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Fractional derivative reconstruction of forced oscillators |
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| Authors: | G Lin B F Feeny T Das |
| Institution: | (1) Department of Electrical and Computer Engineering, University of Maryland, University Park, MD 20742, USA;(2) Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA |
| Abstract: | Fractional derivatives are applied in the reconstruction from a single observable of the dynamics of a Duffing oscillator and a two-well experiment. The fractional derivatives of time series data are obtained in the frequency domain. The derivative fraction is evaluated using the average mutual information between the observable and its fractional derivative. The ability of this reconstruction method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and fractal dimensions. The reconstruction is compared to the true phase space and the delay reconstruction in order to assess the reconstruction parameters and the quality of results. |
| Keywords: | Phase-space reconstructions Fractional derivatives Fractional calculus Chaos Embeddings |
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