I have found Logistic Map
http://mathworld.wolfram.com/LogisticMap.html
Here the system has very different outcomes depending from initial
conditions (now I understand your use of statistics). Yet, each
trajectory is deterministic.
Hence, this was not my question. Sorry for being unclear. Bifurcations
in Logistic Map is a result of uncertainty in initial conditions. I was
thinking more in terms of Transient Equation of Everything. Does it
allow for multiple solutions at some times or not?
In this case, Wolfram seems to support determinism:
http://www.stephenwolfram.com/publications/recent/ultimateknowledge/
"It looks probabilistic because there is a lot of complicated stuff
going on that we’re not seeing–notably in the very structure and
connectivity of space and time."
"But really it’s all completely deterministic."
«That somehow knowing the laws of the universe would tell us how humans
would act–and give us a way to compute and predict human behavior.»
«Of course, to many people this always seemed implausible–because we
feel that we have some form of free will.»
«And now, with computational irreducibility, we can see how this can
still be consistent with deterministic underlying laws.»
Evgenii
On 25.03.2012 06:23 Stephen P. King said the following:
Hi Evgenii,
You might also find Stephen Wolfram's work with cellular automate
replete with examples of bifurcations and symmetry breaking. My thought
was considering how to construct models of the behavior of bifurcating
and symmetry breaking systems. I was thinking in second-order terms, as
it where... Thus the use of statistics...
Onward!
Stephen
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