Flocking with random non-reciprocal interactions

Flocking is ubiquitous in nature and emerges due to short- or long-range alignment interactions among self-propelled agents. Two unfriendly species that antialign or even interact nonreciprocally show more complex collective phenomena, ranging from parallel and antiparallel flocking over run-and-chase behavior to chiral phases. Whether flocking or any of these collective phenomena can survive in the presence of a large number of species with random nonreciprocal interactions remained elusive so far. As a first step here, the extreme case of a Vicsek-like model with fully random nonreciprocal interactions between the individual particles is considered. For infinite-range interaction, as soon as the alignment bias is of the same order as the random interactions, the ordered flocking phase occurs, but deep within this phase, the random nonreciprocal interactions can still support global chiral and oscillating states in which the collective movement direction rotates or oscillates slowly. For short-range interactions, moreover, even without alignment bias self-organized cliques emerge, in which medium-size clusters of particles that have predominantly aligning interactions meet accidentally and stay together for macroscopic times. These results may serve as a starting point for the study of multispecies flocking models with nonrandom but complex nonreciprocal interspecies interactions.

💡 Research Summary

This paper investigates how completely random non‑reciprocal interactions (NRIs) affect collective motion in self‑propelled particle systems. The authors extend the classic Vicsek model by adding a random interaction matrix (J_{ij}) to the usual ferromagnetic alignment term (J_0). Each pair ((J_{ij},J_{ji})) is drawn from a bivariate Gaussian distribution with variance (J^2) and a correlation parameter (\lambda\in