{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook for examples of intergation of systems of ODEs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python initialization" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np #initialization\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "import time # note the new module\n", " \n", "%matplotlib inline " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Predator-Prey growth function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def PredatorPrey(Population, t, r, a, b, d):\n", " \"\"\"\n", " this function returns the growth rate of two populations in the Predator-Prey model as a numpy array\n", " \n", " PredatorPrey(Population, t, args):\n", "\n", " Population -- an array of 2 numbers -- predator and prey current population sizes\n", " t -- time, unused\n", " (r, a, b, d) - the parameters of the population dynamics as described in the lecture\n", " \"\"\"\n", " \n", " dx = Population[0]*(r-a*Population[1])\n", " dy = Population[1]*(b*Population[0]-d)\n", " \n", " return np.array((dx,dy))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integrator functions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def EulerSystem(xPrime, x0, t, args=()):\n", " \"\"\"\n", " Solves a system of ODEs using the Euler method.\n", " \n", " EulerSystem(xPrime,t0=0.0,x0=0.0,T=1.0,dt=0.1)\n", " xPrime -- the system to be integrated, returns the array of derivatives\n", " t -- the array of time points where the solution is needed; the zeroth entry corresponds to x0\n", " x0 -- initial condition\n", " \n", " Note that we do not ask for dt in this implementation of the algorithm\n", " \"\"\"\n", " \n", " x = np.zeros((t.size, x0.size))\n", " x[0,:] = x0\n", " for i in range(1, t.size):\n", " dt = t[i] - t[i-1]\n", " x[i,:] = x[i-1,:] + dt * xPrime(x[i-1,:],t[i-i],*args)\n", "\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constant intialization" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "dt = 1e-4 # time step\n", "SimulationTime = 10.0 # time to solve for\n", "P0 = np.array((1,1)) # initial population size\n", "r = 7.0 # intitalization of the 4 parameters\n", "a = 2.0\n", "b = 1.5\n", "d = 3.0 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running various integrators and comparing them" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler took 0.6168150901794434s to run.\n", "Odeint took 0.011101007461547852s to run.\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t=np.arange(0,SimulationTime,dt)\n", "\n", "tt1 = time.time() # initial time\n", "PEuler = EulerSystem(PredatorPrey, P0, t, args=(r,a,b,d))\n", "tt2 = time.time() # time after euler\n", "POdeInt = odeint(PredatorPrey, P0, t, args=(r,a,b,d))\n", "tt3 = time.time() # time after odeint\n", "\n", "\n", "print('Euler took ', tt2-tt1, 's to run.', sep='' )\n", "print('Odeint took ', tt3-tt2, 's to run.', sep='' )\n", "\n", "\n", "plt.plot(t, PEuler[:,0],label='Prey')\n", "plt.plot(t, PEuler[:,1],label='Predator')\n", "plt.legend()\n", "plt.title('Predator-Prey dynamics: EulerSystem solver')\n", "plt.xlabel('t')\n", "plt.ylabel('population size')\n", "plt.show()\n", "\n", "plt.plot(t, POdeInt[:,0],label='Prey')\n", "plt.plot(t, POdeInt[:,1],label='Predator')\n", "plt.legend()\n", "plt.title('Predator-Prey dynamics: odeint solver')\n", "plt.xlabel('t')\n", "plt.ylabel('population size')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Predator-prey phase portrait')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "coords = np.linspace(0,5,11)\n", "X, Y = np.meshgrid (coords, coords)\n", "Vx, Vy = PredatorPrey((X,Y), 0, r, a, b, d)\n", "p=plt.quiver(X,Y,Vx,Vy)\n", "plt.xlabel('prey')\n", "plt.ylabel('predator')\n", "plt.title('Predator-prey phase portrait')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Predator-prey phase portrait')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.streamplot(X,Y,Vx,Vy)\n", "plt.xlabel('prey')\n", "plt.ylabel('predator')\n", "plt.title('Predator-prey phase portrait')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }