WEAK AND STRONG SYNCHRONIZATION OF CHAOS

It is shown that synchronization in unidirectionally coupled chaotic s ystems develops in two stages as the coupling strength is increased. T he first stage is characterized by a weak synchronization, i.e., a res ponse system subjected to a driving system undergoes a transition and exhibits a behavior completely insensitive to initial conditions. Furt her increase oi the coupling strength causes the dimension decrease of the overall dynamics smd leads finally to a strong synchronization. I n this stage, the dimension of the strange attractor in the full phase space of the two systems saturates to the dimension of the driving at tractor.