How nonreciprocity can influence collective motion

September 08, 2026

Collective motion can be strongly influenced by asymmetric interactions between individuals

Small deviationsin mutual interaction can cause species separation, although the agents do not repel each other

Stronger nonreciprocity gives rise to defect-driven chaos where small fluctuations propagate and reshape motion and density of the collective

Collective motion is commonly observed in nature, such as in groups of animals or also crowds of people. If all individuals follow exactly the same rules for movement, collective motion is quite robust. Yet, real collectives are rarely made of identical agents, as the individual behaviours can be different in strength or even intention. Scientists from the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) investigated how such deviations influence the resulting collective behaviour.

In a moving population, weak nonreciprocity can cause separation and sorting of two species, even though both species attract each other (left). Strong nonreciprocity, where one species is attracted but the other one repelled, causes a rotating state, affecting collective motion.

© MPI-DS, LMP

In a moving population, weak nonreciprocity can cause separation and sorting of two species, even though both species attract each other (left). Strong nonreciprocity, where one species is attracted but the other one repelled, causes a rotating state, affecting collective motion.

© MPI-DS, LMP

Their first study focuses on different types of agents interacting in a similar manner albeit with unequal strengths. The scientists found that such weak nonreciprocity may lead to population sorting even though the agents do not repel each other. “With small asymmetries in the interaction, the population reorganizes its spatial structure and composition, while still moving into the same direction”, explains Benoît Mahault, last author of the studies. Thus, even small deviations in the interaction patterns can create new structures in a moving collective.

In a second study, the scientists investigated how strong nonreciprocity can affect collective motion. In this scenario, agent A aims to align with B, whereas B is avoiding A. As a result, two populations can enter a chasing-like rotating state. “We found that in the case of strong nonreciprocal interaction, the synchronous ordered motion is fragile to spontaneous fluctuations”, Charlotte Myin, fist author of the studies, summarizes the findings.

The interplay between nonreciprocal interactions and collective motion thus gives rise to the new regime of defect-driven chaos. “Topological defects proliferate and can destabilize the global order, inducing strong density fluctuations”, she describes the effect.

Notably, these effects are not temporary disruptions, but continuously generate disturbances that reshape both motion and density of the collective. These findings can be relevant to describe migrating tissues including different cell types or to control heterogeneous robot swarms. The results may also be used to understand collective motion of animal groups or pedestrian crowds, where individual often have competing objectives or different roles.