Question

Consider the system
dx/dt= 2x(1 − x/3) − xy
dy/dt= −2y + 3xy
(a) What might this be a model of?
(b) Find all equilibrium points.
(c) From the differential equations determine (for x > 0, y > 0) where x and y are
decreasing and where they are increasing. (The curves where dx/dt = 0 and
where dy/dt = 0 are called nullclines.)