A general form for models of insect predator (P)–prey (N), or insect parasitism, is where f is a nonlinear function that incorporates assumptions about predators searching, and r > 0 is the rate of...

A general form for models of insect predator (P)–prey (N), or insect parasitism, is

where f is a nonlinear function that incorporates assumptions about predators searching, and r > 0 is the rate of increasing of the prey population. Furthermore, it is assumed that 0 <>

(a) Find conditions on r so that a positive equilibrium point
 exists.

(b) Determine under what conditions
 is asymptotically stable.