IDENTIFYING AND MODELING DELAY FEEDBACK-SYSTEMS

Systems with delayed feedback can possess chaotic attractors with extr emely high dimension, even if only a few physical degrees of freedom a re involved. We propose a state space reconstruction from time series data of a scalar observable, along with a novel method to identify and model such systems, if a single variable is fed back. Making use of s pecial properties of the feedback structure, we can understand the str ucture of the system by constructing equivalent equations of motion in spaces with dimensions which can be much smaller than the dimension o f the chaotic attractor. We verify our method using both numerical and experimental data.