Mathematics, 14.01.2020 22:31 delanorpalmer24
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).
Answers: 1
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Dispersal in exercise 8.5.9 we modeled the dispersal of dragonflies using the recursion xt1+1 =axt,...
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