Audiences clapping together in unison are a familiar and powerful example of synchronization. In this paper, we report on a series of experiments aimed to characterize the dynamics of the clapping coupling system (CCS) and to reveal the regimes of the synchronous processes of the clapping interaction. Our results show that each oscillator in the CCS has inherent clapping characteristics, the interaction between the oscillators is a kind of prejudgment mode, the clapping coupling of two interacting oscillators aperiodically transits between synchronous state and asynchronous state. The results of the numerical simulations based on the theoretical model of the two-individuals clapping process verify well the experimental results. In particular, numerical results indicate that the intermittent dynamic of the clapping coupling system in the experiments consists in coexisting states of synchronous and asynchronous states perturbed by the fluctuation of the clapping period. Our research framework and results can be used not only to explain human clapping, but also to understand other rhythmic behaviors. CCS has the advantages of cheap materials and simple operation; it is very suitable for teaching demonstration and theoretical research on the synchronization phenomenon.

In recent years, clapping synchronization between individuals has been widely studied as one of the typical synchronization phenomena. In this paper, we aim to reveal the synchronization mechanism of clapping interactions by observing two individuals’ clapping rhythms in a series of experiments. We find that the two synchronizing clapping rhythm series exhibit long-range cross-correlations (LRCCs); that is, the interaction of clapping rhythms can be seen as a strong-anticipation process. Previous studies have demonstrated that the interactions in local timescales or global matching in statistical structures of fluctuation in long timescales can be sources of the strong-anticipation process. However, the origin of the strong anticipation process often appears elusive in many complex systems. Here, we find that the clapping synchronization process may result from the local interaction between two clapping individuals and may result from the more global coordination between two clapping individuals. We introduce two stochastic models for mutually interacting clapping individuals that generate the LRCCs and prove theoretically that the generation of clapping synchronization process needs to consider both local interaction and global matching. This study provides a statistical framework for studying the internal synchronization mechanism of other complex systems. Our theoretical model can also be applied to study the dynamics of other complex systems with the LRCCs, including finance, transportation, and climate.

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 inter-

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.