A high dimensional delay selection for the reconstruction of proper phase space with cross auto-correlation

Journal Article (Journal Article)

For the purpose of phase space reconstruction from nonlinear time series, delay selection is one of the most vital criteria. This is normally done by using a general measure viz., mutual information (MI). However, in that case, the delay selection is limited to the estimation of a single delay using MI between two variables only. The corresponding reconstructed phase space is also not satisfactory. To overcome the situation, a high-dimensional estimator of the MI is used; it selects more than one delay between more than two variables. The quality of the reconstructed phase space is tested by shape distortion parameter (SD), it is found that even this multi-dimensional MI sometimes fails to produce a less distorted phase space. In this paper, an alternative nonlinear measure-cross auto-correlation (CAC) is introduced. A comparative study is made between the reconstructed phase spaces of a known three dimensional Neuro-dynamical model, Lorenz dynamical model and a three dimensional food-web model under MI for two and higher dimensions and also under cross auto-correlation separately. It is found that the least distorted phase space is obtained only under the notion of cross auto-correlation. © 2013 Elsevier B.V.

Full Text

Duke Authors

Cited Authors

  • Palit, SK; Mukherjee, S; Bhattacharya, DK

Published Date

  • August 3, 2013

Published In

Volume / Issue

  • 113 /

Start / End Page

  • 49 - 57

Electronic International Standard Serial Number (EISSN)

  • 1872-8286

International Standard Serial Number (ISSN)

  • 0925-2312

Digital Object Identifier (DOI)

  • 10.1016/j.neucom.2013.01.034

Citation Source

  • Scopus