Mathematical Modeling with Excel by Albright Brian; Fox William P.;

Author:Albright, Brian; Fox, William P.;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2019-11-05T00:00:00+00:00

5.5.9 A predator–prey model that takes into account harvesting (i.e., hunting) of the two species is

where x(t) and y(t) are the populations of the prey and predator species, respectively. All parameters are assumed to be positive. Assuming that x ≠ 0 ≠ y, find a formula for the equilibrium point in terms of the parameters.

5.5.10 Consider the predator-prey system in Example 5.5.5 with initial populations of 100 foxes and 1000 rabbits. In this model we used constant values of a1 and a2 (the numbers -0.08 and 0.04). In the terminology of Chapter 4, these are the fox death and rabbit birth factors, respectively. Now suppose these factors change throughout the year. Suppose that during the “summer”, these factors are -0.08 and 0.04, respectively, but during the “winter” they are -0.1 and 0.01, respectively.

Use Euler’s method to estimate the populations from month 0 to month 250 using h = 1. Create one graph of the fox population vs. month and another graph for the rabbit population. Let the winter occur from month 0 through 5, then 12 through 17, and so on.

Compare the populations when the factors are constant to the populations when the factors vary. Do the varying factors cause the ranges of the populations to increase or decrease?

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