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