Continuous wavelet transform in the analysis of burst synchronization in a coupled laser system.

The transition to synchronization of a pair of coupled chaotic CO2 lasers is investigated numerically in a model system. This system displays episodes of bursting of different predominant frequencies. Due to the multiple time scales present in this system, we use a complex continuous wavelet transform to perform the synchronization analysis. Thus it enables us to resolve the time of occurrence as well as the frequency of an event in a given time series up to an intrinsic uncertainty. Furthermore, due to the complex nature of that wavelet transform, it yields a direct estimate of the system's phase. We show that, as the coupling strength of the laser system is increased, the mutual coherency increases differently for different frequencies. Additionally we test our method with experimental data.