Critical Research: Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rössler System

The State Space Reconstruction that integrates a non-linear time series is the first and important step in characterising and predicting the behaviour of a complex system in scientific research. This includes the selection of the necessary time delay T and embedded dimension dE values. Three methods are implemented and explored by the Rössler attractor equations set on nonlinear time series: the Cao method, the C-C method developed by Kim et al., and the C-C-1 method developed by Cai et al. A way is provided to fix a parameter that is needed to enforce the last process. Small size and/or noisy time series have been put into view. By using a metric based on the smoothness of the transformation, the reconstruction quality is measured. This paper offers an overview of embedding parameter methods for optimal selection applied by chaotic time series to the Rössler strange attractor reconstruction.

Author(s) Details

Olivier Delage
Department of Physics, The University of La Reunion, Saint Denis, France.

Alain Bourdier
Department of Physics and Astronomy, The University of New Mexico, Albuquerque, NM, USA.

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