The statistics of simulating chaos

Diamond, Phil and Pokrovskii, Alexei (2001) The statistics of simulating chaos. Statistics and Computing, 11 3: 217-228. doi:10.1023/A:1016648220222

Author Diamond, Phil
Pokrovskii, Alexei
Title The statistics of simulating chaos
Journal name Statistics and Computing   Check publisher's open access policy
ISSN 0960-3174
Publication date 2001-07
Sub-type Article (original research)
DOI 10.1023/A:1016648220222
Volume 11
Issue 3
Start page 217
End page 228
Total pages 12
Editor D. J. Hand
Place of publication The Netherlands
Publisher Kluwer Academic Publishers
Collection year 2001
Language eng
Subject C1
780101 Mathematical sciences
230119 Systems Theory and Control
Formatted abstract
When simulating a dynamical system, the computation is actually of a spatially discretized system, because finite machine arithmetic replaces continuum state space. For chaotic dynamical systems, the discretized simulations often have collapsing effects, to a fixed point or to short cycles. Statistical properties of these phenomena can be modelled with random mappings with an absorbing centre. The model gives results which are very much in line with computational experiments. The effects are discussed with special reference to the family of mappings f (x)=1-|1-2x| ,x [0,1],1,<> ,<> . Computer experiments show close agreement with predictions of the model.
Keyword Computer Science, Theory & Methods
Statistics & Probability
Statistical Properties
Random Mappings
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Created: Tue, 14 Aug 2007, 14:53:32 EST