Influence of noise on the behavior of oscillators near the synchronization boundary

Nonautonomous behavior of oscillators in the presence of noise is considered. The influence of noise on the dynamics of local zero Lyapunov exponents for nonautonomous dynamic systems that are near the synchronization boundary is considered. It is shown that the action of noise on a nonautonomous dynamic system that is near the synchronization boundary produces domains of synchronous motion in the series realization, which alternate with asynchronous domains. In accordance with this, the distribution of local zero Lyapunov exponents corresponding to laminar phases shift toward negative values. This effect is demonstrated with a discrete-time system (map of a circle onto itself) that is a reference model to describe the synchronization phenomenon and also with a reference system exhibiting chaotic dynamics (Ressler system).