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.