Swarming transitions of self-propelled particles with anisotropic social interactions

Abstract

Collective motion in living systems is observed across many scales, from bacterial colonies to insect swarms, fish schools, and bird flocks. In all cases the motility of individual cells or organisms both is influenced by and, in turn, influences the motion of others. While the mechanisms by which individuals sense and respond to others differ greatly among species, simplified models that capture general principles of social interactions, such as the Vicsek model, have proved insightful. Here we introduce anisotropic sensory perception (a feature common to many animal species) into the Vicsek model in order to evaluate how this feature impacts collective motion. We find that, when the anisotropy 𝛼>0, meaning individuals are more influenced by neighbors ahead of them than those behind them, as the anisotropy becomes stronger, the swarming transition changes from the weak first-order transition observed for populations with isotropic perception to a stronger (i.e., more abrupt) first-order transition. Moreover, the critical noise threshold to achieve ordered motion decreases if 𝛼 increases from zero to positive values. By contrast, when the anisotropy 𝛼<0, indicating individuals pay more attention to rearward neighbors, as the anisotropy becomes stronger, the order-disorder transition remains first order (at the thermodynamic limit) but becomes increasingly weak (less abrupt), and the critical noise threshold required to reach ordered motion increases slightly. An even simpler front-back semicircle model and an anisotropic model with vectorial noise are employed to further validate the respective roles those ahead and behind play in the emergence of collective motion. Taken together, our results demonstrate that the contribution of neighboring individuals to the collective motion in such particle systems significantly depends on their relative position to the focal particle. Frontal neighbors primarily enhance the strength of the first-order transition, whereas rearward neighbors progressively weaken it.