Recovery of parameters of delayed-feedback systems from chaotic time series

摘要

Methods for reconstructing a delay differential equation from the time series of an observable quantity are proposed for various classes of time-delay systems. The methods rely on knowledge of the distributions of extrema of the time series of observed oscillations and projection of the infinite-dimensional phase spaces of time-delay systems onto special low-dimensional subspaces. The effectiveness of the proposed methods is demonstrated by reconstructing delay differential equations from their chaotic solutions, including those corrupted by noise, and by constructing models of real time-delay systems from chaotic time series. (C) 2005 Pleiades Publishing, Inc.