The Synchronous Behavior Of The Coupled Metronome

Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex systems,and also a classical setup for classroom demonstration of synchronization behaviors.The detection of synchronous patterns in coupled metronomes has long been a challenging problem in experimental studies.Traditional video-based techniques rely heavily on the camera functions and use some modern techniques of signal analysis.Here we propose the audio-based technique used in detecting the synchronous patterns.As the metronomes tick only twice in a cycle,the audio signals are featured by distinctly equidistant and separated pulses.Combining with features of synchronous patterns,we can easily identify the audio signals corresponding to each synchronous patterns.Meanwhile,this technique is not only more convenient and operational,but also accurate and reliable.First of all,using this new detection method,we study the synchronization patterns of three and four coupled metronomes system on one layer.Especially,we find a new synchronization state in four coupled metronomes system—generalized synchronization splay(GSS)state,in which each two metronomes are of anti-phase in a cluster,and metronomes between different clusters are locked to some value between 0 and ?/2,showing the feature of generalized synchronization.Then,we study the synchronization patterns of coupled metronomes on two layers.Previous studies of metronome synchronization have been concentrating on the symmetric coupling scheme,we turn to the asymmetric case by adopting the scheme of two layers of coupled metronomes.Specifically,we place two metronomes on each layer,and couple the two layers by putting one on top of the other one.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(ASP)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.