Dispersal in exercise 8.5.9 we modeled the dispersal of dragonflies using the recursion xt1+1 =axt, where
a=
[0.8 0.3
0.2 0.7]
(a) verify that the perron-frobenius theorem can be applied to this model.
(b) calculate the eigenvalues of a.
(c) given your answers to parts (a) and (b), what is the
long-term behavior of xt?
(d) using the initial condition x0 =
[1
1], express the solution to the recursion in terms of the eigenvectors and eigenvalues of a.
(e) verify your answer to part (c) using the solution you obtained in part (d).