Assignment 9/12:  due Friday 9/13 at 3PM

Turn in individual solutions. You may work together in solving the problems, or get help from others, but the final write-up should be your own. Do not turn in anything you cannot explain completely.

Calculus p150  #15, 18
                p 164 #25, 26, 27, 29c, 30, 31
                p 173 #15, 17, 19, 29

Chaos Under Control p395 #5.4

1.  Using the website Bifurcation Diagram Applet, magnify the bifurcation diagram for the sine
     map in the range 2.9464<s<2.9784 and 0.1522<x<0.2013 and compare this with the
    bifurcation diagram for the logistic map in the range 3.8284<s<3.8570 and 0.1310<x<0.1755.  
    Find several analogous locations in the bifurcation diagrams of the logistic and sine maps, and 
    compare the magnifications.  Record your observations and any conclusions.  

2.  Using the website Bifurcation Diagram Applet, compute the Feigenbaum quotients for the logistic map
    in this way:  Denote by s₁ the s-value where the stable fixed point curve in the bifurcation diagram
    intersects the line x=1/2, by s₂ the s-value where a branch of the stable 2-cycle curves intersects the
    the line x=1/2, and so on for s₃ (4-cycle), s₄ (8-cycle), and s₅ (16-cycle).  Now compute the
    quotients (s₂ -s₁ )/(s₃ -s₂ ), (s₃ -s₂ )/(s₄ -s₃ ), and (s₄ -s₃ )/(s₅ -s₄ ).  What pattern do you see?
    Repeat this for the bifurcation diagram of the sine function.