Oscillations, Waves, and Interactions - GWDG

426 U. Parlitz
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Figure 17. Experimental synchronisation of chaotic intensity fluctuations of two unidirectionally
coupled semiconductor lasers. The lower trace (red) shows the irregular power
drop outs of the drive laser and the upper trace (blue) the emitted light of the response
laser [73].
5.3 Coupled semiconductor lasers with external cavities
As an example for (almost) identical synchronisation we show here two optically
coupled semiconductor lasers. Each laser possesses an external resonator and the
coupling is unidirectional due to an optical diode (Faraday isolator). Figure 17 show
intensities of both lasers fluctuating in synchrony [19,72,73], a phenomenon we studied
at the DPI with Volker Ahlers and Immo Wedekind.
5.4 Generalised synchronisation and parameter estimation
If the coupled systems are different from each other more sophisticated types of
(generalised) synchronisation of chaotic dynamics may occur where asymptotically
for t → ∞ a function H exists that maps states of the driving system to those of the
driven system [68,74–77].
An application of synchronisation of uni-directionally coupled systems, where generalised
synchronisation plays an important role, is model validation and parameter
estimation. Here, a measured time series drives a computer model and if the model is
sufficiently accurate and all its parameters possess the right values one may achieve
synchronisation between the computer model and the data. In this way, it is possible
to recover those physical variables that have not been measured, as well as unknown
parameters of the system. This is done by changing the parameters of the model
until the (average) synchronisation error is minimized where generalised synchronisation
is required to obtain a well defined (and smooth) error landscape. A practical
example for this approach may be found in Ref. [78], where the parameters of a
chaotic electronic circuit have been recovered, and improved methods are presented
in Ref. [79].