Another population model is one in which species compete for resources, such as a limited food supply. Such a model is given by

\[\begin{aligned} & x^{\prime}=a x-b x^{2}-c x y \\ & y^{\prime}=d y-e y^{2}-f x y \end{aligned}\]

In this case, assume that all constants are positive.

a. Describe the effects/purpose of each terms.

b. Find the fixed points of the model.

c. Linearize the system about each fixed point and determine the stability.

d. From the above, describe the types of solution behavior you might expect, in terms of the model.