0 believing that everything that happens must happen as it does and could not have happened any other way, or relating to this belief:
More important than the first-order approximation are the random fluctuations around the deterministic trajectory of the delay equation.
If this is fixed then the automaton is a fixed structure deterministic or a fixed structure stochastic automaton.
Unlike the smooth expanding maps treated just above, such maps are in general not structurally or measure-theoretically stable with respect to deterministic perturbations.
However, it seems intuitively plausible to suggest that our ex hypothesi deterministic universe is not close to any of these.
To clarify the distinction between the two types of system, let us first define deterministic and stochastic systems.
The / rules are deterministic modulo the choice of fresh variables.
It is useful to recall the dynamic efficiency result for the deterministic model first.
The system may, however, be intractable as a deterministic system in the practical sense, because it contains too many degrees of freedom.
