Persistent Chaos in High Dimensions
D. J. Albers, J. C.
and J. P. Crutchfield
Max Planck Institute for Mathematics in the Sciences, Leipzig 04103,
Center for Computational Science & Engineering and Physics
Department, University of California-Davis, )ne Shields Avenue, Davis,
California 95616, USA
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
Physics Department, University
of Wisconsin, 1150 University Avenue, Madison, WI
Received 19 April 2005; published 2 November 2006
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)
Return to Sprott's Books and Publications.