslA\nPFAXGENqaiqqevLR0DBzxl50vvkm8Tk5JC5eHLR+24FW0pPi8eSNvunhUMuylwFQf7x+wjEaY4w5\nPZawhIk7lmQbsFdVbwio2oo7A8p9ft19fRdwmTvz51IgC7jP7T7qEZFb3WvehDtQF2fPpdvd198B\n9o+y/syM07llC6lnnTXikvvbD7SxamEWcXHjG/YzL20eGYkZ1B2rG/tgY4wxERHRheNmmNtwWky6\nRKTTLftX4EPAJhHpBtqB8wFU9TEReR5owekm+rqq9rjnfQJnRtA9ONO5v+GWfxzY5l6rGyiP+F1N\nET2HD9Pt9ZJ9441B6/v6lR0H2rjpguCtL6MREYpziqk7bgmLMcZEiyUsYaKqdwN3j1CdO8I5V41Q\nvgHYEKS8lcEr/xpX5+bNAKSdH3xR411N7XT29HFm/vgG3A4ozinm8d2Po6ohbZpojDEmvKxLyEwL\nHZs3E5eWRsrKlUHrt+xxZvicU5BzWtcvzi6mvaedQ75Dpx2jMcaY02cJi5kWOl59ldRzzkESgjca\nbmk8Tl56EgW5aad1/eIcZ/a4dQsZY0x0WMJiprzeY8fw19WTdv75Ix7z+p5jnLMk57S7c5blODOF\nbOCtMcZEhyUsZsrrePVVgBETlhZfN7uP+k67OwggMymT+enzrYXFGGOixBIWM+V1bHoVSUkh9YxV\nQetfPzl+JXtCn1OcXWwtLMbMMCKSLSK/EpFaEakRkbeLSK6IPCUide7z6f81FGNExCsi1e7Gu5vd\nspi4X0tYzJTne/FF0i44Hxlhw8NXvcdIiBPOzJ9gwpJTzO7W3fT094x9sDFmuvgP4AlVLQHOwllq\nogJ4RlWLcdbHqhjl/KnoXe6mwgPTLmPifi1hMVNa9759dDc0MOuSS0Y85qXdzawuyCY1KX5Cn7U8\nZzm9/b22RL8xM4SIZAHvAO4FUNVuVT0O3ACsdw9bD7wvOhFOmpi4X0tYzJTme+EFANIvuTRofVtX\nD9X7jvP2pbMn/Fkr85wp0zuad0z4WsaYKaEQOAL8j4i8LiI/FZF0YJ6qHnSPOQTMi1qE4afA0yLy\nmoh83C2Lifu1hMVMaSdeeIHERYtIKvQErd+0u4V+hbcX5QWtH48lmUtIT0y3hMWYaWLNmjWkp6eT\nnp4OEKxPOQE4B7hbVVcDPoZ0h0zGprbhIiIbRMQnIj6cZCyYS1T1bOAaYJ2IvCOwMpr3awmLmbK0\np4eOl14m/dJLRpyu/Le3mklOiGP1BAfcAsRJHCW5JexosYTFmOng/vvvx+fz4fP5wNnuZKh9wD5V\nfcV9/yucBKZJRBYAuM+HJyPeiVLVW1Q1XVXTgaA746rqfvf5MPAb4AJi5H4tYTFTVsdrW+j3+UYd\nv/K3t45ynieHlMSJjV8ZsDJvJTtbdtLb3zv2wcaYKU1VDwF7RWSFW3Q5sAN4DFjrlq0FfheF8MJO\nRNJFJGPgNXAVzqa+MXG/tpeQmbLan34aSUkh/aKLgtYfbO2k9lA7X7y6JGyfuTJvJf4+P28df4sV\nuSvGPsEYM9V9CviFiCQBu4GP4fyx/4iI3Ao0Ah+MYnzhNA/4jdtinQA8oKpPiMirxMD9WsJipiTt\n76f9qadIv+Ri4tKCL7f/bO0RAK4onRu2z12V56z1sqN5hyUsxswAqroVCLar6uWTHUukqepunKnb\nQ8ubiYH7tS4hMyV1bdtGb1MTmVdeOeIxf65tIj8nlWVzZ4Xtc23grTHGRIclLGZKan/qaUhIYNY7\n3xm0vqunjxfqj3J5ydzT3j8omDiJozS3lG1Ht4XtmsYYY8ZmCYuZclSVtv/f3p3HV1WfeRz/PFlu\n9g1CIOwBDBQlLNKgjI5lBEWt+LItKFZrreNoX+KrtrWVqdXW2lZqF2faTkerYjuiRS1asAqCtFq1\nZVGQWHaEEAxkIQkhZCHbM3+cE7wkN7VA7j3nJs8bzitn+d1zv/cScp/8zu+cs/pVUgoLic3ICNnm\n7asnoG4AABLLSURBVD2HaWppZ8a4njsc1GFSziR2VO+gsbWxx/dtjDEmNCtYTNRp2rKFlv0lpF9x\nRbdtXi46RHpiHNN74IJxnU3OmUyrtlovizHGRJAVLD1ERHaJSLuINAWtGyUiVSLS7H4dGbRtlbu+\nWUS+FbT+8yLS5K5/T9zjGSKSJiIl7vpjItL9uby93JHly5GEBNIuvSTk9qaWNlZvK+fSswcRiOv5\nb/GJA5wxaZsrNvf4vo0xxoRmBUvP+Tlwfad1vwM2qGoA2AAsBRCRK4GLgP44I6/vF5F49zGPArcD\nCcAQ4Nvu+seAOndfTwDPhO+l+Jc2N1P3ykrSZs4kNjX0YNo3dlVy7HgrV04cHJYMGQkZjMkcw6aK\nTWHZvzHGmK6sYOkhqvpLoKTT6sl8dBnnhThXSASnIHlDVetU9U2gFviiiEwE4lX1Cffyx0uB+e5j\nZgL/5c5/ExgqPTmaNErUvfEGbbW1ZFw1p9s2L205SL+UANNHn/nl+LszKWcSRRVFtGt72J7DGGPM\nR6xgCa94Vd3izhcBHb0og3EuQNShChgLFADHgtbvwOmFAUgFNgOo6nGgDTgrPLH968izzxGXk9Pt\nxeJq6ptZvbWcKwtyiYsN37f35JzJ1LXUsefInrA9hzHGmI9YwRIhkbphVGNjIyJyYsrL6+7+VtGn\nubiY+rfeIvOaeUhc6GsevrC5lOa2dq4tHB7WLFNynM6yjWUbw/o8xhhjHFawhFeLe5gH92vHDWgO\nAqOC2vUHduL0wgQPzBiH0/sCTs/LZHdfCUAssLvzEyYlJaGqJ6Z9+0Le3yoq1fxuKcTFkTl3bsjt\nqsrSDSVMHJbJJ3LTw5plaNpQhqYOZd3BdWF9HmOMMQ7PChYR6Scia0Rkt/s1q5t2s0Vkp4jsEZGF\nIbZ/XURURHr+/NUz9x6wyJ1fhHtIB/gVcJF75s+FQAbwG/fwUYuI3OyOT7kWd6AusBa4051/CCh1\ne236hPb6eo688ALpl1xCfE7oa6u8u7+G3RXHmP/JYRHJNH3wdDaUbaClvSUiz2eMMX2Zlz0sC4G1\nqnoWzodxqGIkFvgf4DJgPDBfRMYHbR+GczfJzoNdI05E9gNvAAki0ioiTwLXAdNEpBnnFt3zAVR1\nBfAmUI3z2r+nqh2fel/Gec3NwCHgAXf9fwDp7r5upusZSb1azbPP0V5XR78v3NBtm8fe3EtGUnzY\nzg7q7PzB59PQ2kBRZVFEns8YY/oyL29+eBXwKXf+t8DrwN2d2hQCe9wbMiEiS93HddzI5WGcM2Y8\nv7W3qo7oZlO/btqHvIiIqj4FPBVifS0Qma4Dn2k/fpyqJxeTfP55JE2aFLLNB5XHWL2tnAUzxpCS\nEJlv68LcQmIkhr8e/CvnDjw3Is9pjDF9lZc9LANV9ZA7X4ZzW+vOhgAHgpY/dNchIlfhHBbZEuJx\nphc5smwZbZWHyb71tm7bPPaXvQRiY7hx+siI5UoPpDMhewJvl74dsec0xpi+KqwFi4i8JiJ/DzFd\nFdzuVM+gEZFk4FvAfT0c2fhMe309Vf/7CElTppA8rTBkmwPVDbywqZS5U4eSnZoQ0Xwzhs1ga9VW\nDh079PGNjTHGnLawFiyqOlNVzwkxLQfKRSQXwP1aEWIXpZx8GGSou240kAdsEZFid/0mERkUYh95\nIlIfNHU53GL8q2rxk7RWVpJz113d3nX5J6t3EhMDC2ZE/rI0s0bMAuC1ktci/tzGGNOXeHlIaAVw\nozt/I6HHoWwEzhKRPBEJ4Jw1s0JV31fVHFUdqaojcQ4VTVHVshD72KeqKUFT96M2ja+0lFdQtXgx\nabNnkzxlcsg2739Yy/L3DnLzBXkMykiMcEIYnj6c/Kx8XttvBYsxxoSTlwXLImCWiOzGuez8IgAR\nGSwirwCoaiuwAHgV2A48p6pbPcprIqz8+9+HtjZyvv61kNvb25XvvrSVrOR4br1odITTfWTm8Jls\nrthMRUOoTkJjjDE9wbOCRVWrVPViVT3LPXRU7a4/qKqXB7V7RVXzVXW0qv6gm32NVNXDkcpuwu/o\nq6upW7OG7DsWEBgW+uSop9fv5939NdxzxXjSE+NDtomE2XmzUZSXPnjJswzGGNPb2ZVuje+0Hj5M\n2QMPkDh+PP1vuilkm9Ijjfxo1U4uGJPNZ6cMiXDCk+Vl5DElZwov7H6BPnQtP2OMiSgrWIyvaFsb\npd/4Bu3HjpG76MGQ9wxqaWtnwTObAPjh1RO6HYwbSZ/L/xwldSW8U/6O11GMMaZXsoLF+Erlz39B\nw9/WMejee0nMzw/Z5kcrd7C55AiLPjuB4f2TI5wwtJkjZpIWn8bSHUs/vrExxphTZgWL8Y2aZ5+j\n6tFHyZw7l4zPXB2yzTPrS3j8rX184fwRfLogMpf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.,delta=6.67e-6)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.1.2 Oscillatory approach to equilibrium" ] }, { "cell_type": "code", "execution_count": 316, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an egalitarian society (no elites, only workers around)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 47928\n", " Elites: 0\n", " Nature: 20\n", " Wealth: 160\n", "Its carrying capacity is 47928\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 6.667e-06\n" ] }, { "data": { "image/png": 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G1qWtrwJexFptStLGG7DWGrCWmnOda/mx/9F2pW9ibGwMEUk91q5dm8/LXrJE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\nG15a8jS3E5hvgb6GYRhgQsYoEC23/gf9f36GuTd9nuCyZZOe9+0/7eT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.,delta=1.67e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.1.3 Cycles of prosperity, overshoot, collapse and revival" ] }, { "cell_type": "code", "execution_count": 317, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an egalitarian society (no elites, only workers around)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 32777\n", " Elites: 0\n", " Nature: 12\n", " Wealth: 109\n", "Its carrying capacity is 32777\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 6.667e-06\n" ] }, { "data": { "image/png": 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WnAT7lsoysblx040cunRoxeNkbCtALOQlZhX4m0k0voAq6wbUVeLr4+qOq/G5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\nuE8TD8MioLoKY0YGb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.,delta=2.67e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## 5.1.4 Irreversible Type-N collapse (not reproduced)" ] }, { "cell_type": "code", "execution_count": 318, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an egalitarian society (no elites, only workers around)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 24773\n", " Elites: 0\n", " Nature: 9\n", " Wealth: 83\n", "Its carrying capacity is 24773\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 6.667e-06\n" ] }, { "data": { "image/png": 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t2BGnY2SSKpn3PvrcPi5ouaBki0z8xAlS0SiB800h42lsxN3UxMzR3OX5MwPV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\n3coveLZsIWHevG7FM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.,delta=3.67e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 5.2 Equitable societies\n", "\n", "## 5.2.1 Soft landing to optimal equilibrium" ] }, { "cell_type": "code", "execution_count": 319, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an equitable society (no inequality, but elites don't work)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 60000\n", " Elites: 15000\n", " Nature: 50\n", " Wealth: 250\n", "Its carrying capacity is 75000\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 8.333e-06\n" ] }, { "data": { "image/png": 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v7MZN/eoEz/V+4BmvJyMmVPV8VU1R1RTgc8BBVV0MbALKvcPK8R7vAD8ELvJm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\nZIwxccQeD5kJpc3vJ72oCEka+Fe7seE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=25.,kappa=1,delta=8.33e-6)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.2.2 Oscillatory approach to equilibrium" ] }, { "cell_type": "code", "execution_count": 320, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an equitable society (no inequality, but elites don't work)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 36846\n", " Elites: 9211\n", " Nature: 19\n", " Wealth: 154\n", "Its carrying capacity is 46057\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 8.333e-06\n" ] }, { "data": { "image/png": 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FjGXV8eaWN9MQbOD2529f0Lxsn2kU6WlqKnneXRMlPzKKqpJPGFETrnaK6XnCBPPxkvMs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=25.,kappa=1,delta=2.2e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.2.3 Cylces of prosperity, overshoot, collapse and revival" ] }, { "cell_type": "code", "execution_count": 321, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an equitable society (no inequality, but elites don't work)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 28704\n", " Elites: 7176\n", " Nature: 14\n", " Wealth: 120\n", "Its carrying capacity is 35880\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 8.333e-06\n" ] }, { "data": { "image/png": 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/61tJPfwjSunaOhuR4gJGQAc0ZySKrwMxYyirLcOyejk+j48rBq7g8VOPO953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\nK0pY7rCf6NQUzvWLq8yA4rZJ9x3wxlzEE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6yAOUxhJcqUiBDiaRQF+57lliWOEKIA+Gvg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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=25.,kappa=1,delta=3.0e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.2.4 Full collapse (not reproduced)" ] }, { "cell_type": "code", "execution_count": 322, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an equitable society (no inequality, but elites don't work)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 20872\n", " Elites: 5218\n", " Nature: 10\n", " Wealth: 87\n", "Its carrying capacity is 26090\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 8.333e-06\n" ] }, { "data": { "image/png": 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yFBsMZqxHZTuD+biLR7MVc5VSJB9+hMgrX0HkulcCkP5J7cUjOa3FjC/ST8nf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fSOMTXJTMTWBBVy3hoMnTSTlNI3mWnktwHYG9frz2XEbet/D5FoNT7GkGYKTedzsxYXtfQyDsKl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\nvM9yzts+ZPgeQ/HavWTZs2jpV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=25.,kappa=1,delta=4.33e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.2.5 Preventing full collapse by decreasing average depletion per capita (less workers)" ] }, { "cell_type": "code", "execution_count": 323, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an equitable society (no inequality, but elites don't work)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 10650\n", " Elites: 63897\n", " Nature: 54\n", " Wealth: 248\n", "Its carrying capacity is 74547\n", "Maximum carrying capacity would be 75000\n", "... attained at depletion rate 4.667e-05\n" ] }, { "data": { "image/png": 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VBe7jzzDgPNSgiAvmzVX168DXAUTkA8DXVPVmEbkXWAaUuc9/cKs8CzwmIj8E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\nKaWUigpatCillFIqKmjRopRSSqmo8P/Gs4qnx8datQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=600.,kappa=1.,delta=4.33e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 5.3 Unequal societies" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.3.1 Type-L collapse" ] }, { "cell_type": "code", "execution_count": 324, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an unequal society (elites present and richer than workers)\n", "No equilibrium is possible for this society\n" ] }, { "data": { "image/png": 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qTFj9x8IoJlPno8BvRaQfK17kOuB9wPkiEsAyc70XQFUfArYD7VgKx1dVNWgf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\nRK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.001,kappa=100.,delta=6.67e-6)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.3.2 Type-N collapse (paper cut-off at t=500, but our simulations last longer)" ] }, { "cell_type": "code", "execution_count": 325, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an unequal society (elites present and richer than workers)\n", "No equilibrium is possible for this society\n" ] }, { "data": { "image/png": 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IRK5wht4LNGPETEqJ78Bx7wC3AJc4GUEXAyXA7Y4rKSYiH3NMku/DCd7FBPpe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\nRvIu8BrwVePxfUCDlEO/etrtdqSU/VttbW16XlkMev75T6TPR/7HPpb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(x_E=0.20,kappa=100.,delta=1.0e-4)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.3.3 Soft landing" ] }, { "cell_type": "code", "execution_count": 326, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an unequal society (elites present and richer than workers)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 79088\n", " Elites: 52090\n", " Nature: 50\n", " Wealth: 250\n", "Its carrying capacity is 131178\n", "Maximum carrying capacity would be 131181\n", "... attained at depletion rate 6.322e-06\n" ] }, { "data": { "image/png": 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AxipbOWSMMSOABS1mQKycupJtx7fR0tZyTnlDYSGxM2YQk9b9wdy7SqsByJ5u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\nNcaY9kZVH1DVLFXNAgqaqHPUPZ4EFgITSZJ5aeK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RmZJJZmpmokMxxrSOXsBC13OdCryt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\nqR02AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(beta_C=6.5e-2,beta_E=2.0e-2,x_C=1.0e4,x_E=3.0e3,kappa=10.,delta=6.35e-6)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.3.4 Oscillatory approach" ] }, { "cell_type": "code", "execution_count": 327, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is an unequal society (elites present and richer than workers)\n", "A theoretical equilibrium for this society is:\n", " Commoners: 73490\n", " Elites: 2883\n", " Nature: 4\n", " Wealth: 43\n", "Its carrying capacity is 76373\n", "Maximum carrying capacity would be 447857\n", "... attained at depletion rate 1.160e-06\n" ] }, { "data": { "image/png": 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9aXQWjQ287o7E3Jiwix1JUpJ5kcKwu5rFxDAMw8iRY+nKuRx4wX+ATyofv0/0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\nA7db9meshmI7RGQbsEBEdgLZSql3AETkKXQP/xeH0/8jmUh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solution = handy(beta_C=6.5e-2,beta_E=2.0e-2,x_C=1.0e4,x_E=3.0e3,kappa=10.,delta=1.3e-5)\n", "visualize(solution)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Discussion\n", "I was not able to reproduce all of the events as presented in the paper, particularly N-type collapses. Using a simple Euler scheme (like the authors) allowed me to reproduce them, but distorted some other results. This suggests that some of the irreversible collapses are actually artefacts of the numerical implementation. Testing with single precision (like the authors) is unfortunately not easily done with python." ] }, { "cell_type": "code", "execution_count": 340, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 366, "metadata": { "collapsed": false }, "outputs": [], "source": [ "deltas = [0.0001,0.00001,0.000001,0.0000001]\n", "kappas = [0.1,1,2,5,10,20,50,100,200,500,1000]\n", "data = np.zeros((len(deltas),len(kappas)))\n", "\n", "for i,delta in enumerate(deltas):\n", " for j,kappa in enumerate(kappas):\n", " solution = handy(beta_C=6.5e-2,beta_E=2.0e-2,x_C=1.0e4,x_E=3.0e3,kappa=kappa,delta=delta,verbose=False)\n", " data[i,j] = solution[0,-1]+solution[1,-1]" ] }, { "cell_type": "code", "execution_count": 367, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 367, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YBswDPgZ8LyKmAt9Lx0ialj4/DZgNXCNpWDrdtcBCYGraZqf4AmBPRJwMXA0s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\nzMysLv8fEFXT9MoS3CsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots()\n", "plt.contourf(kappas,deltas,data)\n", "plt.xlabel('stratification')\n", "plt.ylabel('depletion')\n", "plt.xticks(kappas)\n", "plt.yticks(deltas)\n", "ax.set_xscale(\"log\", nonposx='clip')\n", "ax.set_yscale(\"log\", nonposy='clip')\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }