Fractional derivatives are applied in the reconstruction of the phase space of dynamical systems with a single observable. The fractional derivatives of time series data are obtained in the frequency domain. The method is applied to a Duffing oscillator, the Lorenz system, and data from a two-well experiment. 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 method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.

This content is only available via PDF.
You do not currently have access to this content.