Deep in the redwood forest of California, dusky-footed wood rats provide up to 80% of the diet for the spotted owl, the main predator of the wood rat, which is being modelled using the following...

Deep in the redwood forest of California, dusky-footed wood rats provide up to 80% of the
diet for the spotted owl, the main predator of the wood rat, which is being modelled using
the following discrete dynamical system. Denote the owl and wood rat populations at time
k by xk = [
Ok
Rk
], where k is the time in months.

Ok+1 = 0.5Ok + 0.4Rk
Rk+1 = −0.104Ok + 1.1Rk
Determine the evolution of this system after 5 years. Discuss the evolution of system
after large time has been passed.