Table of Contents
Journal of Complex Systems
Volume 2015 (2015), Article ID 932750, 12 pages
http://dx.doi.org/10.1155/2015/932750
Research Article

Use of False Nearest Neighbours for Selecting Variables and Embedding Parameters for State Space Reconstruction

Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská Cesta 9, 842 19 Bratislava, Slovakia

Received 18 September 2014; Revised 5 January 2015; Accepted 24 February 2015

Academic Editor: Yang Tang

Copyright © 2015 Anna Krakovská et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

If data are generated by a system with a d-dimensional attractor, then Takens’ theorem guarantees that reconstruction that is diffeomorphic to the original attractor can be built from the single time series in -dimensional phase space. However, under certain conditions, reconstruction is possible even in a space of smaller dimension. This topic is very important because the size of the reconstruction space relates to the effectiveness of the whole subsequent analysis. In this paper, the false nearest neighbour (FNN) methods are revisited to estimate the optimum embedding parameters and the most appropriate observables for state space reconstruction. A modification of the false nearest neighbour method is introduced. The findings contribute to evidence that the length of the embedding time window (TW) is more important than the reconstruction delay time and the embedding dimension (ED) separately. Moreover, if several time series of the same system are observed, the choice of the one that is used for the reconstruction could also be critical. The results are demonstrated on two chaotic benchmark systems.