Fractional Derivatives Applied to Phase-Space Reconstructions |
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| Authors: | B F Feeny and G Lin |
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| Institution: | (1) Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, U.S.A.;(2) Department of Electrical and Computer Engineering, University of Maryland, University Park, MD, 20472, U.S.A. |
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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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| Keywords: | chaos embeddings fractional derivatives phase-space reconstructions |
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