Joint time-frequency analysis of synchronized chaos

Joint time-frequency analysis (JTFA) which expands signal in both time and frequency domain is widely used to study non-stationary time series. In this paper, a generalized JTFA is proposed to study the synchronization of chaos. A similarity function constructed from generalized time-frequency spectra was used to reveal phase portrait of synchronized chaos. This scheme is applied to analyze the experimental data sets of unsynchronized, phase-squeezed and synchronized chaos from a recent experiment with microchip solid-state laser array. When synchronized chaos established, a mirror symmetry appeared in the portrait together with power law distribution self-similar structure. Similar power law scaling is also found numerically for the Lorenz model.