Two-dimensional representation of a delayed dynamical system

A nonlinear system with delayed feedback, whenever the delay time is much longer than the intrinsic correlation time, displays two widely separated time scales. In such a case, a two-dimensional representation becomes appropriate, because it discloses features otherwise hidden in the one-dimensional sequence of data, and allows use of recognition algorithms developed for spatiotemporal chaos. As an illustration, chaotic time sequences from a single-mode laser with delayed feedback are analyzed using this representation.