Collective formation of flocks with population density Information: Asymmetry interactions and motifs

It has been reported that population density of biological groups may play an important role in the collective swarming, which, however, has been neglected in previous studies of mathematical models. In this paper, we propose a novel attraction/repulsion model driven by the population density and focus on the special collective process of our model. In our work, an agent can adjusts its asymmetric A/R(attraction/repulsion) function during the collective process under the influence of local population density. Such roles of asymmetric interactions different from the symmetric ones in traditional models have been analyzed by complex network theory with extensive illustrations, and different motifs of collective formation patterns have been visualized.