  In this paper, new schemes to synchronize linearly or nonlinearly coupled
chaotic systems with an adaptive coupling strength are proposed. Unlike other
adaptive schemes, which synchronize coupled chaotic systems to a special
trajectory (or an equilibrium point) of the uncoupled node by adding negative
feedbacks adaptively; here, adaptive schemes for the coupling strength are used
to synchronize coupled chaotic systems without knowing the synchronization
trajectory. Moreover, in many applications, the state variables are not
observable; instead, some functions of the states can be observed. How to
synchronize coupled systems with the observed data is of great significance. In
this paper, synchronization of nonlinearly coupled chaotic systems with an
adaptive coupling strength is also discussed. The validity of those schemes are
proved rigorously. Moreover, simulations show that by choosing some proper
parameter $\alpha$, the coupling strength obtained by adaptation could be much
smaller. It means that chaos oscillators can be easily synchronized with a very
weak coupling.
