Estimation of delay times from a delayed optical feedback laser experiment

Abstract

We estimate delay times from high-dimensional chaotic time series experimentally obtained from a fast optical time-delayed feedback system. The experiment consists of a semi- conductor laser, where the instabilities are induced by an external T-shaped cavity introducing two delay times into the laser. The delay times are determined by a lling factor analysis and found to give a better estimate than those obtained by autocorrelation functions. Finally, the possibility of this method for the reconstruction of the system's dierential equations is discussed. The characterization of nonlinear dynamical behavior and the identication of the underly- ing deterministic time-evolution laws from experimental time series has turned out to be one of the key problems in the study of nonlinear dynamical systems. For dynamical systems with a low number of degrees of freedom, embedding techniques (1) have been exceptionally successful for the computation of chaotic indicators (dimensions, Lyapunov exponents, entropies), and for the modelling of these systems (for an overview see, e.g. (2)). However, severe problems arise for systems which exhibit a number of dynamical degrees of freedom distinctly larger than N 5. A prominent class of dynamical systems that can have a large number of dynamical degrees of freedom are nonlinear systems with a time-delayed feedback. The study of such systems with time-delayed feedback were initiated by Ikeda et al. (3). The Ikeda scenario turned out to be a paradigm for the dynamical behavior of delayed-feedback systems under the variation of control parameters. The key features of the Ikeda scenario are the occurrence of multistability of periodic or chaotic attractors and the onset of high-dimensional deterministic chaos via attractor merging. Recently, a semiconductor laser system has been