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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