If no lynx are present, we will assume that the hares reproduce at a rate proportional to their population and are not affected by overcrowding.We will make the following assumptions for our predator-prey model. We will denote the population of hares by H(t) and the population of lynx by L(t), where t is the time measured in years. The primary prey for the Canadian lynx is the snowshoe hare. The ten year cycle for lynx can be best understood using a system of differential equations. The company noticed that the number of pelts varied from year to year and that the number of lynx pelts reached a peak about every ten years. The Hudson Bay Company kept accurate records on the number of lynx pelts that were bought from trappers from 1821 to 1940. This large Canadian retail company, which owns and operates a large number of retail stores in North America and Europe, including Galeria Kaufhof, Hudson's Bay, Home Outfitters, Lord & Taylor, and Saks Fifth Avenue, was originally founded in 1670 as a fur trading company. For example, we can model how the population of Canadian lynx (lynx Canadians) interacts with a the population of snowshoe hare (lepus americanis) (see ).Ī good historical data are known for the populations of the lynx and snowshoe hare from the Hudson Bay Company. We might use a system of differential equations to model two interacting species, say where one species preys on the other. Some situations require more than one differential equation to model a particular situation. Introduction to Linear Algebra with Mathematica Glossary Return to Part III of the course APMA0340 Return to the main page for the second course APMA0340 Return to the main page for the first course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to Mathematica tutorial for the first course APMA0330 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace equation in spherical coordinates.Numerical solutions of Laplace equation.Laplace equation in infinite semi-stripe. Boundary Value Problems for heat equation.Part VI: Partial Differential Equations.Part III: Non-linear Systems of Ordinary Differential Equations.Part II: Linear Systems of Ordinary Differential Equations.
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