Reconstruction of time-delayed feedback systems from time series

For various classes of time-delay systems we propose the methods of their model delay-differential equation reconstruction from time series. The methods are based on the characteristic location of extrema in the time series of time-delay systems and the projection of infinite-dimensional phase space of these systems to suitably chosen low-dimensional subspaces. We verify our methods by using them for the recovery of time-delay differential equations from their chaotic solutions and for modelling experimental systems with delay-induced dynamics from their chaotic time series. (c) 2005 Elsevier B.V. All rights reserved.