Detecting Optimal Delay Time for Chaotic Time Series Data

Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. Embedding techniques for reconstructing the phase space of chaotic time series from experimental data are important. To reconstruct an embedded attractor in the phase space from a time series, finding an optimal delay time which is used to build to delay space is a key ingredient for the analysis of chaotic time series. In present article, using time series from chaotic dynamical systems, we present a novel method for finding an optimal delay time for the delay coordinate systems. We present that chaotic attractors may be classified by the number of holes in their shape in the topological point of view and the delay time may be expressed by the number of holes and an average return time.