With ,
the logistic map becomes
|
(1)
|
The first 50 iterations of this map are illustrated above for initial values and 0.4.
The solution can be written in the form
|
(2)
|
with
and
its inverse function (Wolfram 2002, p. 1098). Explicitly,
this then gives the formula
|
(5)
|
has the Maclaurin
series
(OEIS A059944).
See also
Logistic Map,
Logistic
Map--r=2,
Logistic Map--r=2
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References
MathPages. "Closed Forms for the Logistic Map." http://www.mathpages.com/home/kmath188.htm.Sloane,
N. J. A. Sequence A059944 in "The
On-Line Encyclopedia of Integer Sequences."Wolfram, S. A
New Kind of Science. Champaign, IL: Wolfram Media, p. 1098,
2002.
Cite this as:
Weisstein, Eric W. "Logistic Map--r=-2."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogisticMapR=-2.html
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