Unformatted text preview: < f < 1. Use parametric xy plots to ﬁnd where period doubling transitions occur.] What happens to the solutions when n = 1? Brieﬂy explain. (b) The case of n = 3 is particularly interesting. Repeat part (a) for this case and show that period doubling ﬁrst occurs near f = 0 . 69 and that the solution appears to become chaotic near f = 0 . 80. Be careful to make sure that the initial transients have died out; this can be a little tricky as the value of f is increased. Investigate what happens as f is increased from 0.80 to 0.90 and show that the xy orbits become less complex at some point. What happens as f is increase above 0.9? Do the solutions go through another period doubling sequence?...
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 Fall '09
 brewer
 Chemistry, Chemical Engineering, Santa Barbara, different values, Department of Chemical Engineering, David Pine, parametric xy plots

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