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 oi the coupling strength causes the dimension decrease of the overall dynamics smd 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.
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