  Coupled metronomes serve as a paradigmatic model for exploring the collective
behaviors of complex dynamical systems, as well as a classical setup for
classroom demonstrations of synchronization phenomena. Whereas previous studies
of metronome synchronization have been concentrating on symmetric coupling
schemes, here we consider the asymmetric case by adopting the scheme of layered
metronomes. Specifically, we place two metronomes on each layer, and couple two
layers by placing one on top of the other. By varying the initial conditions of
the metronomes and adjusting the friction between the two layers, a variety of
synchronous patterns are observed in experiment, including the splay
synchronization (SS) state, the generalized splay synchronization (GSS) state ,
the anti-phase synchronization (APS) state, the in-phase delay synchronization
(IPDS) state, and the in-phase synchronization (IPS) state. In particular, the
IPDS state, in which the metronomes on each layer are synchronized in phase but
are of a constant phase delay to metronomes on the other layer, is observed for
the first time. In addition, a new technique based on audio signals is proposed
for pattern detection, which is more convenient and easier to apply than the
existing acquisition techniques. Furthermore, a theoretical model is developed
to explain the experimental observations, and is employed to explore the
dynamical properties of the patterns, including the basin distributions and the
pattern transitions. Our study sheds new lights on the collective behaviors of
coupled metronomes, and the developed setup can be used in the classroom for
demonstration purposes.
