Influence of chaotic synchronization on mixing in the phase space of interacting systems.

Using the concept of the relative metric entropy, we study the influence of the synchronization phenomenon on mixing rate in the phase space of deterministic and noisy chaotic systems. We show that transition to both complete and phase synchronization of chaos is accompanied by the decrease of the level of mixing induced by internal nonlinear mechanisms of interacting systems as well as by external noise influence. Therefore, the decrease of the mixing rate in the phase space of interacting systems may indicate transition to synchronization. The obtained results are important for time series analysis in various types of real noisy systems (e.g., biological, social, and financial systems).