Higher-order topology for collective motions

Abstract

Collective motions are prevalent in various natural groups, such as ant colonies, bird flocks, fish schools and mammal herds. Physical or mathematical models have been developed to formalize and/or regularize these collective behaviors. However, these models usually follow pairwise topology and seldom maintain better responsiveness and persistence simultaneously, particularly in the face of sudden predator-like invasion. In this paper, we propose a specified higher-order topology, rather than the pairwise individual-to-individual pattern, to enable optimal responsiveness-persistence trade-off in collective motion. Then, interactions in hypergraph are designed between both individuals and sub-groups. It not only enhances connectivity of the interaction network but also mitigates its localized feature. Simulation results validate the effectiveness of the proposed approach in achieving a subtle balance between responsiveness and persistence even under external disturbances.