A paradigm for optimal state-space reconstruction with nonuniform time delays is proposed. A comparison based on a diffeomorphic measure and a smoothness cost function shows that the proposed methodology achieves a better reconstruction compared to a reconstruction based on time delays that are multiples of the first minimum of mutual information. It is also shown how the proposed methodology is a more reliable approach to determining the embedding dimension.
Automated protocols have been developed to characterize time series data in terms of stability. These techniques are applied to the output power time series of an optically injected vertical cavity surface emitting laser (VCSEL) subject to varying injection strength and optical frequency detuning between master and slave lasers. Dynamic maps, generated from high resolution, computer controlled experiments, identify regions of dynamic instability in the parameter space.
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