Three People Can Synchronize as Coupled Oscillators during Sports Activities

We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter. Author Summary: Synchronization is very interesting as both a natural phenomenon and scientific topic in physical and biological systems. Examples include the Belousov-Zhabotinsky (BZ) reaction, the oscillation of metronomes, the flash of fireflies, and the calling behavior of Japanese tree frogs. The symmetric Hopf bifurcation theory, which is based on group theory, has been proposed as a useful approach for spatiotemporal pattern formation in coupled oscillator systems. This theory has been applied to various types of quadrupedal gaits in terms of symmetrically coupled oscillators, and to rings and chains of coupled oscillators of plasmodial slime molds. Here we report that the spatiotemporal pattern formation in three-person coupling during dynamic human movement, such as sports activity, conforms to symmetry-breaking theory. Our present study is salient because the spatiotemporal synchronization patterns among three people corresponded to the predicted patterns derived from symmetric Hopf bifurcation theory, as with pattern formation in slime molds, even though the actors were not connected physically but informationally. Moreover, although informational coupling between two people has been shown previously in well controlled experiments, we demonstrate three-person coupling using perceptual information in a real-life setting.