Identifying how group interactions can help a system synchronize

Heart pacemaker cells, the flashing of fireflies, and people walking in step: These are all examples of synchronization, a system converging to behave in unison.

A widely used framework for studying this phenomenon describes a system as a set of coupled oscillators interacting in pairs. But real-world systems often involve interactions among more than two units at once, so Muolo et al. studied the effects of such higher-order interactions on synchronization.

“Synchronization is everywhere,” said author Marco Coraggio. “Sometimes we want it, as in a stable power grid or coordinated robots. Sometimes we want to avoid it, as in epileptic seizures, or in certain mechanical structures where it can cause problems, such as the famous wobbling of London’s Millennium Bridge.”

In comparing pairwise interactions and three-body “triangular” interactions, the group found that both play an important role in synchronization — to an extent.

“Think of an audience applauding, where people gradually fall into a common rhythm,” Coraggio said.

Once a common rhythm begins to emerge, a small amount of group interaction provides the extra pull needed to bring people clapping slightly faster or slower in toward the group. On the other hand, if the group interactions are too strong and the system starts from a disordered state, the population can split into opposing camps, like some audience members clapping on the beat while others clap off the beat.

Previous studies primarily focused on this detrimental impact of group interactions. Here, the researchers identified a sweet spot: a weak but nonzero group interaction strength where synchronization is highest. These weak group interactions naturally arise as small corrections in many physical systems.

“Our results show that the answer is not simply ‘more is better’ or ‘more is worse,’” Coraggio said. “The amount matters.”

The group’s work can help guide designs for engineered systems and better understand natural ones.

Source: “When higher-order interactions enhance synchronization: The case of the Kuramoto model,” by Riccardo Muolo, Hiroya Nakao, and Marco Coraggio, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0354134 .