
rate of new predators entering the environment at time ‘‘t,’’ and a, b, c, l, and k are parameters
of the system.
(a) Find the nontr ivial equilibrium points (
x, y) in the x, y plane when the two inputs are
u
x
¼ u
x
¼ 0, u
y
¼ u
y
¼ 0, t 0. Leave your answers for x and y in terms of the system
parameters.
(b) Introduce deviation variables D x, Dy, Du
x
, and Du
y
and choose the outputs as Dy
1
¼Dx
and Dy
2
¼Dy. Linearize the state equations about the operating point where x ¼ x, y ¼ y ,
u
x
¼ u
x
, and u
y
¼ u
y
and find the linearized system matrices A, B, C, and D in terms of the
system parameters.
(c) Find the transfer functions Dx(s)=Du
x
(s), Dx(s)=Du
y
(s), Dy(s)=Du
x
(