how is the logistic function characterized by the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

df(x)/dx = f(x)(1-f(x))

[with solution f(x)=1/(1+e^{-x}), but this is irrelevant to the question]

the continuous version of the logistic map, given by the recursive function:

x_{n+1}= x_{n}(1-x_{n})?

It would seem to me that, in order for the limit of the latter, as n goes to zero, to go to the former, you would need the latter to look like this:

x_{n+1}-x_{n}= x_{n}(1-x_{n})

A second question: usually the logistic map is given by

x_{n+1}= r.x_{n}(1-x_{n}) for some real r.

when taking the continuous version, does the r survive as

df(x)/dx = r.f(x)(1-f(x))?

Thanks.

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# Recursive logistic map vs continuous logistic function

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