{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE30338](https://jckantor.github.io/CBE30338)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE30338.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Continuous Product Blending](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/02.04-Continuous-Product-Blending.ipynb) | [Contents](toc.ipynb) | [Exothermic Continuous Stirred Tank Reactor](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/02.06-Exothermic-CSTR.ipynb) >
" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "GZFOPAaKuBCU" }, "source": [ "# Hare and Lynx Population Dynamics\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "This notebook provides an introduction to nonlinear dynamics using a well-known model for the preditor-prey interaction of Snowshoe Hare and Canadian Lynx. Topics include limit cycles, the existence of multiple steady states, and simple phase plane analysis using nullclines. This notebook can be displayed as a slide presentation." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "482JFcV_uBCW" }, "source": [ "## Introduction\n", "\n", "[Snowshoe hare](https://en.wikipedia.org/wiki/Snowshoe_hare) (*Lepus americanus*) are the primary food for the [Canadian lynx](https://en.wikipedia.org/wiki/Canada_lynx) (*Lynx canadensis*) in the Northern boreal forests of North America. When hare are abundant, Lynx will eat hare about two every three days almost to the complete exclusion of other foods. As a consequence, the population dynamics of the two species are closely linked. \n", "\n", "
\n", "\n", "kdee64 (Keith Williams) [CC BY 2.0], via Wikimedia Commons\n", " | \n", "\n", "\n", "D. Gordon E. Robertson [CC BY-SA 3.0], via Wikimedia Commons\n", " | \n", "