An extensive statistical survey of
universal approximators shows that as the dimension of a typical
dissipative dynamical system is increased, the number of positive
Lyapunov exponents increases monotonically and the number of parameter
windows with periodic behavior decreases. A subset of parameter space
remains where noncatastrophic topological change induced by a small
parameter variation becomes inevitable. A geometric mechanism depending
on dimension and an associated conjecture depict why topological change
is expected but not catastrophic, thus providing an explanation of how
and why deterministic chaos persists in high dimensions.
Ref: D. J. Albers,
J. C. Sprott, and J. P.
Crutchfield, Physical Review E
74,
057201-1 - 057201-4 (2006)