
7.3 A three-species predator – prey model (Edelstein-Keshet 1988) is
dx
dt
¼ axz þ bxy yx
dy
dt
¼ dy exy
dz
dt
¼ mz(n z) lxy
where
x is a predator
y and z are its prey
(a) Express the nontrivial equilibrium pt (x
e
, y
e
, z
e
) in terms of the system parameters.
(b) Use the ‘‘trim’’ function to find the equilibrium pt when the system parameters are
a ¼0.075, b ¼0.009, g ¼0.2, d ¼0.1, e ¼0.025, m ¼0.0015, n ¼10, and l ¼0.003.
Compare the answer with the value obtained using the result in part (a).
(c) The equilibrium point is asymptotically stable. Verify by simulating the response of the
autonomous system starting from various randomly selected points in