mathfoxandrabbit

mathfoxandrabbit - The fox and rabbit model reflects two...

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The fox and rabbit model reflects two interdependent populations whose growths are defined by the current population of both the foxes and the rabbits. Our purpose is to define equations for the growth patterns, and investigate the relationships between the two populations. 1. a) In the absence of foxes, the rabbit population grows at a constant per capita rate. This can be expressed by the following differential equation: dR dt = C 1 R where the upward arrow indicates that this refers only to the increasing portion of growth rate. b) The population of rabbits declines at a rate proportional to the product RF. This seems reasonable because the growth rate of rabbits would decrease when there are more foxes, because more foxes eat more rabbits. The decrease in growth rate should also be dependent on the rabbit population, because when there are more rabbits, more rabbits are likely to die of natural causes. This equation can be expressed as follows: dR dt = C 2 RF
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