Persistent Chaos in High Dimensions

Details Persistent Chaos in High Dimensions Persistent Chaos in High Dimensions

2005-04-19

arxiv.org/abs/nlin/0504040v2

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures; Changes in response to referee comments

Scientific paper

10.1103/PhysRevE.74.057201

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 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.

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