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Comparison of algorithms calculating optimal embedding parameters for delay time coordinates

1992; Elsevier BV; Volume: 58; Issue: 1-4 Linguagem: Inglês

10.1016/0167-2789(92)90104-u

1872-8022

Thorsten M. Buzug, G. Pfister,

Plant and Biological Electrophysiology Studies

The success of noise reduction processes and forecasting methods as well as accurate calculations of fractal dimensions and Lyapunov exponents from scalar time series depends strongly on the quality of the reconstructed phase space. We present a comparison of four methods, which simultaneously estimate the two embedding parameters (delay time τ and sufficiently large embedding dimension dimE) for Takens' delay time coordinates. Recently we introduced a global geometrical measure, the fill-factor, and a local dynamical measure, the averaged integral local deformation. We will discuss these methods briefly and compare them to the topological wavering-product. In addition a simple algorithm is presented, which observes the spreading of trajectories at the transition from dimE to dimE + 1 and gives the opportunity to estimate the correlation entropy K2. We applied these algorithms to experimental data series measured from a rotational Taylor-Couette experiment and verified the quality of the obtained embedding parameters by the estimation of correlation dimensions for different reconstructed attractors.