  We study the global synchronization of hierarchically-organized Stuart-Landau
oscillators, where each subsystem consists of three oscillators with
activity-dependent couplings. We consider all possible coupling signs between
the three oscillators, and find that they can generate different numbers of
phase attractors depending on the network motif. Here, the subsystems are
coupled through mean activities of total oscillators. Under weak
inter-subsystem couplings, we demonstrate that the synchronization between
subsystems is highly correlated with the number of attractors in uncoupled
subsystems. Among the network motifs, perfect anti-symmetric ones are unique to
generate both single and multiple attractors depending on the activities of
oscillators. The flexible local complexity can make global synchronization
controllable.
