6. Knowing the time series comes from the logistic map xn+1 =
s*xn*(1 - xn), the parameter is easy to find:
s = xn+1/xn*(1 - xn). From the
first two terms we find s = .960/.429*(1 - .429) = 3.92. From the
15th and 16th entries, for example, we find s = .333/.906*(1 - .906) =
3.91. (Some errors are to be expected, since we are rounding the time series
to three digits.)
Since the fourth entry of the time series is 0.500, we know the next entry is s/4.
(Recall for the logistic map if xn = 1/2, then xn+1 = s/4.)
Consequently, s/4 = 0.98 and so s = 3.92.
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