Author(s)

Olivier Delage¹, Alain Bourdier²

¹Department of Physics, The University of La Reunion, Saint Denis, France.
²Department of Physics and Astronomy, The University of New Mexico, Albuquerque, NM, USA.

Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension d_E. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.

Phase Space Reconstruction, Embedding Window, Rössler System, Time Series, Correlation Integral, Delay Time

Delage, O. and Bourdier, A. (2017) Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rössler System. Journal of Modern Physics, 8, 1607-1632. doi: 10.4236/jmp.2017.89096.