Dispersal In Exercise 8.5.9 we modeled the dispersal of dragonflies using the recursion
Chapter 8, Problem 36(choose chapter or problem)
Dispersal In Exercise 8.5.9 we modeled the dispersal of dragonflies using the recursion xt11 Axt, where A c 0.8 0.3 0.2 0.7d (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 c 1 1 d, express the solu tion 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).
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