a. A model due to Beddington and May for the competitive behavior of whales and krill (a small type of shrimp) is
x' = x(1 - x) - xy
y' = y(1 - y/x).
Here y is the population of whales. The carrying capacity for the whale population is not constant; rather, it is given by x and therefore depends on the krill population. Find the equilibrium points for this system.
b. Determine the types of the equilibria for the system above.
c. Use nullclines and the computer to paint the picture of the phase plane for this system.