Differential equations sometimes occur in systems consisting of two or more interlinked differential equations. A classical example is a simple model of the populations of competing species. This is a simple model of competing species labeled P (the prey)and W (the predators) given by the following equations:
The first equation dictates the growth of the prey species P, which, without any predators, would be exponential growth. The second equation dictates the growth of the predator species W, which, without any prey, would be exponential decay. Of course, these two equations are coupled; each population change depends on both populations. The predators consume the prey at a rate proportional to the product of their two populations, and the predators grow at a rate proportional to the relative abundance of prey (again the product of the two populations).
In this recipe, we will will analyze...