{"cells": [{"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["***\n", "# **EDO -- L3 MEU 2022/2023 -- Universit\u00e9 Paris-Saclay**\n", "***\n", "\n", "\n", "\n", "# TP 2 : Deux mod\u00e8les d'EDO pour l'interaction proie-pr\u00e9dateur\n", "\n", "\n", "## Mod\u00e8le de Lotka-Volterra\n", "\n", "Apr\u00e8s la premi\u00e8re guerre mondiale, le zoologiste Umberto d'Anconna \u00e9tudia les effets de la guerre sur la p\u00eache de la sardine dans les ports de la mer Adriatique. Le r\u00e9sultat de cette \u00e9tude surprenait : alors que pendant la guerre la p\u00eache \u00e0 la sardine avait diminu\u00e9, la part de celles-ci dans les captures, qui aurait d\u00fb augmenter, avait pourtant baiss\u00e9 au profit de leurs pr\u00e9dateurs dont les requins, ce qui est paradoxal. Ce comportement fut observ\u00e9 simultan\u00e9ment dans les ports de Trieste et de Fiume.\n", "\n", "D'Anconna demanda alors \u00e0 Vito Volterra, qui \u00e9tait un des grands math\u00e9maticiens de l'\u00e9poque, s'il pouvait trouver une explication math\u00e9matique \u00e0 ce ph\u00e9nom\u00e8ne. Il \u00e9crivit un mod\u00e8le math\u00e9matique bas\u00e9 sur un syst\u00e8me d'\u00e9quations diff\u00e9rentielles r\u00e9gissant la dynamique des esp\u00e8ces consid\u00e9r\u00e9es.\\\\\n", "\n", "L'objectif de ce TP est d'\u00e9tudier ce mod\u00e8le ainsi que de justifier le paradoxe observ\u00e9 par d'Anconna."]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["On se donne donc deux populations $H(t)$ de sardines (les proies) et $P(t)$ de requins (les pr\u00e9dateurs) au temps $t,$ dont l'\u00e9volution au cours du temps suit la loi :\n", "\n", "\\begin{equation}\n", "\\label{LV}\n", " \\begin{cases}\n", " H'(t) = H(t)(a - b P(t)) \\\\\n", " P'(t) = P(t)(-c + d H(t)),\n", " \\end{cases}\n", "\\tag{LV}\n", "\\end{equation}\n", "\n", "o\u00f9 $a,b,c,d >0$.\n", "On suppose connues les populations de sardines et de requins \u00e0 l'instant initial $t_0=0$ :\n", "\\begin{equation}\n", "\\label{lvdi}\n", "\\tag{CI}\n", " \\begin{cases}\n", " H(0) = H_0, \\\\\n", " P(0) = P_0,\n", " \\end{cases}\n", "\\end{equation}\n", "o\u00f9 $H_0\\ge 0$ et $P_0\\ge 0$ sont donn\u00e9s."]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["## 1. Analyse du mod\u00e8le\n", "\n", "**Q1)** En posant $Y = (H,P)$, r\u00e9\u00e9crire le syst\u00e8me \\eqref{LV} sous la forme $Y' = F(Y)$ o\u00f9 $F=(F_1,F_2)$ avec $F_1,F_2$ deux fonctions d\u00e9finies sur $\\mathbb{R}^2$ \u00e0 valeurs dans $\\mathbb{R}$.\n", "\n", "> **R\u00e9ponse:** \n", "\n", "$F_1(Y)=H(a-bP)$ et $F_2(Y)=P(-c+dH)$"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["On suppose ici que le probl\u00e8me de Cauchy \\eqref{LV}-\\eqref{lvdi} admet une unique solution maximale d\u00e9finie sur un intervalle $J$ contenant $[0,+\\infty).$ \n", "\n", "**Q2)** D\u00e9terminer les points d'\u00e9quilibre de l'\u00e9quation diff\u00e9rentielle c'est-\u00e0-dire les points $(H_{eq},P_{eq})$ v\u00e9rifiant $F_1(H_{eq},P_{eq})=F_2(H_{eq},P_{eq})=0$ (ce sont les solutions stationnaires du syst\u00e8me diff\u00e9rentiel). Que se passe-t-il si on choisit $(H_{eq},P_{eq})$ comme condition initiale?\n", "\n", "> **R\u00e9ponse:** \n", "$(H_{eq},P_{eq})=(0,0)$ et $(H_{eq},P_{eq})=(c/d,a/b)$.\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q3)** Dans le plan $(H,P)$, repr\u00e9sentez les points d'\u00e9quilibre du syst\u00e8me. Etudier le signe des d\u00e9riv\u00e9es $H'$ et $P'$ et repr\u00e9senter le sens et la direction des champ de vecteurs dans le plan $(H,P),$ suivant la position de $H$ et $P$ par rapport aux points stationnaires. Quel sera le comportement des solutions $(H,P)$ suivant la condition initiale?\n", "\n", "**Q4)** Soit $Q = \\{ (x,y)\\in \\mathbb R^2\\mid x,y >0\\}$. D\u00e9montrer que si la\n", "condition initiale $(H_0,P_0)\\in Q$, alors $(H(t),P(t)) \\in Q$ pour\n", "tout temps $t>0$ o\u00f9 la solution est d\u00e9finie.\n", "\n", "**Q5)** On suppose encore que $(H_0,P_0) \\in Q$ et soit \n", "$(H,P)$ la solution maximale du probl\u00e8me de Cauchy \\eqref{LV}-\\eqref{lvdi}. Montrer une in\u00e9galit\u00e9\n", "diff\u00e9rentielle faisant appara\u00eetre la quantit\u00e9 $\\phi(t) := dH(t) +\n", "bP(t)$ au cours du temps. En d\u00e9duire que la solution $(H,P)$ est\n", "d\u00e9finie sur $\\mathbb R^+$.\n", "\n", "**Q6)** Construire une fonction $E(x,y) = k(x) + \\ell(y)$\n", "v\u00e9rifiant \n", "\\begin{equation}E(H(t),P(t)) = \\mathrm{cst}\\;\\text{ et telle que}\\; \\lim_{X\\in Q,\n", " \\|X\\|\\to +\\infty} E(X) = +\\infty\n", "\\end{equation} \n", "o\u00f9 $|X|$ d\u00e9signe ici une norme du vecteur $X$. En d\u00e9duire que les trajectoires\n", "de la solution maximale restent born\u00e9es.\n", "\n", "**Q7)** D\u00e9montrez que si $(H,P)$ converge quand $t\\rightarrow+\\infty$, c'est n\u00e9cessairement vers un point d'\u00e9quilibre.\n", "\n", "**Q8)** (* plus difficile) Tracer les nulloclines $\\{ (x,y)\\in\n", "Q\\mid F_i(x,y) = 0 \\}$ et les points d'\u00e9quilibre. Les nulloclines divisent le quart de plan $Q$ en quatre ouverts\n", "\\begin{align*}\n", " &A = \\{ (x,y) \\in Q \\mid F_1(x,y) > 0 \\hbox{ et } F_2(x,y) < 0 \\}\\\\\n", " &B = \\{ (x,y) \\in Q \\mid F_1(x,y) > 0 \\hbox{ et } F_2(x,y) > 0 \\}\\\\\n", " &C = \\{ (x,y) \\in Q \\mid F_1(x,y) < 0 \\hbox{ et } F_2(x,y) > 0 \\}\\\\\n", " &D = \\{ (x,y) \\in Q \\mid F_1(x,y) < 0 \\hbox{ et } F_2(x,y) < 0 \\}\n", "\\end{align*}\n", "\n", "D\u00e9montrer que si $(H_0,P_0)\\in A$, alors la trajectoire $(H(t),P(t))$\n", "va parcourir successivement les ensembles $A,B,C,D,A,B,$ etc. Montrer\n", "que les deux points de passage successifs de la solution \u00e0 l'interface\n", "$AB$ sont \u00e9gaux, en d\u00e9duire que les solutions sont p\u00e9riodiques.\n", "\n", "\n", "\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["## 2. Approximation num\u00e9rique\n", "\n", "On s'int\u00e9resse dans cette partie \u00e0 l'approximation num\u00e9rique de la solution de \\eqref{LV}-\\eqref{lvdi}, dans un intervalle de temps de la forme $[0,T].$ \n", "\n", "Pour toutes les applications num\u00e9riques, on choisit dans la suite\n", "$a=0,1$, $b=d=5\\cdot 10^{-5},$ $c=0,04$ et $T=200$ ans. On choisit une population initiale de $H_0=2000$ sardines et $P_0=1000$ requins.\n", "\n", "**Q1)** Dans une premi\u00e8re figure, repr\u00e9sentez dans l'espace des phases $(H,P)$ le champ de vecteur associ\u00e9\n", "\u00e0 ce syst\u00e8me d'\u00e9quations via\n", "\n", "`x, y = np.meshgrid(np.linspace(0 , 3000, 20) , np.linspace (0 , 4500, 30))\n", "n=np.sqrt(F1(x,y)**2+F2(x,y)**2) \n", "plt.quiver (x , y, F1(x , y)/n, F2 (x , y)/n,angles='xy',scale=20,color='blue')`\n", "\n", "Confrontez le r\u00e9sultat \u00e0 la question **Q1.3**.\n"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"name": "stderr", "output_type": "stream", "text": [":31: RuntimeWarning: invalid value encountered in true_divide\n", " plt.quiver (x , y, f1(x , y)/np.sqrt(f1(x,y)**2+f2(x,y)**2), f2 (x , y)/np.sqrt(f1(x,y)**2+f2(x,y)**2),angles='xy',scale=20,color='blue')\n"]}, {"data": {"text/plain": ["Text(0, 0.5, 'P')"]}, "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": ["import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "a=0.1\n", "b=5*10**(-5)\n", "c=0.04\n", "d=b\n", "\n", "T=200\n", "\n", "H0=2000\n", "P0=1000\n", "\n", "p=0.02\n", "# D\u00e9finition du second membre F\n", "\n", "def f1(x,y):\n", " return a*x-b*x*y\n", "def f2(x,y):\n", " return -c*y+d*x*y\n", "\n", "# Intervalle de temps\n", "\n", "t = np.linspace(0, T, 2000)\n", "\n", "plt.figure(1)\n", "[x, y] = np.meshgrid(np.linspace(0 , 3000, 20) , np.linspace (0 , 4500, 30))\n", "plt.quiver (x , y, f1(x , y)/np.sqrt(f1(x,y)**2+f2(x,y)**2), f2 (x , y)/np.sqrt(f1(x,y)**2+f2(x,y)**2),angles='xy',scale=20,color='blue')\n", "plt.xlabel('H')\n", "plt.ylabel('P')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["On s'int\u00e9resse maintenant \u00e0 calculer une solution approch\u00e9e du probl\u00e8me de Cauchy \\eqref{LV}-\\eqref{lvdi} par la m\u00e9thode d'Euler explicite, vue au TP1. On reprend les m\u00eames notations que dans le TP1 : on se donne un pas $\\Delta t=\\frac{T}{N}>0,$ o\u00f9 $N\\in\\mathbb N,$ on consid\u00e8re une subdivision uniforme de pas $\\Delta t$ de l'intervalle $[0, T],$ d\u00e9finie par les $(N+1)$ points \n", "$$\n", "t_0=0,\\ t_1:=\\Delta t,\\ \\cdots,\\ t_N:=N\\Delta t=T, \n", "$$\n", "et on note note $H^n$ (resp. $P^n$) la valeur approch\u00e9e de $H(t_n)$ (resp. $P(t_n)$) \u00e0 l'instant $t_n$ pour $n=0,\\cdots,N$.\n", "\n", "**Q2)** Ecrire le sch\u00e9ma d'Euler explicite associ\u00e9 au mod\u00e8le de Lotka Volterra\n", "\n", "> **R\u00e9ponse:** \n", "\n", "\\begin{equation}\n", " \\begin{cases}\n", " &H^{n+1} = H^{n} +\\Delta t H^{n}(a - b P^{n}) \\\\\n", " &P^{n+1} = P^{n}+\\Delta t P^{n}(-c + d H^{n}),\n", " \\end{cases}\n", "\\end{equation}"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q3)** Ecrire une fonction `LvoltEE(T,Y0,dt)` prenant en argument le temps final `T`, la donn\u00e9e initiale `Y_0=[H_0,P_0]` correspondant aux valeurs des populations initiales en `t=0` et le pas de temps `dt` (on pourra prendre en argument `N` le nombre de points de la discr\u00e9tisation, au lieu de `dt`), et qui calcule une solution approch\u00e9e de \\eqref{LV}-\\eqref{lvdi} par le sch\u00e9ma d'Euler explicite.\n", "\n", "Cette fonction retournera trois tableaux:\n", "- `[$t_0,...,t_N$]` tableau numpy de taille $(N+1)\\times 1$ contenant les instants de la subdivision en temps ;\n", "- `[$H_0,...,H_N$]` tableau numpy de taille $(N+1)\\times 1$ contenant les valeurs approch\u00e9es aux instantes $t_n$ de la population de sardines ;\n", "- `[$P_0,...,P_N$]` tableau numpy de taille $(N+1)\\times 1$ contenant les valeurs approch\u00e9es aux instantes $t_n$ de la population de requins."]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": ["def LV_EE(T,Y0,dt):\n", " t=np.arange(0,T+dt,dt)\n", " N=t.size\n", " H=np.zeros((N,1))\n", " P=np.zeros((N,1))\n", " H[0]=Y0[0]\n", " P[0]=Y0[1]\n", " for n in range(N-1):\n", " H[n+1]=H[n]+dt*f1(H[n],P[n])\n", " P[n+1]=P[n]+dt*f2(H[n],P[n])\n", " return t,H,P\n", "\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q4)** Tracer dans la m\u00eame figure les solutions approch\u00e9es $[H_0,H_1,\\ldots,H_N]$ et $[P_0,P_1,\\ldots,P_N]$ en fonction du temps, obtenues % $[t_0,\\ldots,t_N]$ avec $\\Delta t=0.01$. Rajouter des l\u00e9gendes et des titres \u00e0 votre figure."]}, {"cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0, 0.5, 'H,P')"]}, "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": ["X0=[H0,P0]\n", "\n", "# Pas de temps\n", "\n", "dt=0.01\n", "\n", "t_ap,H,P=LV_EE(T,X0,dt)\n", " \n", "plt.figure(2)\n", "plt.plot(t_ap,H,'r',label='sardines')\n", "plt.plot(t_ap,P,'k',label='requins')\n", "plt.plot(0,X0[0],'r*')\n", "plt.plot(0,X0[1],'k*')\n", "plt.legend()\n", "plt.title('solutions approch\u00e9es')\n", "plt.xlabel('t')\n", "plt.ylabel('H,P')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q5)** Cr\u00e9er une seconde figure et tracer $P$ en fonction de $H$ dans le plan $(H,P)$ (portrait de phase). Refaire cette repr\u00e9sentation dans la m\u00eame figure de la question **Q1)**."]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0.5, 1.0, 'Trajectoires')"]}, "execution_count": 4, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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\n", "text/plain": ["
"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["plt.figure(1)\n", "plt.plot(H,P,'g')\n", "plt.plot(X0[0],X0[1],'r*')\n", "plt.xlabel('H')\n", "plt.ylabel('P')\n", "plt.title('Champ de vecteurs et trajectoires')\n", "\n", "plt.figure(3)\n", "plt.plot(H,P,'g')\n", "plt.plot(X0[0],X0[1],'r*')\n", "plt.xlabel('H')\n", "plt.ylabel('P')\n", "plt.title('Trajectoires')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q6)** Calculer la solution approch\u00e9e de \\eqref{LV}-\\eqref{lvdi}, en prenant comme condition initiale un des points d'\u00e9quilibre du syst\u00e8me. Ceci confirme-t-il la solution th\u00e9orique?"]}, {"cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0, 0.5, 'H,P')"]}, "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": ["X0=[.0,.0]\n", "\n", "# Pas de temps\n", "\n", "dt=0.01\n", "\n", "t_ap,H,P=LV_EE(T,X0,dt)\n", " \n", "plt.figure(4)\n", "plt.plot(t_ap,H,'r',label='sardines')\n", "plt.plot(t_ap,P,'k',label='requins')\n", "plt.plot(0,X0[0],'r*')\n", "plt.plot(0,X0[1],'k*')\n", "plt.legend()\n", "plt.title('solutions approch\u00e9es')\n", "plt.xlabel('t')\n", "plt.ylabel('H,P')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q7)** **(L'impact de la p\u00eache)** Nous p\u00eachons maintenant une m\u00eame proportion $p$ de requins et de sardines ce qui se traduit par les deux termes n\u00e9gatifs $-pH(t)$ et $-pP(t)$ dans les \u00e9quations. Le mod\u00e8le devient\n", "\\begin{equation*}\n", " \\begin{cases}\n", " H'(t)&=(a-p)H(t)-bH(t)P(t),\\\\\n", " P'(t)&=(-c-p)P(t)+dH(t)P(t).\n", " \\end{cases}\n", "\\end{equation*}\n", "On choisit $p=0.02$. Reprendre les questions pr\u00e9c\u00e9dentes et expliquer quel est l'impact de la p\u00eache sur l'\u00e9volution des populations. Quelle esp\u00e8ce est favoris\u00e9e par la p\u00eache? "]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["def f3(x,y):\n", " return (a-p)*x-b*x*y\n", "def f4(x,y):\n", " return (-c-p)*y+d*x*y\n", "\n", "def LV_EEP(T,X0,dt):\n", " t=np.arange(0,T+dt,dt)\n", " N=t.size\n", " H=np.zeros((N,1))\n", " P=np.zeros((N,1))\n", " H[0]=X0[0]\n", " P[0]=X0[1]\n", " for n in range(N-1):\n", " H[n+1]=H[n]+dt*f3(H[n],P[n])\n", " P[n+1]=P[n]+dt*f4(H[n],P[n])\n", " return t,H,P\n", "\n", "X0=[H0,P0]\n", "\n", "t_ap,H,P=LV_EEP(T,X0,dt)\n", "\n", "plt.figure(5)\n", "plt.plot(t_ap,H,'r',label='sardines')\n", "plt.plot(t_ap,P,'k',label='requins')\n", "plt.plot(0,X0[0],'r*')\n", "plt.plot(0,X0[1],'k*')\n", "plt.legend()\n", "plt.title('Probl\u00e8me avec p\u00eache')\n", "plt.xlabel('t')\n", "plt.ylabel('H,P')\n", "\n", "plt.figure(6)\n", "plt.plot(H,P)\n", "plt.plot(X0[0],X0[1],'b*')\n", "plt.xlabel('H')\n", "plt.ylabel('P')\n", "plt.title('Trajectoires p\u00eache')\n", "\n"]}, {"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": "3.8.5"}, "celltoolbar": "None"}, "nbformat": 4, "nbformat_minor": 2}