Chaotic time series Part I: Estimation of invariant properies in state space

Details Chaotic time series Part I: Estimation of invariant properies in state space Chaotic time series Part I: Estimation of invariant properies in state space

1994-01-14

arxiv.org/abs/chao-dyn/9401004v3

Nonlinear Sciences

Chaotic Dynamics

17 pages and 8 pages with figures all in uuencoded tar-compressed postscript format. Sent to

Scientific paper

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows for construction of more realistic and better models and thus improved predictive capabilities. This paper describes key features of chaotic systems including strange attractors and Lyapunov exponents. The emphasis is on state space reconstruction techniques that are used to estimate these properties, given scalar observations. Data generated from equations known to display chaotic behaviour are used for illustration. A compilation of applications to real data from widely different fields is given. If chaos is found to be present, one may proceed to build non-linear models, which is the topic of the second paper in this series.

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