B - Description of the experimental data sets
Published online by Cambridge University Press: 06 July 2010
Summary
Throughout the text we have tried to illustrate all relevant issues by the help of experimental data sets, some of them appearing in several different contexts. In order to avoid repeats and to concentrate on the actual topic we did not describe the data and the systems they come from in any detail in the examples given in the text. This leeway we want to make up in this appendix, together with a list of all places where each set is referred to.
Lorenz-like chaos in an NH3 laser
This data set was created at the PTB Braunschweig in Germany in an experiment run by U. Hübner, N. B. Abraham, C. O. Weiss and collaborators (1993). Within the time series competition organised in 1992 by N. A. Gershenfeld and A. Weigend at the Santa Fe Institute it served as one of the sample series and is available on the SFI server by anonymous FTP to sfi.santafe.edu.
A paradigmatic mathematical model for low dimensional chaos is the Lorenz system, Lorenz (1969), describing the convective motion of a fluid heated from below in a Rayleigh–Benard cell. Haken (1975) showed that under certain conditions a laser can be described by exactly the same equations, only the variables and constants have different physical meaning. The experiment in Braunschweig was designed to fulfil the conditions of being describable by the Lorenz–Haken equations as closely as possible.
The time series is a record of the output power of the laser, consisting of 10 000 data items. Part of it is shown in Fig. B.1. Similarly to the Lorenz model, the system exhibits regular oscillations with slowly increasing amplitude.
- Type
- Chapter
- Information
- Nonlinear Time Series Analysis , pp. 338 - 349Publisher: Cambridge University PressPrint publication year: 2003