{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Qualitative analysis and Bifurcation diagram Tutorial\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.ipynb?create=1).*\n", "\n", "## Exploring the parameter space: bifurcation diagrams\n", "\n", "Bifurcation diagrams represent the (long-term) solutions of a model as a function of some key variable. The idea is that, as this parameter changes, the solutions change in a \"well-behaved\" way, and that helps us understand better the general behavior of the model.\n", "\n", "In this tutorial, we are going to study a simple predator-prey model (the Rosenzweig-MacArthur), and see how the amount of resources for prey ($K$) changes the dynamics.\n", "\n", "### The Rosenzweig-MacArthur consumer-resource model\n", "\n", "This model is expressed as:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dR}{dt} &= rR \\left( 1 - \\frac{R}{K} \\right) - \\frac{a R C}{1+ahR} \\\\\n", "\\frac{dC}{dt} &= \\frac{e a R C}{1+ahR} - d C\n", "\\end{aligned} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rosenzweig–MacArthur model solutions\n", "\n", "We use the same method as before to integrate this model numerically:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from numpy import *\n", "from scipy.integrate import odeint\n", "from matplotlib.pyplot import *\n", "ion()\n", "\n", "def RM(y, t, r, K, a, h, e, d):\n", " return array([ y[0] * ( r*(1-y[0]/K) - a*y[1]/(1+a*h*y[0]) ),\n", " y[1] * (e*a*y[0]/(1+a*h*y[0]) - d) ])\n", "\n", "t = arange(0, 1000, .1)\n", "y0 = [1, 1.]\n", "pars = (1., 10, 1., 0.1, 0.1, 0.1)\n", "\n", "y = odeint(RM, y0, t, pars)\n", "plot(t, y)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "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": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Consumer')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot the solution in the phase space\n", "plot(y[:,0], y[:,1])\n", "# defines a grid of points\n", "R, C = meshgrid(arange(0.95, 1.25, .05), arange(0.95, 1.04, 0.01))\n", "# calculates the value of the derivative at the point in the grid\n", "dy = RM(array([R, C]), 0, *pars)\n", "# plots arrows on the points of the grid, with the difection \n", "# and length determined by the derivative dy\n", "# This is a picture of the flow of the solution in the phase space\n", "quiver(R, C, dy[0,:], dy[1,:], scale_units='xy', angles='xy')\n", "xlabel('Resource')\n", "ylabel('Consumer')" ] }, { "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": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# now K = 15\n", "t = arange(0, 1000, .1)\n", "pars = (1., 15., 1., 0.1, 0.1, 0.1)\n", "y_osc = odeint(RM, y0, t, pars)\n", "plot(t, y_osc)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "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": { "text/plain": [ "Text(0, 0.5, 'C')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(y_osc[:,0], y_osc[:,1])\n", "R, C = meshgrid(arange(0, 6., .4), arange(0, 2.1, 0.2))\n", "dy = RM(array([R, C]), 0, *pars)\n", "quiver(R, C, dy[0,:], dy[1,:], scale_units='xy', angles='xy')\n", "xlabel('R')\n", "ylabel('C')" ] }, { "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": { "text/plain": [ "Text(0, 0.5, 'min / max population')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(10., y[-500:,0].min(), 'og')\n", "plot(10., y[-500:,0].max(), 'og')\n", "plot(10., y[-500:,1].min(), 'ob')\n", "plot(10., y[-500:,1].max(), 'ob')\n", "plot(15., y_osc[-500:,0].min(), 'og')\n", "plot(15., y_osc[-500:,0].max(), 'og')\n", "plot(15., y_osc[-500:,1].min(), 'ob')\n", "plot(15., y_osc[-500:,1].max(), 'ob')\n", "xlim((0, 20))\n", "yscale('log')\n", "xlabel('K')\n", "ylabel('min / max population')" ] }, { "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": 6, "metadata": {}, "outputs": [], "source": [ "## this block calculates solutions for many K's, it should take some time\n", "# empty lists to append the values later\n", "ymin = []\n", "ymax = []\n", "KK = arange(.5, 25, .5)\n", "t = arange(0, 6000, 1.)\n", "# loop over the values of K (KK)\n", "for K in KK:\n", " # redefine the parameters using the new K\n", " pars = (1., K, 1., 0.1, 0.1, 0.1)\n", " # integrate again the equation, with new parameters\n", " # strictly speaking, we should start each simulation with\n", " # the state obtained in the last iteration;\n", " # y0 = y[-1,;]\n", " y = odeint(RM, y0, t, pars)\n", " # calculate the minimum and maximum of the populations, but\n", " # only for the last 1000 steps (the long-term solution),\n", " # appending the result to the list\n", " # question: is 1000 enough? When it wouldn't be?\n", " ymin.append(y[-1000:,:].min(axis=0))\n", " ymax.append(y[-1000:,:].max(axis=0))\n", "# convert the lists into arrays\n", "ymin = array(ymin)\n", "ymax = array(ymax)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# and now, we plot the bifurcation diagram\n", "plot(KK, ymin[:,0], 'g', label='resource')\n", "plot(KK, ymax[:,0], 'g')\n", "plot(KK, ymin[:,1], 'b', label='consumer')\n", "plot(KK, ymax[:,1], 'b')\n", "xlabel('$K$')\n", "ylabel('min/max populations')\n", "legend(loc='best')\n", "# use a log scale in the y-axis\n", "yscale('linear')" ] }, { "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": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def RM_season(y, t, r, alpha, T, K, a, h, e, d):\n", " # in this function, `t` appears explicitly\n", " return array([ y[0] * ( r * (1+alpha*sin(2*pi*t/T)) *\n", " (1-y[0]/K) - a*y[1]/(1+a*h*y[0]) ),\n", " y[1] * (e*a*y[0]/(1+a*h*y[0]) - d) ])\n", "\n", "t = arange(0, 2000, 1.)\n", "y0 = [1., 1.]\n", "pars = (1., 0.1, 80., 10., 1., 0.1, 0.1, 0.1)\n", "y = odeint(RM_season, y0, t, pars)\n", "plot(t, y)\n", "xlabel('time')\n", "ylabel('population')\n", "legend(['resource', 'consumer'])" ] }, { "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": 10, "metadata": {}, "outputs": [], "source": [ "ymin = []\n", "ymax = []\n", "t = arange(0, 6000, 1.) # times\n", "TT = arange(1, 80, 2) # periods\n", "for T in TT:\n", " pars = (1., 0.1, T, 10., 1., 0.1, 0.1, 0.1)\n", " y = odeint(RM_season, y0, t, pars)\n", " ymin.append(y[-1000:,:].min(axis=0))\n", " ymax.append(y[-1000:,:].max(axis=0))\n", "ymin = array(ymin)\n", "ymax = array(ymax)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(TT, ymin[:,0], 'g', label='resource')\n", "plot(TT, ymax[:,0], 'g')\n", "plot(TT, ymin[:,1], 'b', label='consumer')\n", "plot(TT, ymax[:,1], 'b')\n", "xlabel('$T$')\n", "ylabel('min/max populations')\n", "legend(loc='best')\n", "yscale('log')" ] }, { "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 balancĂ­n)." ] }, { "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": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.1" } }, "nbformat": 4, "nbformat_minor": 1 }