Consider a predator–prey model in which predators search over a constant area and have unlimited capacity for consuming the prey: where  is the size of the prey population, and P(t) is the size of the...

Consider a predator–prey model in which predators search over a constant area and have unlimited capacity for consuming the prey:

where
 is the size of the prey population, and P(t) is the size of the predator population at time period t.

(a) Find the positive equilibrium point

(b) Determine the local stability of
using linearization.