- #1

- 80

- 0

_{k+1}=f(x

_{k}), oscillation can occur; for example, the function x

_{k+1}=x

_{n}

^{2}-1 experiences oscillation under the starting value 0:

(x

_{2}=x

_{1}

^{2}-1=x

_{2}=0

^{2}-1→x

_{2}=-1→x

_{3}=x

_{2}

^{2}-1=x

_{3}=-1

^{2}-1→x

_{3}=0)

This type of oscillation must be capable of detection before actually pluggin in the numbers. How can you figure out that a dynamic model will oscillate in such a way?