- #1
nomadreid
Gold Member
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how is the logistic function characterized by the differential equation
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:
xn+1 = xn(1-xn)?
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:
xn+1-xn = xn(1-xn)
A second question: usually the logistic map is given by
xn+1 = r.xn(1-xn) for some real r.
when taking the continuous version, does the r survive as
df(x)/dx = r.f(x)(1-f(x))?
Thanks.
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:
xn+1 = xn(1-xn)?
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:
xn+1-xn = xn(1-xn)
A second question: usually the logistic map is given by
xn+1 = r.xn(1-xn) for some real r.
when taking the continuous version, does the r survive as
df(x)/dx = r.f(x)(1-f(x))?
Thanks.