Synchronization of complex human networks

Synchronization in coupled systems is a ubiquitous phenomenon observed across diverse fields, from biology and astronomy to economics and politics. The synchronization of human networks, in particular, is crucial for societal functioning and individual well-being, impacting areas such as stock market dynamics, traffic management, and epidemic control. Previous research on human ensembles and crowd synchrony has been limited by noisy environments and a focus on all-to-all coupling, unlike the complex structures of real-world social networks. This study addresses these limitations by investigating the synchronization of professional violin players in a controlled setting, offering complete control over network parameters (connectivity, coupling strength, and delay). This experimental setup allows for a deeper understanding of the dynamics of human networks and the strategies employed to achieve synchronization.

Existing research on human synchronization often involves limited control over network parameters and noisy environments, typically focusing on all-to-all coupling. Studies have shown synchronization in various human activities, including stock market trading, pedestrian movement on bridges, concert audiences, dancers, and musical ensembles. However, these studies lacked the controlled environment and granular control over network parameters crucial for a complete understanding of human synchronization dynamics in complex networks. This study fills this gap by investigating synchronization in a controlled environment with a focus on complex coupling configurations.

The experiment involved 16 isolated electric violin players repeatedly playing a specially composed musical phrase. The players wore noise-canceling headphones, receiving audio input controlled by a computer-based mixing system. This system allowed precise manipulation of network connectivity, coupling strength, and delay between players. The playing period, phase, volume, and frequency of each player were monitored. Different network configurations were tested, including one-dimensional chains, all-to-all coupling, and two-dimensional lattices (square and triangular). The delay between coupled players was systematically varied. The study also developed and used extended versions of the Kuramoto model to analyze the synchronization dynamics, incorporating the unique abilities of human participants to adjust their playing periods and ignore conflicting signals.

The study reveals several key findings: 1. **Uncoupled players:** Without coupling, individual playing periods naturally deviate. 2. **Coupled players without delay:** In coupled networks, all-to-all configurations showed higher synchronization than one-dimensional chains. 3. **Two coupled players with delay:** Increasing the delay disrupted in-phase synchronization. Players adjusted their playing period to maintain synchronization, initially in-phase, then transitioning to an out-of-phase state at delays approximately equal to half the playing period. 4. **Even numbers of coupled players:** With even numbers of players (4, 6, 8), a similar pattern emerged with in-phase synchronization transitioning to vortex or arrowhead states and eventually highly stable out-of-phase synchronization at a delay roughly equal to half the playing period. 5. **Odd numbers of coupled players:** With odd numbers of players (3, 5), the out-of-phase state was unstable. Players resolved this by ignoring some connections, effectively changing the network topology to achieve a stable state. 6. **Larger networks:** With nine or more players, a combination of out-of-phase synchronization and vortex states was observed. 7. **Two-dimensional lattices:** In two-dimensional lattices, players either achieved out-of-phase synchronization by forming stable configurations (square lattice) or adapted by ignoring connections to form smaller, more stable sub-networks (triangular lattice). 8. **Numerical models:** Standard Kuramoto models failed to accurately predict the observed behavior, while modified models incorporating broad bandwidth and the ability to ignore signals better reflected experimental results. Three different strategies for choosing which connections to keep when conflicting inputs were encountered (similar playing period, similar phase, or random choice) led to the same outcome: stable out-of-phase synchronization through connection removal.

The results demonstrate that human networks exhibit distinct dynamics compared to those predicted by conventional models. The ability of individuals to adjust their rhythm and selectively ignore inputs leads to novel synchronization strategies. The emergence of out-of-phase synchronization and adaptive network topology modification highlights the flexibility and adaptability of human interaction networks. The findings have important implications for understanding complex systems involving human interaction, such as economic markets, social dynamics, and the spread of information or disease. The adaptive mechanisms observed suggest potential for improving the efficiency of decentralized systems.

This study provides novel insights into the synchronization of human networks by using a controlled experimental setup and a refined mathematical model. The ability of individuals to adjust their internal rhythms and selectively ignore disruptive signals is crucial for understanding human synchronization. Future research could explore different types of human interactions and network structures, investigating the role of communication and social dynamics in synchronization processes. The development of more sophisticated models that accurately capture human decision-making could yield valuable insights into various real-world scenarios.

The study focuses on a specific task (rhythmic playing) with professional musicians. Generalization to other types of synchronization and to less homogeneous populations requires further investigation. The size of the network was limited by the experimental setup. Furthermore, the relatively small sample size of participants in each configuration could have affected some of the statistical power of the results.