Interacting with the farthest neighbor promotes cohesion and polarization in collective motion

The collective behavior generated from self-organization is one of the most prominent characteristics of animal populations. Typically, it is assumed that the interactions between individuals are average and synchronous. However, recent empirical studies have shown that interactions between individuals are selective and update their positions and directions asynchronously. Especially the feature factor of distance is widely used in theoretical modeling, but there is no detailed analysis and discussion on it in pairwise interaction. In this work, the effect of pairwise interactions on group motion is investigated under three distance features: nearest, medium, and farthest, based on a self-propelled particle model and combined with an asynchronous update scheme. The research results indicate that simple pairwise interaction can achieve group-level cohesion, especially by selecting the farthest neighbor instead of only interacting with the nearest neighbor, and the proportion of topological neighbors required to achieve cohesion is independent of the group size. In addition, we found that there is a visual angle range that is conducive to achieving cohesion and consistent movement in the group. This study provides insight into selective interaction, especially the great significance of the distance factor in pairwise interaction.