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MiS Preprint

Persistent chaos in high dimensions

J. Crutchfield, David Albers and J. Sprott


n 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 in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.

MSC Codes:
37-XX, 34-XX
05., 87.18.Sn, 95.10.Fh
higd-dimensional dynamics, stability conjecture, highientropy

Related publications

2006 Repository Open Access
David J. Albers, J. C. Sprott and James P. Crutchfield

Persistent chaos in high dimensions

In: Physical review / E, 74 (2006) 5, p. 057201