{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### **Course**: BIO-341 [_Dynamical systems in biology_](https://moodle.epfl.ch/course/info.php?id=14291)\n", "\n", "**Professor**: _Julian Shillcock_ & _Felix Naef_\n", "\n", "SSV, BA5, 2025\n", "\n", "Note that this document is primarily aimed at being consulted as a Jupyter notebook, the PDF rendering being not optimal." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/8w/hhwzbx0d6zg_2q5hrl31_yn00000gq/T/ipykernel_4675/3620943358.py:9: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n", " set_matplotlib_formats(\"png\", \"pdf\")\n" ] } ], "source": [ "# import important libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact\n", "from scipy.integrate import odeint\n", "from IPython.display import set_matplotlib_formats\n", "from matplotlib.markers import MarkerStyle\n", "\n", "set_matplotlib_formats(\"png\", \"pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Insect outbreak and bifurcations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this exercise is to study a model of insect outbreak in which the solutions change qualitatively when the environment parameters are modified. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bifurcations (Paper and pencil)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the 1st-order systems\n", "\n", "1. $\\dot{x} = (x-2)(x-r)$\n", "\n", "2. $\\dot{x} = x^2 + b$\n", "\n", "**A. Discuss the fixed points and their stability in function of the parameters $r$ or $b$.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">1. $x^* = 2$ and $x^* = r$ are the fixed points. \n", " For $r>2$, $x^*=r$ is unstable, $x^* = 2$ is stable. \n", " For $r=2$ there is only one semi-stable fixed point in $x^* = 2$. \n", " For $r<2$, $x^*=r$ is stable, $x^* = 2$ is unstable. \n", "\n", ">2. $\\dot{x} = x^2 + b$ thus $x^* = \\pm\\sqrt{-b}$ are the fixed points for $b<0$. \n", "We get $x^* = -\\sqrt{-b}$ stable and $x^* = \\sqrt{-b}$ unstable. \n", "If $b =0$, the fixed point $x^* =0$ is semi-stable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**B. Linearize the equation for the dynamical system to obtain explicit solution near the fixed points. Linearization refers to finding the linear approximation to a function at a given point:** $\\dot{\\eta} = \\eta \\cdot F'(x^*)$ with $\\eta(t) = x(t) - x^*$ and the solution $\\eta = \\eta_0e^{tF'(x^*)}$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">To study the solution near the fixed points we use the linearization: $\\dot{\\eta} = \\eta \\cdot F'(x^*)$ with $\\eta(t) = x(t) - x^*$ (cf. chapter 1 for derivation). So it is only necessary to compute the derivatives at the fixed points $F'(x^*)$.\n", "\n", ">1. As $F'(x^*) = 2x-r-2$, we have $F'(2) = 2-r$ and $F'(r) = -(2-r)$. As the solution of the linearization is $\\eta = \\eta_0e^{tF'(x^*)}$, we get $\\eta(t) = \\eta_0e^{\\pm t(2-r)}$ \n", " ⠀⠀\n", "\n", ">2. As $F'(x) = 2x$, we have $F'(\\pm\\sqrt{-b})=\\pm2\\sqrt{-b}$. As the solution of the linearization is $\\eta = \\eta_0e^{tF'(x^*)}$, we get $\\eta(t) = \\eta_0e^{\\pm t 2\\sqrt{-b}}$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**C. Bifurcation diagrams: Plot the position of the fixed points in function of $r$ or $b$, using a solid line for the stable branch and a dashed line for unstable branch.**\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot for system 1\n", "stable_r = np.linspace(-5, 2, 100)\n", "unstable_r = np.linspace(2, 5, 100)\n", "line = np.linspace(-5, 5, 100)\n", "\n", "plt.plot(stable_r, stable_r, color=\"r\", ls=\"-\", label = '$x^*$ = r stable')\n", "plt.plot(unstable_r, unstable_r, color=\"r\", ls=\"--\", label = '$x^*$ = r unstable')\n", "\n", "\n", "plt.plot([-5, 2], [2, 2], color=\"b\", ls=\"--\", label=\"$x^*$ = 2 unstable\")\n", "plt.plot([2, 5], [2, 2], color=\"b\", ls=\"-\", label=\"$x^*$ = 2 stable\")\n", "\n", "plt.xlabel(\"r\")\n", "plt.ylabel(r\"$x^*$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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", "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot for system 2\n", "domain_b = np.linspace(-10, 0, 1000)\n", "stable = -np.sqrt(-domain_b)\n", "unstable = np.sqrt(-domain_b)\n", "plt.plot(domain_b, stable, ls=\"-\", label=\"stable\")\n", "plt.plot(domain_b, unstable, ls=\"--\", label=\"unstable\")\n", "\n", "plt.xlabel(\"b\")\n", "plt.ylabel(r\"$x^*$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Insect outbreak (epidemy) (paper and pencil & code)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](Choristoneura_fumiferana_larva_small.jpg \"Title\")\n", "\n", "The spruce budworm (Choristoneura fumiferana), commonly known as T.B.E., is without doubt the insect pest best known to foresters and the general public. Having been very present in Quebec forests during the 60's and 70's, the T.B.E. did not win the sympathy of the population. In fact, the damage caused by E.B.T. during the last epidemic amounted to more than 235 million cubic metres of wood, the equivalent of ten years' harvest for the forestry industry. Needless to say, the spruce budworm has considerably altered the forest landscape in many parts of Quebec. \n", " \n", "\n", "\n", "During an epidemy, the spruce budworm can defoliate and kill entire forests within few years. In a simple model for the insect population $N$, the available foliage allows for a relative growth rate $r_B$ and the environment has a maximal capacity $K$ as in the logistic growth model. At the same time, insects are eaten by birds at a certain rate, which leads to the population model:\n", "\n", "$$\n", "\\dot N = \\dfrac{dN}{dt}= r_B N (1-\\frac{N}{K}) - p(N)\n", "$$\n", " \n", "The death rate $p(N)$ is assumed to take the form:\n", "\n", "$$\n", "p(N) = B\\frac{N^2}{A^2 + N^2} \\; \\text{with} \\: A,B >0\n", "$$\n", " \n", "This term is small when the budworms population is small and the birds seek for food elsewhere, and then saturates for larger $N$ when all birds eat as much worms as they can." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**A. Plot the function $p(N)$ and discuss the meaning of the parameters $A$ and $B$.**" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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wMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAxIDQ2MCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAzMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4MzggNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1NiA1NTcgODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjExIDY4NSAzOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNTAgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyOCA2MDAgNTI1IDYxMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTcgODM4IDM2MSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxNyA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA4CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5OTUgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE2IDAgb2JqCjw8IC9OIDE3IDAgUiAvcCAxOCAwIFIgPj4KZW5kb2JqCjIzIDAgb2JqCjw8IC9MZW5ndGggOTEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNYy7DcAwCER7prgR+DiA94miFPb+bYgtF9w96YnzbGBknYcjtOMWsqZwU0xSTqh3DGqlNx076CXN/TTJei4a9A9x9RW2mwOSUSSRh0SXy5Vn5V98PgxvHGIKZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvTGVuZ3RoIDI2NCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9UrmRAzEMy7cKlsBfUj2+uXFg958ewD07MTFLEQBB925RORs/bSXLj/zYZWdJ5Jb3oG3yuqLqBqmbIHPJcckVYpbyuBIkFi1lJtZnqoPycQ1qFb7wEzMT0yFJxBJyUo8irI+vg9f1HNxfN+n8GhkfdGxQekuSq6BUw75ytBI7lupdg+yDppvS6jPTruyApfGGrNSkTn8d9b8jLMKk3khFByEWv9PLHbIspBzU27l+A+Fd7YJYT6087BBp3lZ6SxXM5swETBltO6yAtVljwlQJ8BbNIdRaiMwXOq2I+eTc0cE0VXkaIsNShYPtPaM1XOgaEkvD+UnGBOa/8PqsyG1//wBwaGe6CmVuZHN0cmVhbQplbmRvYmoKMjUgMCBvYmoKPDwgL0xlbmd0aCA3NyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1jcENwDAIA/9MwQg4hVD2qao+0v2/LUR87DMI7HqycKRME/YRfIH+nPTSOFC0yEwZaNqzvtgkuYOXI5QnmtKrYvXnRQ/dH8meGAwKZW5kc3RyZWFtCmVuZG9iagoyNiAwIG9iago8PCAvTGVuZ3RoIDc0IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nLMwtlAwUDA0MFMwNDdSMDc2UjAxNVFIMeQCCYGYuVwwwRwwyxioLAcsi2BBZDPAbCNTU6geEAuixxCuEsGCyGZwpQEAUb4ZFgplbmRzdHJlYW0KZW5kb2JqCjI3IDAgb2JqCjw8IC9MZW5ndGggMjQ5IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nE1RSYoDMAy75xX6QCFek7ynQ5lD5//Xyg6FOQQJr5KTlphYCw8xhB8sPfiRIXM3/Rt+otm7WXqSydn/mOciU1H4UqguYkJdiBvPoRHwPaFrElmxvfE5LKOZc74HH4W4BDOhAWN9STK5qOaVIRNODHUcDlqkwrhrYsPiWtE8jdxu+0ZmZSaEDY9kQtwYgIgg6wKyGCyUNjYTMlnOA+0NyQ1aYNepG1GLgiuU1gl0olbEqszgs+bWdjdDLfLgqH3x+mhWl2CF0Uv1WHhfhT6YqZl27pJCeuFNOyLMHgqkMjstK7V7xOpugfo/y1Lw/cn3+B2vD838XJwKZW5kc3RyZWFtCmVuZG9iagoyOCAwIG9iago8PCAvTGVuZ3RoIDk0IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nEWNwRHAIAgE/1RBCQoK2k8mk4f2/40QMnxg5w7uhAULtnlGHwWVJl4VWAdKY9xQj0C94XItydwFD3Anf9rQVJyW03dpkUlVKdykEnn/DmcmkKh50WOd9wtj+yM8CmVuZHN0cmVhbQplbmRvYmoKMjkgMCBvYmoKPDwgL0xlbmd0aCA4MyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxFjLsNwDAIRHumYAR+JvY+UZTC3r8NECVuuCfdPVwdCZkpbjPDQwaeDCyGXXGB9JYwC1xHUI6d7KNh1b7qBI31plLz7w+Unuys4obrAQJCGmYKZW5kc3RyZWFtCmVuZG9iagozMCAwIG9iago8PCAvTGVuZ3RoIDIzOSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxNUMltBDEM+7sKNTDA6By7HgeLPLL9f0PKCZKXaEviofKUW5bKZfcjOW/JuuVDh06VafJu0M2vsf6jDAJ2/1BUEK0lsUrMXNJusTRJL9nDOI2Xa7WO56l7hFmjePDj2NMpgek9MsFms705MKs9zg6QTrjGr+rTO5UkA4m6kPNCpQrrHtQloo8r25hSnU4t5RiXn+h7fI4APcXejdzRx8sXjEa1LajRapU4DzATU9GVcauRgZQTBkNnR1c0C6XIynpCNcKNOaGZvcNwYAPLs4Skpa1SvA9lAegCXdo64zRKgo4Awt8ojPX6Bqr8XjcKZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvTGVuZ3RoIDE1MCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9TzkOwzAM2/0KfiCAdVi23pMi6JD+f63ooB0EEaB4yLKjYwUOMYFJxxyJl7Qf/DSNQCyDmiN6QsUwLHA2SYGHQVZJVz5bnEwhtQVeSPjWFDwbTWSCnseIHbiTyegD71JbsXXoAe0QVSRdswxjsa26cD1hBDXFehXm9TBjiZJHn1VL6wEFE/jS+X/ubu92fQFgxTBdCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0xlbmd0aCAxNTEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNY/LDcMwDEPvmoILBNDPsjxPiqCHdP9rJacFDJgwySfZFoORjENMYOyYY+ElVE+tPiQjt7pJORCpUDcET2hMDDOcpEvglem+ZTy3eDmt1AWdkMjdWW00RBnNPIajp+wVTvovc5OolRllDsisU91OyMqCFZgX1HLfz7itcqETHrYrw6I7xYhymxlp+P3vpDddX9x4MNUKZW5kc3RyZWFtCmVuZG9iagozMyAwIG9iago8PCAvTGVuZ3RoIDMyMCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UktuBTEI288puECl8E/O86qqi777b2sTvRVMMGDjKS9Z0ku+1CXbpcPkWx/3JbFC3o/tmsxSxfcWsxTPLa9HzxG3LQoEURM9WJkvFSLUz/ToOqhwSp+BVwi3FBu8g0kAg2r4Bx6lMyBQ50DGu2IyUgOCJNhzaXEIiXImiX+kvJ7fJ62kofQ9WZnL35NLpdAdTU7oAcXKxUmgXUn5oJmYSkSSl+t9sUL0hsCSPD5HMcmA7DaJbaIFJucepSXMxBQ6sMcCvGaa1VXoYMIehymMVwuzqB5s8lsTlaQdreMZ2TDeyzBTYqHhsAXU5mJlgu7l4zWvwojtUZNdw3Duls13CNFo/hsWyuBjFZKAR6exEg1pOMCIwJ5eOMVe8xM5DsCIY52aLAxjaCaneo6JwNCes6VhxsceWvXzD1TpfIcKZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvTGVuZ3RoIDM0MCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UjluBDEM6/0KfSCAbtvv2SBIkfy/DanZFANxdFKUO1pUdsuHhVS17HT5tJXaEjfkd2WFxAnJqxLtUoZIqLxWIdXvmTKvtzVnBMhSpcLkpORxyYI/w6WnC8f5trGv5cgdjx5YFSOhRMAyxcToGpbO7rBmW36WacCPeIScK9Ytx1gFUhvdOO2K96F5LbIGiL2ZlooKHVaJFn5B8aBHjX32GFRYINHtHElwjIlQkYB2gdpIDDl7LHZRH/QzKDET6NobRdxBgSWSmDnFunT03/jQsaD+2Iw3vzoq6VtaWWPSPhvtlMYsMul6WPR089bHgws076L859UMEjRljZLGB63aOYaimVFWeLdDkw3NMcch8w6ewxkJSvo8FL+PJRMdlMjfDg2hf18eo4ycNt4C5qI/bRUHDuKzw165gRVKF2uS9wGpTOiB6f+v8bW+19cfHe2AxgplbmRzdHJlYW0KZW5kb2JqCjM1IDAgb2JqCjw8IC9MZW5ndGggMjUxIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nC1RSXIDQQi7zyv0hGan32OXK4fk/9cIygcGDYtAdFrioIyfICxXvOWRq2jD3zMxgt8Fh34r121Y5EBUIEljUDWhdvF69B7YcZgJzJPWsAxmrA/8jCnc6MXhMRlnt9dl1BDsXa89mUHJrFzEJRMXTNVhI2cOP5kyLrRzPTcg50ZYl2GQblYaMxKONIVIIYWqm6TOBEESjK5GjTZyFPulL490hlWNqDHscy1tX89NOGvQ7Fis8uSUHl1xLicXL6wc9PU2AxdRaazyQEjA/W4P9XOyk994S+fOFtPje83J8sJUYMWb125ANtXi37yI4/uMr+fn+fwDX2BbiAplbmRzdHJlYW0KZW5kb2JqCjM2IDAgb2JqCjw8IC9MZW5ndGggODkgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNU25EYAwDOs9hUfAj0i8D8dRhP1b7IQ0lk6fEcoHa+QBguGNLyH4oi8ZhLULDyr7SHTYRA1nFSQTw68s8KqcFW1zJRPZWUyjs0HL9K3tb4Meuj/djhwKCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL0xlbmd0aCAxNDEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicPY/BDsMwCEPv+Qr/QKTYKaF8T6dqh+7/ryNLuwt6AmOMhdDQG6qaw4Zgm+PF0iVUa/gUxUAlN8iZYA6lpNIdR5F6YjgYXB60G47isej6EbuSZn3QxkK6JWiAe6xTadymcRPEHTUF6inqnKO8ELmfqWfYNJLdNLOSc7gNv3vPU9f/p6u8y/kFvXcu/gplbmRzdHJlYW0KZW5kb2JqCjM4IDAgb2JqCjw8IC9MZW5ndGggMjE1IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDVROQ4DIQzs9xX+QCSML3hPoijN/r/NjNFWHsFchrSUIZnyUpOoIeVTPnqZLpy63NfMajTnlrQtc4C4trwvrZLAiWaIg8FpmLgBmjwBQ9fRqFFDFx7Q1KVTKLDcBD6Kt24P3WO1gZe2IeeJIGIoGSxBzalFExZtzyekNb9eixvel+3dyFOlxpYYgQYBVjgc1+jX8JU9TybRdBUy1Ks1yxgJE0UiPPmOptUT61o00jIS1MYRrGoDvDv9ME4AABNxywJkn0qUs+TEb7H0swZX+v4Bn0dUlgplbmRzdHJlYW0KZW5kb2JqCjIxIDAgb2JqCjw8IC9UeXBlIC9Gb250IC9CYXNlRm9udCAvQk1RUURWK0RlamFWdVNhbnMgL0ZpcnN0Q2hhciAwIC9MYXN0Q2hhciAyNTUKL0ZvbnREZXNjcmlwdG9yIDIwIDAgUiAvU3VidHlwZSAvVHlwZTMgL05hbWUgL0JNUVFEVitEZWphVnVTYW5zCi9Gb250QkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0KL0NoYXJQcm9jcyAyMiAwIFIKL0VuY29kaW5nIDw8IC9UeXBlIC9FbmNvZGluZwovRGlmZmVyZW5jZXMgWyA0MCAvcGFyZW5sZWZ0IC9wYXJlbnJpZ2h0IDQ4IC96ZXJvIC9vbmUgL3R3byAvdGhyZWUgL2ZvdXIgL2ZpdmUgL3NpeCA2MQovZXF1YWwgNjUgL0EgL0IgNzggL04gMTEyIC9wIDEyMCAveCAveSBdCj4+Ci9XaWR0aHMgMTkgMCBSID4+CmVuZG9iagoyMCAwIG9iago8PCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL0ZvbnROYW1lIC9CTVFRRFYrRGVqYVZ1U2FucyAvRmxhZ3MgMzIKL0ZvbnRCQm94IFsgLTEwMjEgLTQ2MyAxNzk0IDEyMzMgXSAvQXNjZW50IDkyOSAvRGVzY2VudCAtMjM2IC9DYXBIZWlnaHQgMAovWEhlaWdodCAwIC9JdGFsaWNBbmdsZSAwIC9TdGVtViAwIC9NYXhXaWR0aCAxMzQyID4+CmVuZG9iagoxOSAwIG9iagpbIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwCjYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgMzE4IDQwMSA0NjAgODM4IDYzNgo5NTAgNzgwIDI3NSAzOTAgMzkwIDUwMCA4MzggMzE4IDM2MSAzMTggMzM3IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYKNjM2IDYzNiAzMzcgMzM3IDgzOCA4MzggODM4IDUzMSAxMDAwIDY4NCA2ODYgNjk4IDc3MCA2MzIgNTc1IDc3NSA3NTIgMjk1CjI5NSA2NTYgNTU3IDg2MyA3NDggNzg3IDYwMyA3ODcgNjk1IDYzNSA2MTEgNzMyIDY4NCA5ODkgNjg1IDYxMSA2ODUgMzkwIDMzNwozOTAgODM4IDUwMCA1MDAgNjEzIDYzNSA1NTAgNjM1IDYxNSAzNTIgNjM1IDYzNCAyNzggMjc4IDU3OSAyNzggOTc0IDYzNCA2MTIKNjM1IDYzNSA0MTEgNTIxIDM5MiA2MzQgNTkyIDgxOCA1OTIgNTkyIDUyNSA2MzYgMzM3IDYzNiA4MzggNjAwIDYzNiA2MDAgMzE4CjM1MiA1MTggMTAwMCA1MDAgNTAwIDUwMCAxMzQyIDYzNSA0MDAgMTA3MCA2MDAgNjg1IDYwMCA2MDAgMzE4IDMxOCA1MTggNTE4CjU5MCA1MDAgMTAwMCA1MDAgMTAwMCA1MjEgNDAwIDEwMjMgNjAwIDUyNSA2MTEgMzE4IDQwMSA2MzYgNjM2IDYzNiA2MzYgMzM3CjUwMCA1MDAgMTAwMCA0NzEgNjEyIDgzOCAzNjEgMTAwMCA1MDAgNTAwIDgzOCA0MDEgNDAxIDUwMCA2MzYgNjM2IDMxOCA1MDAKNDAxIDQ3MSA2MTIgOTY5IDk2OSA5NjkgNTMxIDY4NCA2ODQgNjg0IDY4NCA2ODQgNjg0IDk3NCA2OTggNjMyIDYzMiA2MzIgNjMyCjI5NSAyOTUgMjk1IDI5NSA3NzUgNzQ4IDc4NyA3ODcgNzg3IDc4NyA3ODcgODM4IDc4NyA3MzIgNzMyIDczMiA3MzIgNjExIDYwNQo2MzAgNjEzIDYxMyA2MTMgNjEzIDYxMyA2MTMgOTgyIDU1MCA2MTUgNjE1IDYxNSA2MTUgMjc4IDI3OCAyNzggMjc4IDYxMiA2MzQKNjEyIDYxMiA2MTIgNjEyIDYxMiA4MzggNjEyIDYzNCA2MzQgNjM0IDYzNCA1OTIgNjM1IDU5MiBdCmVuZG9iagoyMiAwIG9iago8PCAvQSAyMyAwIFIgL0IgMjQgMCBSIC9OIDI1IDAgUiAvZXF1YWwgMjYgMCBSIC9maXZlIDI3IDAgUiAvZm91ciAyOCAwIFIKL29uZSAyOSAwIFIgL3AgMzAgMCBSIC9wYXJlbmxlZnQgMzEgMCBSIC9wYXJlbnJpZ2h0IDMyIDAgUiAvc2l4IDMzIDAgUgovdGhyZWUgMzQgMCBSIC90d28gMzUgMCBSIC94IDM2IDAgUiAveSAzNyAwIFIgL3plcm8gMzggMCBSID4+CmVuZG9iagozIDAgb2JqCjw8IC9GMiAxNSAwIFIgL0YxIDIxIDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMCAvY2EgMSA+PgovQTIgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMSAvY2EgMSA+PgovQTMgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMC44IC9jYSAwLjggPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgPj4KZW5kb2JqCjIgMCBvYmoKPDwgL1R5cGUgL1BhZ2VzIC9LaWRzIFsgMTEgMCBSIF0gL0NvdW50IDEgPj4KZW5kb2JqCjM5IDAgb2JqCjw8IC9DcmVhdG9yIChNYXRwbG90bGliIHYzLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZykKL1Byb2R1Y2VyIChNYXRwbG90bGliIHBkZiBiYWNrZW5kIHYzLjcuMikKL0NyZWF0aW9uRGF0ZSAoRDoyMDI0MDkyNzEwNDc0MCswMicwMCcpID4+CmVuZG9iagp4cmVmCjAgNDAKMDAwMDAwMDAwMCA2NTUzNSBmIAowMDAwMDAwMDE2IDAwMDAwIG4gCjAwMDAwMTA5NTQgMDAwMDAgbiAKMDAwMDAxMDcwNiAwMDAwMCBuIAowMDAwMDEwNzQ5IDAwMDAwIG4gCjAwMDAwMTA4OTEgMDAwMDAgbiAKMDAwMDAxMDkxMiAwMDAwMCBuIAowMDAwMDEwOTMzIDAwMDAwIG4gCjAwMDAwMDAwNjUgMDAwMDAgbiAKMDAwMDAwMDM0NCAwMDAwMCBuIAowMDAwMDAyNTg5IDAwMDAwIG4gCjAwMDAwMDAyMDggMDAwMDAgbiAKMDAwMDAwMjU2OCAwMDAwMCBuIAowMDAwMDAzNzIxIDAwMDAwIG4gCjAwMDAwMDM1MDYgMDAwMDAgbiAKMDAwMDAwMzE3MCAwMDAwMCBuIAowMDAwMDA0Nzc0IDAwMDAwIG4gCjAwMDAwMDI2MDkgMDAwMDAgbiAKMDAwMDAwMjc2NCAwMDAwMCBuIAowMDAwMDA5NDMxIDAwMDAwIG4gCjAwMDAwMDkyMjQgMDAwMDAgbiAKMDAwMDAwODgwNiAwMDAwMCBuIAowMDAwMDEwNDg0IDAwMDAwIG4gCjAwMDAwMDQ4MTYgMDAwMDAgbiAKMDAwMDAwNDk3OSAwMDAwMCBuIAowMDAwMDA1MzE2IDAwMDAwIG4gCjAwMDAwMDU0NjUgMDAwMDAgbiAKMDAwMDAwNTYxMSAwMDAwMCBuIAowMDAwMDA1OTMzIDAwMDAwIG4gCjAwMDAwMDYwOTkgMDAwMDAgbiAKMDAwMDAwNjI1NCAwMDAwMCBuIAowMDAwMDA2NTY2IDAwMDAwIG4gCjAwMDAwMDY3ODkgMDAwMDAgbiAKMDAwMDAwNzAxMyAwMDAwMCBuIAowMDAwMDA3NDA2IDAwMDAwIG4gCjAwMDAwMDc4MTkgMDAwMDAgbiAKMDAwMDAwODE0MyAwMDAwMCBuIAowMDAwMDA4MzA0IDAwMDAwIG4gCjAwMDAwMDg1MTggMDAwMDAgbiAKMDAwMDAxMTAxNCAwMDAwMCBuIAp0cmFpbGVyCjw8IC9TaXplIDQwIC9Sb290IDEgMCBSIC9JbmZvIDM5IDAgUiA+PgpzdGFydHhyZWYKMTExNzEKJSVFT0YK", "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here is an example of plot where A=1 and B=5.\n", "def p(N, A, B):\n", " return B * N**2 / (A**2 + N**2)\n", "\n", "\n", "A = 1\n", "B = 5\n", "N_domain = np.linspace(0, 5, 100)\n", "plt.plot(N_domain, p(N_domain, A, B), label=\"p(N)\")\n", "plt.axvline(x=A, ls=\"--\", c='r',label=\"x=A\")\n", "plt.axhline(y=B, ls=\"--\", label=\"y=B\")\n", "plt.ylim([0, 6])\n", "plt.ylabel(r\"$p(N)$\")\n", "plt.xlabel(r\"$N$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">$A$ is the value of $N$ when $p(N)$ is at half maximum. $B$ is the saturation value of $p(N)$ for large $N$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**B. Discuss the fixed points and stability properties of this model in function of $r$ and $k$ by the following steps:** \n", "\t\t\n", "1) For convenience, let's first change variables: $x = \\dfrac{N}{A}, \\; r=r_B \\;\\dfrac{A}{B}, \\; k=\\dfrac{K}{A}, \\; \\tau = \\dfrac{Bt}{A}$. \n", "Verify that this leads to the dimensionless form with two dimensionless parameters $r,k$. \n", "$$\n", "\\dfrac{dx}{d\\tau} = r x (1-\\frac{x}{k}) - \\frac{x^2}{1+x^2} = x(f(x) - h(x))\n", "$$\t\t\t\t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">We have $dx = \\dfrac{dN}{A}$ and $d\\tau = \\dfrac{Bdt}{A}$ so $\\dfrac{dN}{dt} = \\dfrac{Adx}{dt}=\\dfrac{Bdx}{d\\tau}$. If we substitute all the other variables, we get: $B\\dfrac{dx}{d\\tau}=Brx(1-\\dfrac{x}{k})-B\\dfrac{x^{2}}{1+x^{2}}$ which we simplify by B to get the dimensionless form. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2) Consider the following three qualitatively different situations and plot in each case the two terms $f(x)= r(1-\\dfrac{x}{k})$ and $h(x)= \\dfrac{x}{1+x^2}$ in function of x. Note that the intersections correspond to the fixed points (cf. the genetic switch in Chapter 2).\t\t\t\n", " * intermediate $r$, intermediate $k$ (one fixed point, called the refuge)\n", " * small $r$ , large $k$ (3 fixed points, called the bistable region)\n", " * large $r$ , large $k$ (one fixed points, called the outbreak).\n", " \n", "Hint: Here, small will be less than 1, intermediate will be around 1, and large will be more than 2. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">To calculate the fixed points, we use the condition $r(1-\\dfrac{x}{k}) =\\dfrac{x}{1+x^{2}}$ (Note that only the left side is dependent on $r$ and $k$). \n", "We observe 1 to 3 fixed points $x^{*}$ at the intersections of the terms $r(1-\\dfrac{x}{k})$ and $\\dfrac{x}{1+x^{2}}$ depending on $r$ and $k$. ⠀⠀" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.0, 10, 100)\n", "\n", "\n", "def f(r, k, x):\n", " return r * (1 - x / k)\n", "\n", "\n", "def h(x):\n", " return x / (1 + x**2)\n", "\n", "\n", "plt.plot(x, h(x), label=\"h(x)\")\n", "\n", "# medium r, medium k\n", "r = 1.0\n", "k = 1.0\n", "plt.plot(x, f(r, k, x), label=\"f(x) with medium r, medium k\")\n", "\n", "# small r, large k\n", "r = 0.5\n", "k = 10.0\n", "plt.plot(x, f(r, k, x), label=\"f(x) with small r, large k\")\n", "\n", "# large r, large k\n", "r = 4.0\n", "k = 4.0\n", "plt.plot(x, f(r, k, x), label=\"f(x) with large r, large k\")\n", "\n", "plt.axhline(y=0, color=\"black\", lw=1)\n", "plt.legend()\n", "plt.xlabel(\"x\")\n", "plt.ylim([-0.5, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3) For each situation sketched previously (small, intermediate and large $r$), plot $\\dfrac{dx}{d\\tau}$ in function of $x$ and characterize the stability of the fixed points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">In addition to 1-3 fixed points found in b., we have $x^*=0$ which is an unstable fixed point." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.0, 10, 1000)\n", "\n", "\n", "def F(r, k, x):\n", " return x * (f(r, k, x) - h(x))\n", "\n", "\n", "# medium r, medium k\n", "r = 1.0\n", "k = 1.0\n", "plt.plot(x, F(r, k, x), label=\"F(x) with medium r, medium k\", color=\"green\")\n", "# look for intersection and stability (dirty way)\n", "zeros = [y if abs(F(r, k, y)) < 10**-3 else np.nan for y in x]\n", "stability = [\n", " \"-\" if F(r, k, y2) - F(r, k, y1) > 0 else \"+\" for y1, y2 in zip(x[:-1], x[1:])\n", "]\n", "for zero, stab in zip(zeros, stability):\n", " if stab == \"+\":\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"green\")\n", " else:\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"green\", facecolor=\"none\")\n", "\n", "\n", "# small r, large k\n", "r = 0.5\n", "k = 10.0\n", "plt.plot(x, F(r, k, x), label=\"F(x) with small r, large k\", color=\"orange\")\n", "# look for intersection and stability (dirty way)\n", "zeros = [y if abs(F(r, k, y)) < 10**-3 else np.nan for y in x]\n", "stability = [\n", " \"-\" if F(r, k, y2) - F(r, k, y1) > 0 else \"+\" for y1, y2 in zip(x[:-1], x[1:])\n", "]\n", "for zero, stab in zip(zeros, stability):\n", " if stab == \"+\":\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"orange\")\n", " else:\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"orange\", facecolor=\"none\")\n", "\n", "# large r, large k\n", "r = 4.0\n", "k = 4.0\n", "plt.plot(x, F(r, k, x), label=\"F(x) with large r, large k\", color=\"blue\")\n", "# look for intersection and stability (dirty way)\n", "zeros = [y if abs(F(r, k, y)) < 10**-2 else np.nan for y in x]\n", "stability = [\n", " \"-\" if F(r, k, y2) - F(r, k, y1) > 0 else \"+\" for y1, y2 in zip(x[:-1], x[1:])\n", "]\n", "for zero, stab in zip(zeros, stability):\n", " if stab == \"+\":\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"blue\")\n", " else:\n", " plt.scatter(x=zero, y=0, marker=\"o\", s=50, color=\"blue\", facecolor=\"none\")\n", "\n", "\n", "plt.axhline(y=0, color=\"black\", lw=1)\n", "plt.legend()\n", "plt.xlabel(\"x\")\n", "plt.ylabel(r\"$F(x) = \\frac{dx}{d\\tau}$\")\n", "plt.ylim([-0.5, 2])\n", "plt.xlim([-0.5, 8])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**C. Bifurcation diagram: Find the boundaries in the ($r,k$)-plane between the single and triple fixed points regions. Proceed stepwise:** \n", "\n", "1) Express mathematically the requirement that the two curves $f(x)=r(1-\\dfrac{x}{k})$ and $h(x)= \\dfrac{x}{1+x^2}$ are _tangent_. Use this requirement to express $r,k$ at the tangents in function of $x$. (Control: $r(x) = \\dfrac{2x^3}{(1+x^2)^2}$ and $k(x) = \\dfrac{-2x^3}{(1-x^2)}$ ). \n", "Hint: To be tangent, the values of the curves and the derivatives must be equal at the *touching* points $x$.\n", "\t\t\t\n", "\t\t\t\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">For the functions $f(x)$ and $h(x)$ to be tangent, and therefore ensuring the semistability condition, they have to fulfill the following two conditions:\n", "1. $f(x)=h(x)$\n", "2. $f^{'}(x)= h^{'}(x)$ \n", "\n", ">We start solving the derivatives, which gives $r=-\\dfrac{k(1-x^2)}{(1+x^2)^2}$ \n", "By insertion into $r(1-\\dfrac{x}{k})=\\dfrac{x}{1+x^2}$, we can express $r$ and $k$ in parametric form where the parameter is $x$. \n", "\\begin{equation}\n", " r(x) , k(x)\n", "\\end{equation}\n", "Note that $x\\geq0$ is required for positive $r$ and $k$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2) Plot the bifurcation diagram with Python, that means plot $(r(x^*),k(x^*))$ pairs of the tangent in the $(r,k)$ plane for $x^* \\in [1,\\infty]$. Use axis-limits $r \\in [0,1]$ and $k \\in [0,10]$. \n", "\t\t\t\n", "**Notice**: since the capacity parameter $k$ is positive, $x$ is restricted to $x^* \\in [1,\\infty]$. That means that there are no tangential contacts between the two curves for the other values of $x^{*}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">We can distinguish the three different sections by recalling exercise B.2. It may be confusing that there is no clear difference between outbreak and refuge for small k. But keep in mind that at a small capacity the line between both is actually irrelevant." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/8w/hhwzbx0d6zg_2q5hrl31_yn00000gq/T/ipykernel_4675/2511889505.py:4: RuntimeWarning: divide by zero encountered in divide\n", " k = -2 * x**3 / (1 - x**2)\n" ] }, { "data": { "application/pdf": 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M+Jy0zoM5Fbr344k2B02N2ujs9xNpKi9Sux1anX51EpXdGOcYEpdnfxnfZP/5B/6HWiIKZW5kc3RyZWFtCmVuZG9iagoyMyAwIG9iago8PCAvTGVuZ3RoIDM5NSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9UktuxUAI2+cUXKDS8JvPeVJV3bz7b2tDUqkqvIkxxjB9ypC55UtdEnGFybderls8pnwuW1qZeYi7i40lPrbcl+4htl10LrE4HUfyCzKdKkSozarRofhCloUHkE7woQvCfTn+4y+AwdewDbjhPTJBsCTmKULGblEZmhJBEWHnkRWopFCfWcLfUe7r9zIFam+MpQtjHPQJtAVCbUjEAupAAETslFStkI5nJBO/Fd1nYhxg59GyAa4ZVESWe+zHiKnOqIy8RMQ+T036KJZMLVbGblMZX/yUjNR8dAUqqTTylPLQVbPQC1iJeRL2OfxI+OfWbCGGOm7W8onlHzPFMhLOYEs5YKGX40fg21l1Ea4dubjOdIEfldZwTLTrfsj1T/5021rNdbxyCKJA5U1B8LsOrkaxxMQyPp2NKXqiLLAamrxGM8FhEBHW98PIAxr9crwQNKdrIrRYIpu1YkSNimxzPb0E1kzvxTnWwxPCbO+d1qGyMzMqIYLauoZq60B2s77zcLafPzPoom0KZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvTGVuZ3RoIDEzNiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxNj0EOAzEIA+95hZ9AIEB4z1ZVD9v/X0vYdtMLHsmAbFEGgSWHeIcb4dHbD99FNhVn45xfUiliIZhPcJ8wUxyNKXfyY4+AcZRqLKdoeF5Lzk3DFy13Ey2lrZeTGW+47pf3R5VtkQ1Fzy0LQtdskvkygQd8GJhHdeNppcfd9myv9vwAzmw0SQplbmRzdHJlYW0KZW5kb2JqCjI1IDAgb2JqCjw8IC9MZW5ndGggMjQ5IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nE1RSYoDMAy75xX6QCFek7ynQ5lD5//Xyg6FOQQJr5KTlphYCw8xhB8sPfiRIXM3/Rt+otm7WXqSydn/mOciU1H4UqguYkJdiBvPoRHwPaFrElmxvfE5LKOZc74HH4W4BDOhAWN9STK5qOaVIRNODHUcDlqkwrhrYsPiWtE8jdxu+0ZmZSaEDY9kQtwYgIgg6wKyGCyUNjYTMlnOA+0NyQ1aYNepG1GLgiuU1gl0olbEqszgs+bWdjdDLfLgqH3x+mhWl2CF0Uv1WHhfhT6YqZl27pJCeuFNOyLMHgqkMjstK7V7xOpugfo/y1Lw/cn3+B2vD838XJwKZW5kc3RyZWFtCmVuZG9iagoyNiAwIG9iago8PCAvTGVuZ3RoIDk0IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nEWNwRHAIAgE/1RBCQoK2k8mk4f2/40QMnxg5w7uhAULtnlGHwWVJl4VWAdKY9xQj0C94XItydwFD3Anf9rQVJyW03dpkUlVKdykEnn/DmcmkKh50WOd9wtj+yM8CmVuZHN0cmVhbQplbmRvYmoKMjcgMCBvYmoKPDwgL0xlbmd0aCAzNDEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRVJLbkQxCNu/U3CBSOGXkPO0qrqY3n9bm0zVzeAJYGx4y1OmZMqwuSUjJNeUT30iQ6ym/DRyJCKm+EkJBXaVj8drS6yN7JGoFJ/a8eOx9Eam2RVa9e7Rpc2iUc3KyDnIEKGeFbqye9QO2fB6XEi675TNIRzL/1CBLGXdcgolQVvQd+wR3w8droIrgmGway6D7WUy1P/6hxZc7333YscugBas577BDgCopxO0BcgZ2u42KWgAVbqLScKj8npudqJso1Xp+RwAMw4wcsCIJVsdvtHeAJZ9XehFjYr9K0BRWUD8yNV2wd4xyUhwFuYGjr1wPMWZcEs4xgJAir3iGHrwJdjmL1euiJrwCXW6ZC+8wp7a5udCkwh3rQAOXmTDraujqJbt6TyC9mdFckaM1Is4OiGSWtI5guLSoB5a41w3seJtI7G5V9/uH+GcL1z26xdL7ITECmVuZHN0cmVhbQplbmRvYmoKMjggMCBvYmoKPDwgL0xlbmd0aCA3MiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlxAvqmJuUIuF0gMxMoBswyAtCWcgohngJggbRDFIBZEsZmJGUQdnAGRy+BKAwAl2xbJCmVuZHN0cmVhbQplbmRvYmoKMjkgMCBvYmoKPDwgL0xlbmd0aCA4MyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9zDkSgDAIBdCeU/wjhMgi93Eci3j/VjDRBh6reqAhOIO6wa3hYMq6dBPvU+PVxpwSCah4Sk2Wugt61LS+1L5o4Lvr5kvViT/NzxedD7sdGd0KZW5kc3RyZWFtCmVuZG9iagozMCAwIG9iago8PCAvTGVuZ3RoIDQ3IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDMyt1AwULA0ARKGFiYK5mYGCimGXJYQVi4XTCwHzALRlnAKIp7BlQYAuWcNJwplbmRzdHJlYW0KZW5kb2JqCjMxIDAgb2JqCjw8IC9MZW5ndGggODMgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRYy7DcAwCER7pmAEfib2PlGUwt6/DRAlbrgn3T1cHQmZKW4zw0MGngwshl1xgfSWMAtcR1COneyjYdW+6gSN9aZS8+8PlJ7srOKG6wECQhpmCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0xlbmd0aCA1MSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzNrRQMFAwNDAHkkaGQJaRiUKKIRdIAMTM5YIJ5oBZBkAaojgHriaHK4MrDQDhtA2YCmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0xlbmd0aCAxNjAgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRZA5EgMxCARzvYInSFyC96zLtcH6/6kH1kei6QI0HLoWTcp6FGg+6bFGobrQa+gsSpJEwRaSHVCnY4g7KEhMSGOSSLYegyOaWLNdmJlUKrNS4bRpxcK/2VrVyESNcI38iekGVPxP6lyU8E2Dr5Ix+hhUvDuDjEn4XkXcWjHt/kQwsRn2CW9FJgWEibGp2b7PYIbM9wrXOMfzDUyCN+sKZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvTGVuZ3RoIDMzNCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwtUktyxSAM23MKXaAz+AfkPOl0uni9/7aSk0VGDmD0MeWGiUp8WSC3o9bEt43MQIXhr6vMhc9I28g6iMuQi7iSLYV7RCzkMcQ8xILvq/EeHvmszMmzB8Yv2XcPK/bUhGUh48UZ2mEVx2EV5FiwdSGqe3hTpMOpJNjji/8+xXMtBC18RtCAX+Sfr47g+ZIWafeYbdOuerBMO6qksBxsT3NeJl9aZ7k6Hs8Hyfau2BFSuwIUhbkzznPhKNNWRrQWdjZIalxsb479WErQhW5cRoojkJ+pIjygpMnMJgrij5wecioDYeqarnRyG1Vxp57MNZuLtzNJZuu+SLGZwnldOLP+DFNmtXknz3Ki1KkI77FnS9DQOa6evZZZaHSbE7ykhM/GTk9Ovlcz6yE5FQmpYlpXwWkUmWIJ2xJfU1FTmnoZ/vvy7vE7fv4BLHN8cwplbmRzdHJlYW0KZW5kb2JqCjM1IDAgb2JqCjw8IC9MZW5ndGggNzAgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicMzM2UzBQsDACEqamhgrmRpYKKYZcQD6IlcsFE8sBs8wszIEsIwuQlhwuQwtjMG1ibKRgZmIGZFkgMSC6MrjSAJiaEwMKZW5kc3RyZWFtCmVuZG9iagozNiAwIG9iago8PCAvTGVuZ3RoIDMyMCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UktuBTEI288puECl8E/O86qqi777b2sTvRVMMGDjKS9Z0ku+1CXbpcPkWx/3JbFC3o/tmsxSxfcWsxTPLa9HzxG3LQoEURM9WJkvFSLUz/ToOqhwSp+BVwi3FBu8g0kAg2r4Bx6lMyBQ50DGu2IyUgOCJNhzaXEIiXImiX+kvJ7fJ62kofQ9WZnL35NLpdAdTU7oAcXKxUmgXUn5oJmYSkSSl+t9sUL0hsCSPD5HMcmA7DaJbaIFJucepSXMxBQ6sMcCvGaa1VXoYMIehymMVwuzqB5s8lsTlaQdreMZ2TDeyzBTYqHhsAXU5mJlgu7l4zWvwojtUZNdw3Duls13CNFo/hsWyuBjFZKAR6exEg1pOMCIwJ5eOMVe8xM5DsCIY52aLAxjaCaneo6JwNCes6VhxsceWvXzD1TpfIcKZW5kc3RyZWFtCmVuZG9iagozNyAwIG9iago8PCAvTGVuZ3RoIDEzMyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxFj0sOBCEIRPecoo7Axx/ncTLphXP/7YCdbhNjPYVUgbmCoT0uawOdFR8hGbbxt6mWjkVZPlR6UlYPyeCHrMbLIdygLPCCSSqGIVCLmBqRLWVut4DbNg2yspVTpY6wi6Mwj/a0bBUeX6JbInWSP4PEKi/c47odyKXWu96ii75/pAExCQplbmRzdHJlYW0KZW5kb2JqCjM4IDAgb2JqCjw8IC9MZW5ndGggMjUxIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nC1RSXIDQQi7zyv0hGan32OXK4fk/9cIygcGDYtAdFrioIyfICxXvOWRq2jD3zMxgt8Fh34r121Y5EBUIEljUDWhdvF69B7YcZgJzJPWsAxmrA/8jCnc6MXhMRlnt9dl1BDsXa89mUHJrFzEJRMXTNVhI2cOP5kyLrRzPTcg50ZYl2GQblYaMxKONIVIIYWqm6TOBEESjK5GjTZyFPulL490hlWNqDHscy1tX89NOGvQ7Fis8uSUHl1xLicXL6wc9PU2AxdRaazyQEjA/W4P9XOyk994S+fOFtPje83J8sJUYMWb125ANtXi37yI4/uMr+fn+fwDX2BbiAplbmRzdHJlYW0KZW5kb2JqCjM5IDAgb2JqCjw8IC9MZW5ndGggMTc0IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nE2QSQ5DIQxD95zCF6iEM8DnPL+qumjvv61DB3WB/OQgcDw80HEkLnRk6IyOK5sc48CzIGPi0Tj/ybg+xDFB3aItWJd2x9nMEnPCMjECtkbJ2TyiwA/HXAgSZJcfvsAgIl2P+VbzWZP0z7c73Y+6tGZfPaLAiewIxbABV4D9useBS8L5XtPklyolYxOH8oHqIlI2O6EQtVTscqqKs92bK3AV9PzRQ+7tBbUjPN8KZW5kc3RyZWFtCmVuZG9iago0MCAwIG9iago8PCAvTGVuZ3RoIDE0MSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9j8EOwzAIQ+/5Cv9ApNgpoXxPp2qH7v+vI0u7C3oCY4yF0NAbqprDhmCb48XSJVRr+BTFQCU3yJlgDqWk0h1HkXpiOBhcHrQbjuKx6PoRu5JmfdDGQrolaIB7rFNp3KZxE8QdNQXqKeqco7wQuZ+pZ9g0kt00s5JzuA2/e89T1/+nq7zL+QW9dy7+CmVuZHN0cmVhbQplbmRvYmoKNDEgMCBvYmoKPDwgL0xlbmd0aCAyMTUgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNVE5DgMhDOz3Ff5AJIwveE+iKM3+v82M0VYewVyGtJQhmfJSk6gh5VM+epkunLrc18xqNOeWtC1zgLi2vC+tksCJZoiDwWmYuAGaPAFD19GoUUMXHtDUpVMosNwEPoq3bg/dY7WBl7Yh54kgYigZLEHNqUUTFm3PJ6Q1v16LG96X7d3IU6XGlhiBBgFWOBzX6NfwlT1PJtF0FTLUqzXLGAkTRSI8+Y6m1RPrWjTSMhLUxhGsagO8O/0wTgAAE3HLAmSfSpSz5MRvsfSzBlf6/gGfR1SWCmVuZHN0cmVhbQplbmRvYmoKMTUgMCBvYmoKPDwgL1R5cGUgL0ZvbnQgL0Jhc2VGb250IC9CTVFRRFYrRGVqYVZ1U2FucyAvRmlyc3RDaGFyIDAgL0xhc3RDaGFyIDI1NQovRm9udERlc2NyaXB0b3IgMTQgMCBSIC9TdWJ0eXBlIC9UeXBlMyAvTmFtZSAvQk1RUURWK0RlamFWdVNhbnMKL0ZvbnRCQm94IFsgLTEwMjEgLTQ2MyAxNzk0IDEyMzMgXSAvRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXQovQ2hhclByb2NzIDE2IDAgUgovRW5jb2RpbmcgPDwgL1R5cGUgL0VuY29kaW5nCi9EaWZmZXJlbmNlcyBbIDQ2IC9wZXJpb2QgNDggL3plcm8gL29uZSAvdHdvIDUyIC9mb3VyIC9maXZlIC9zaXggL3NldmVuIC9laWdodCA2NiAvQiA3OQovTyA4MiAvUiA5NyAvYSAvYiAxMDEgL2UgL2YgL2cgMTA1IC9pIDEwNyAvayAvbCAxMTQgL3IgL3MgL3QgL3UgMTIxIC95IF0KPj4KL1dpZHRocyAxMyAwIFIgPj4KZW5kb2JqCjE0IDAgb2JqCjw8IC9UeXBlIC9Gb250RGVzY3JpcHRvciAvRm9udE5hbWUgL0JNUVFEVitEZWphVnVTYW5zIC9GbGFncyAzMgovRm9udEJCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9Bc2NlbnQgOTI5IC9EZXNjZW50IC0yMzYgL0NhcEhlaWdodCAwCi9YSGVpZ2h0IDAgL0l0YWxpY0FuZ2xlIDAgL1N0ZW1WIDAgL01heFdpZHRoIDEzNDIgPj4KZW5kb2JqCjEzIDAgb2JqClsgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAxIDQ2MCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAzMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4MzggNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1NiA1NTcgODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjExIDY4NSAzOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNDIgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyMyA2MDAgNTI1IDYxMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTIgODM4IDM2MSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxMiA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA1CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5ODIgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE2IDAgb2JqCjw8IC9CIDE3IDAgUiAvTyAxOCAwIFIgL1IgMTkgMCBSIC9hIDIwIDAgUiAvYiAyMSAwIFIgL2UgMjIgMCBSCi9laWdodCAyMyAwIFIgL2YgMjQgMCBSIC9maXZlIDI1IDAgUiAvZm91ciAyNiAwIFIgL2cgMjcgMCBSIC9pIDI4IDAgUgovayAyOSAwIFIgL2wgMzAgMCBSIC9vbmUgMzEgMCBSIC9wZXJpb2QgMzIgMCBSIC9yIDMzIDAgUiAvcyAzNCAwIFIKL3NldmVuIDM1IDAgUiAvc2l4IDM2IDAgUiAvdCAzNyAwIFIgL3R3byAzOCAwIFIgL3UgMzkgMCBSIC95IDQwIDAgUgovemVybyA0MSAwIFIgPj4KZW5kb2JqCjMgMCBvYmoKPDwgL0YxIDE1IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMCAvY2EgMSA+PgovQTIgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMSAvY2EgMSA+PiA+PgplbmRvYmoKNSAwIG9iago8PCA+PgplbmRvYmoKNiAwIG9iago8PCA+PgplbmRvYmoKNyAwIG9iago8PCA+PgplbmRvYmoKMiAwIG9iago8PCAvVHlwZSAvUGFnZXMgL0tpZHMgWyAxMSAwIFIgXSAvQ291bnQgMSA+PgplbmRvYmoKNDIgMCBvYmoKPDwgL0NyZWF0b3IgKE1hdHBsb3RsaWIgdjMuNy4yLCBodHRwczovL21hdHBsb3RsaWIub3JnKQovUHJvZHVjZXIgKE1hdHBsb3RsaWIgcGRmIGJhY2tlbmQgdjMuNy4yKQovQ3JlYXRpb25EYXRlIChEOjIwMjQwOTI3MTA0NzUyKzAyJzAwJykgPj4KZW5kb2JqCnhyZWYKMCA0MwowMDAwMDAwMDAwIDY1NTM1IGYgCjAwMDAwMDAwMTYgMDAwMDAgbiAKMDAwMDAxMDc1MiAwMDAwMCBuIAowMDAwMDEwNTU4IDAwMDAwIG4gCjAwMDAwMTA1OTAgMDAwMDAgbiAKMDAwMDAxMDY4OSAwMDAwMCBuIAowMDAwMDEwNzEwIDAwMDAwIG4gCjAwMDAwMTA3MzEgMDAwMDAgbiAKMDAwMDAwMDA2NSAwMDAwMCBuIAowMDAwMDAwMzQ0IDAwMDAwIG4gCjAwMDAwMDE4NDkgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDAxODI4IDAwMDAwIG4gCjAwMDAwMDkyMDUgMDAwMDAgbiAKMDAwMDAwODk5OCAwMDAwMCBuIAowMDAwMDA4NTQ3IDAwMDAwIG4gCjAwMDAwMTAyNTggMDAwMDAgbiAKMDAwMDAwMTg2OSAwMDAwMCBuIAowMDAwMDAyMjA2IDAwMDAwIG4gCjAwMDAwMDI0OTQgMDAwMDAgbiAKMDAwMDAwMjc5OSAwMDAwMCBuIAowMDAwMDAzMTc5IDAwMDAwIG4gCjAwMDAwMDM0OTYgMDAwMDAgbiAKMDAwMDAwMzgxOCAwMDAwMCBuIAowMDAwMDA0Mjg2IDAwMDAwIG4gCjAwMDAwMDQ0OTUgMDAwMDAgbiAKMDAwMDAwNDgxNyAwMDAwMCBuIAowMDAwMDA0OTgzIDAwMDAwIG4gCjAwMDAwMDUzOTcgMDAwMDAgbiAKMDAwMDAwNTU0MSAwMDAwMCBuIAowMDAwMDA1Njk2IDAwMDAwIG4gCjAwMDAwMDU4MTUgMDAwMDAgbiAKMDAwMDAwNTk3MCAwMDAwMCBuIAowMDAwMDA2MDkzIDAwMDAwIG4gCjAwMDAwMDYzMjYgMDAwMDAgbiAKMDAwMDAwNjczMyAwMDAwMCBuIAowMDAwMDA2ODc1IDAwMDAwIG4gCjAwMDAwMDcyNjggMDAwMDAgbiAKMDAwMDAwNzQ3NCAwMDAwMCBuIAowMDAwMDA3Nzk4IDAwMDAwIG4gCjAwMDAwMDgwNDUgMDAwMDAgbiAKMDAwMDAwODI1OSAwMDAwMCBuIAowMDAwMDEwODEyIDAwMDAwIG4gCnRyYWlsZXIKPDwgL1NpemUgNDMgL1Jvb3QgMSAwIFIgL0luZm8gNDIgMCBSID4+CnN0YXJ0eHJlZgoxMDk2OQolJUVPRgo=", "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# x = np.linspace(1.01,10,1000)\n", "x = np.linspace(1, 10, 1000)\n", "r = 2 * x**3 / (1 + x**2) ** 2\n", "k = -2 * x**3 / (1 - x**2)\n", "plt.plot(r, k)\n", "plt.xlim([0, 1])\n", "plt.ylim([0, 20])\n", "plt.xlabel(\"r\")\n", "plt.ylabel(\"k\")\n", "plt.text(x=0.05, y=15, s=\"Refuge\")\n", "plt.text(x=0.3, y=15, s=\"Bistability\")\n", "plt.text(x=0.7, y=15, s=\"Outbreak\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3) **A biological catastrophe**: Bistability and hysteresis. Sketch what happens to a budworm population that lives in an environment where the growth rate $r$ is low, then slowly increases to high values, and finally decreases again to its low value (consider and compare the two cases $k=7$ and $k=3$). Assume that the budworm population equilibrates very fast when the environment changes (it is always at a fixed point) and that it is initially in its low (refuge) state. Use the representation of $f(x)$ and $h(x)$ similar as in B.2 to plot the results and to explain the behavior through time of the population of budworms. \n", "__Hint__: Vary $r$ while keeping $k$ constant in your results of B.2\n", "\t\t\t\n", "\t\n", "\n", "\n", "\n", "\n", "\t\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">The plots below show $r(1-\\dfrac{x}{k})$ and $\\dfrac{x}{1+x^2}$ vs. $x$. The intersection(s) is (are) $x^{*}$. When $k = 7$, at the beginning for a low value of $r$, the population is at the stable fixed point (refuge). As $r$ increases (the slope of $f(x)$ increases), the two curves become tangential and there are two fixed points (saddle node). Then, we enter the bistable region, where there are three fixed points: a stable one at a low value, an unstable one at an intermediate value and a stable one at a high value. The population is still at the left-most stable fixed point. As $r$ keeps increasing, the two curves are again tangential. Then, only one fixed point remains. The population grows and reaches that fixed point (outbreak). Next, $r$ is decreasing. The population remains at the right-most stable fixed point when entering the bistable region again (crossing the value of $r$ for which the two curves are tangent again). As $r$ keeps decreasing, we leave the bistable region and the population goes back to the only remaining fixed point, at a low value. \n", "\t\t\n", ">Note how the $r(1-\\dfrac{x}{k}$) curve rotates around the $x=k$ point. When $k = 3$, there is only one fixed point, and we cannot reach the bistable region." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/pdf": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.0, 15, 100)\n", "\n", "k = 7.0\n", "plt.plot(x, h(x), label=\"h(x)\")\n", "plt.axhline(y=0, color=\"black\", lw=1)\n", "plt.text(7, 0.02, \"k\")\n", "for r in [0.25, 0.41, 0.51, 0.56, 0.6, 1.0]:\n", " plt.plot(x, f(r, k, x), label=\"f(x) with r = \" + str(r))\n", "plt.legend()\n", "plt.xlabel(\"x\")\n", "plt.ylim([-0.2, 0.8])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/8w/hhwzbx0d6zg_2q5hrl31_yn00000gq/T/ipykernel_4675/3093461399.py:10: RuntimeWarning: divide by zero encountered in divide\n", " k_ = -2 * xxx**3 / (1 - xxx**2)\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e75395030d51469085681f27042eda24", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.62, description='r', max=1.0, min=0.25, step=0.01), Output()), _dom_…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# play with this, maybe not crazy big values\n", "k = 7.\n", "\n", "#plot 2\n", "xx = np.linspace(0.0, 6.0, 100)\n", "\n", "#plot 3 , bifurcation diagram\n", "xxx = np.linspace(1, 10, 1000)\n", "r_ = 2 * xxx**3 / (1 + xxx**2) ** 2\n", "k_ = -2 * xxx**3 / (1 - xxx**2)\n", "\n", "def f_anim(r):\n", " # prapre double plot\n", " plt.figure(figsize=(15, 5))\n", " plt.suptitle(\"r=\" + str(r))\n", " plt.subplot(131)\n", " plt.plot(x, h(x), label=\"h(x)\")\n", " plt.plot(x, f(r, k, x), label=\"f(x)\")\n", " plt.axhline(y=0, color=\"black\", lw=1)\n", " plt.text(k, 0.02, \"k\")\n", " plt.xlabel(\"x\")\n", " plt.title(\"r=\" + str(r))\n", " plt.ylim([-0.2, 0.8])\n", " plt.legend()\n", "\n", " plt.subplot(132)\n", " plt.plot(xx, F(r, k, xx), label=\"F(x) = x( f(x)-h(x) )\")\n", " plt.axhline(y=0, color=\"black\", lw=1)\n", " plt.xlabel(\"x\")\n", " plt.ylabel(\"F(x)\")\n", " plt.title(\"r=\" + str(r))\n", " plt.legend()\n", "\n", " plt.subplot(133)\n", " plt.plot(r_, k_)\n", " plt.xlim([0, 1])\n", " plt.ylim([0, 20])\n", " plt.xlabel(\"r\")\n", " plt.ylabel(\"k\")\n", " plt.text(x=0.05, y=15, s=\"Refuge\")\n", " plt.text(x=0.3, y=15, s=\"Bistability\")\n", " plt.text(x=0.7, y=15, s=\"Outbreak\")\n", " plt.scatter(r , k , color=\"red\", s=30, label=\"chosen point in parameter space\")\n", " plt.axhline(y= k, color=\"black\", lw=1)\n", " plt.legend()\n", "\n", "\n", "interact(f_anim, r=(0.25, 1.0, 0.01))" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.11.5" }, "title": "Exercise 3: Insect outbreak and bifurcations" }, "nbformat": 4, "nbformat_minor": 4 }