101 0.8- 0.61 0.4

[answerhappygod]

101 0 8 0 61 0 4 0 2 0 0 02 0 4 0 6 0 8 1 0 Figure 12 35 Graphs Of X Against X The 45 Line And Of The Logistic 1 (29.28 KiB) Viewed 28 times

101 0.8- 0.61 0.4 <! 0.2- 0- 0 02 0.4 0.6 0.8 1.0 Figure 12.35 Graphs of x against x (the 45° line) and of the logistic function f(x)=rx(1 - x) (the two curves) for two choices of r, one less than and one greater than 1. The fixed points of the logistic map lie at the intersections of the line with the curve. When r < I there is just one intersection, atx* = 0; when r> I there are two intersections, one still at x = 0 and the other at an x > 0. 12.23. Computer Consider the sine map :+1 = f(x) where f(x)=sin(x). The interesting behavior of this map is for 0<< 1 and 0 srs 1. so restrict your attention to these ranges. (a) Using a plot analogous to Figure 12.35, discuss the fixed points of this map Show that the map has either one or two fixed points, depending on the value ofr. Show that when is small there is just one fixed point, which is stable. (b) At what value ofr (callitre) does the second fixed point appear? Show that o is also the value ofr at which the first fixed point becomes unstable (c) Asr increases, the second fixed point eventually becomes unstable. Find numerically the value at which this occurs.