- #1

nomadreid

Gold Member

- 1,497

- 155

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.