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“Chaotic time series. Part I. Estimation of some invariant properties in state-space”

Authors: Dimitris Kugiumtzis, Bjørn Lillekjendlie and Nils Christophersen,
Affiliation: University of Oslo and SINTEF
Reference: 1994, Vol 15, No 4, pp. 205-224.

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Keywords: Time series, non-linear systems, chaos, noise, reconstruction, dimension of attractor, Lyapunov exponents

Abstract: 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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DOI forward links to this article:
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BibTeX:
@article{MIC-1994-4-1,
  title={{Chaotic time series. Part I. Estimation of some invariant properties in state-space}},
  author={Kugiumtzis, Dimitris and Lillekjendlie, Bjørn and Christophersen, Nils},
  journal={Modeling, Identification and Control},
  volume={15},
  number={4},
  pages={205--224},
  year={1994},
  doi={10.4173/mic.1994.4.1},
  publisher={Norwegian Society of Automatic Control}
};

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