3 research outputs found
Local dimension and finite time prediction in spatiotemporal chaotic systems
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett.
81 5878 (2001)] provides a direct relationship between dimension and
predictability in spatiotemporal chaotic systems. Regions of low dimension are
identified as having high predictability and vice-versa. This conclusion is
reached by using methods from dynamical systems theory and Bayesian modelling.
We emphasize in this work the consequences for short time forecasting and
examine the relevance for factor analysis. Although we concentrate on coupled
map lattices and coupled nonlinear oscillators for convenience, any other
spatially distributed system could be used instead, such as turbulent fluid
flows.Comment: 5 pagers, 7 EPS figure
Detecting Determinism in High Dimensional Chaotic Systems
A method based upon the statistical evaluation of the differentiability of
the measure along the trajectory is used to identify in high dimensional
systems. The results show that the method is suitable for discriminating
stochastic from deterministic systems even if the dimension of the latter is as
high as 13. The method is shown to succeed in identifying determinism in
electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E
(25 apr 2001
Using Topological Statistics to Detect Determinism in Time Series
Statistical differentiability of the measure along the reconstructed
trajectory is a good candidate to quantify determinism in time series. The
procedure is based upon a formula that explicitly shows the sensitivity of the
measure to stochasticity. Numerical results for partially surrogated time
series and series derived from several stochastic models, illustrate the
usefulness of the method proposed here. The method is shown to work also for
high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review