Fractal Dimension for Poincaré Recurrences as an Indicator of Synchronized Chaotic Regimes

The studies of the phenomenon of chaos synchronization are usually based upon the analysis of the existence of transversely stable invariant manifold that contains an invariant set of trajectories corresponding to synchronous motions. In this paper we develop a new approach that relies on the notions of topological synchronization and the dimension for Poincaré recurrences. We show that the dimension of Poincaré recurrences may serve as an indicator for the onset of synchronized chaotic oscillations. This indicator is capable of detecting the regimes of chaos synchronization characterized by the frequency ratio p : q.