Suppose that individuals of type b reduce the per capita type a growth rate by half as much as individuals of type a, and that individuals of type a reduce the per capita type b growth rate by half as much as individuals of type b. The equations are (There should be four equilibria.)In our model of competition, the per

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

(There should be four equilibria.)
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.