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## Main Question or Discussion Point

For a general family of dynamic models, x

(x

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?

_{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?