4. Let a represent the prey and y represent the predators. Then the system of difference equations is

x t+1 =xt (1-xt/K) -xtYt,

Yt+1 = XtYt + byt,

where K and b are constants, K>0, and 0 < b < 1.

(a) Find the equilibria to this predator-prey system.

(b) Assess under what conditions there is convergence to each equilibrium.