Experimental study on dynamics of the multi-individual clapping interacting system

Abstract Clapping synchronization in the concert hall is one of the paradigmatic phenomena in daily life. Though the multi-individual clapping system has been widely investigated for its rich dynamics, little is known about the interaction - a foundation of synchronization. The goal of this study is to uncover the dynamics underlying interaction by observing individuals synchronizing clapping rhythms. We find three coupling states in the multi-individual clapping process: local synchronization, complete synchronization, and complete desynchronization. The statistical analysis shows that the clapping rhythms of arbitrary two individuals in the system exhibit long-range cross-correlations, i.e., the next clapping beat to be played by one individual is dependent on the entire history of the system. Surprisingly, we find that the mean-field for the system with a small number of individuals (N<5) is not necessary for the emergence of the synchronization process. To understand these findings, we propose a theoretical model for mutually interacting individuals, which can well reproduce the statistical characteristics of the multi-individual clapping process and suggest a physiologically motivated explanation for the occurrence of the multi-individual clapping synchronization. Though this study provides an understanding about the fundamental characteristics of the multi-individual clapping interacting system, the statistical framework and theoretical model may also be applied to study the dynamics of other complex systems with multiple coupled oscillators.