Persistent Chaos in High Dimensions

D. J. Albers, J. C. Sprott, and J. P. Crutchfield

Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany
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 53706, USA

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)

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