Synchronization of chaotic oscillators with type-I intermittency

We study phase synchronization effects of chaotic oscillators with type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown. The mechanism of synchronization is explained. It is demonstrated that the considered synchronization can be described using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization. Synchronization of chaotic oscillations is a fundamental phenomenon observed in nature and science. Three main types of synchronization have been studied, namely, complete (or full) synchronization, generalized synchronization, and phase synchronization (for a review about chaotic synchronization). Complete synchronization of identical systems occurs when the states of coupled systems coincide. Generalized synchronization implies that the output of one system is associated with a given function of the output of the other system. Chaotic phase synchronization (CPS) is very similar to the synchronization of periodic oscillations and is manifested in the coincidence of characteristic time scales of coupled systems. Till now CPS has been observed for rather phase coherent chaotic attractors that occur after the cascade of period doubling bifurcations. However there are several other routes to chaos and observation of synchronization of corresponding chaotic attractors is still absent.