Unformatted text preview: x t on the vertical axis. A Fxed point occurs where f ( x t − 1 ) cuts the 45 ◦-line, as shown in Fgure 3.18, where we have three such Fxed points. Since f ( x ) = x 3 then y = f ( y ) and satisFes y = y 3 or y ( y 2 − 1) = 0. This results in three values for y , y = , − 1 and 1. It is to be noted that we have drawn x t = f ( x t − 1 ) as a continuous function, which we also assume to be differentiable. We have also established that x ∗ is an attractor, a stable point, if there exists a number ε such that when | x − x ∗ | < ε then x t approaches x ∗ in the limit, otherwise it is unstable. In the present illustration we can consider only local stability or Figure 3.18....
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- Fall '11
- Economics, Xt, Nonlinear Difference Equations