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Fractional Derivatives Applied to Phase-Space Reconstructions

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Abstract

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, U.S.A.

    B. F. Feeny

  2. Department of Electrical and Computer Engineering, University of Maryland, University Park, MD, 20472, U.S.A.

    G. Lin

Authors
  1. B. F. Feeny
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  2. G. Lin
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Correspondence to B. F. Feeny.

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Feeny, B., Lin, G. Fractional Derivatives Applied to Phase-Space Reconstructions. Nonlinear Dyn 38, 85–99 (2004). https://doi.org/10.1007/s11071-004-3748-6

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  • DOI: https://doi.org/10.1007/s11071-004-3748-6

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