Suppose that individuals of type b reduce the per capita growth rate of type a by half as much as individuals of type a, and that individuals of type a reduce the per capita type b growth rate by twice as much as individuals of type b. The equations are

In our model of competition, the per capita growth rate of types a and b are functions only of the total population size. This means that reproduction is reduced just as much by an individual of type a as by an individual of type b. In many systems, each type interferes differently with type a than with type b. Check that the given set of equations matches the assumptions in each of the following cases, and find and graph the equilibria and nullclines.

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da dt 100) a +b/2 a b 1000 db b.