Weak and strong synchronization of chaos

Abstract

It is shown that synchronization in unidirectionally coupled chaotic systems develops in two stages as the coupling strength is increased. The first stage is characterized by a weak synchronization, i.e., a response system subjected to a driving system undergoes a transition and exhibits a behavior completely insensitive to initial conditions. Further increase of the coupling strength causes the dimension decrease of the overall dynamics and leads finally to a strong synchronization. In this stage, the dimension of the strange attractor in the full phase space of the two systems saturates to the dimension of the driving attractor.