Reconstruction of time-delay systems from chaotic time series

Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 2):056216. doi: 10.1103/PhysRevE.64.056216. Epub 2001 Oct 22.

Abstract

We propose a method that allows one to estimate the parameters of model scalar time-delay differential equations from time series. The method is based on a statistical analysis of time intervals between extrema in the time series. We verify our method by using it for the reconstruction of time-delay differential equations from their chaotic solutions and for modeling experimental systems with delay-induced dynamics from their chaotic time series.