{ "cells": [ { "cell_type": "markdown", "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/https%3A%2F%2Fgitlab.dsi.universite-paris-saclay.fr%2Fbruno.denis%2Fintro_jupyter/HEAD?labpath=notebooks%2Flokta_volterra.ipynb) \n", "[![NbViewer](https://badgen.net/static/render/NbViewer/orange)](https://nbviewer.org/urls/gitlab.dsi.universite-paris-saclay.fr/bruno.denis/intro_jupyter/-/raw/main/notebooks/lokta_volterra.ipynb) \n", "\n", "# Équations Lotka-Volterra\n", "\n", "Également connues sous le nom d'équations prédateur-proie, elles décrivent la variation des populations de deux espèces qui interagissent par le biais de la prédation. Il s'agit d'un modèle classique pour représenter la dynamique de deux populations où $x$ représente la quantité des proies et $y$ celles des prédateurs.\n", "\n", "$$\n", "\\left \\{\n", "\\begin{array}{rcl}\n", "\\dot{x} &=& \\alpha x - \\beta x y \\\\\n", "\\dot{y} &=& -\\delta y + \\gamma x y\n", "\\end{array}\n", "\\right .\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "editable": true, "slideshow": { "slide_type": "slide" }, "tags": [] }, "outputs": [], "source": [ "import numpy\n", "import scipy\n", "import matplotlib.pyplot as plt\n", "\n", "def derivative(X, t, alpha=0.8, beta=1, delta=0.5, gamma=1):\n", " x, y = X\n", " dotx = x * (alpha - beta * y)\n", " doty = y * (-delta + gamma * x)\n", " return numpy.array([dotx, doty])" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "editable": true, "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = numpy.linspace(0., 50, 1000)\n", "X0 = [1, .1]\n", "res = scipy.integrate.odeint(derivative, X0, t)\n", "prey, predator = res.T\n", "\n", "fig, ax = plt.subplots(figsize=[5.0, 2.0])\n", "ax.plot(t, prey, label='proies')\n", "ax.plot(t, predator, label='prédateurs')\n", "ax.set_xlabel('temps')\n", "ax.set_ylabel('Population')\n", "ax.legend()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 4 }