Reconstruction of systems with delayed feedback: II. Application

We apply a recently proposed method for the analysis of time series from sy stems with delayed feedback to experimental data generated by a CO2 laser. The method allows estimating the delay time with an error of the order of t he sampling interval, while an approach based on the peaks of either the au tocorrelation function, or the time delayed mutual information would yield systematically larger values. We reconstruct rather accurately the equation s of motion and, in turn, estimate the Lyapunov spectrum even for high dime nsional attractors. By comparing models constructed for different "embeddin g dimensions" with the original data, we are able to find the minimal faith ful model. For short delays, the results of our procedure have been cross-c hecked using a conventional Takens time-delay embedding. For large delays, the standard analysis is inapplicable since the dynamics becomes hyperchaot ic. In such a regime we provide the first experimental evidence that the Ly apunov spectrum, rescaled according to the delay time, is independent of th e delay time itself. This is in full analogy with the independence of the s ystem size found in spatially extended systems.