Phase synchronization based on a Dual-Tree Complex Wavelet Transform

In this work, we show the applicability of our Discrete Complex Wavelet Approach (DCWA) to verify the phenomenon of phase synchronization transition in two coupled chaotic Lorenz systems. DCWA is based on the phase assignment from complex wavelet coefficients obtained by using a Dual-Tree Complex Wavelet Transform (DT-CWT). We analyzed two coupled chaotic Lorenz systems, aiming to detect the transition from non-phase synchronization to phase synchronization. In addition, we check how good is the method in detecting periods of 2 pi phase-slips. In all experiments, DCWA is compared with classical phase detection methods such as the ones based on arctangent and Hilbert transform showing a much better performance.