Collective behaviors of animal groups may stem from visual lateralization-Tending to obtain information through one eye.

Animal groups exhibit various captivating movement patterns, which manifest as intricate interactions among group members. Several models have been proposed to elucidate collective behaviors in animal groups. These models achieve a certain degree of efficacy; however, inconsistent experimental findings suggest insufficient accuracy. Experiments have shown that some organisms employ a single information channel and visual lateralization to glean knowledge from other individuals in collective movements. In this study, we consider individuals' visual lateralization and a single information channel and develop a self-propelled particle model to describe the collective behavior of large groups. The results suggest that homogeneous visual lateralization gives the group a strong sense of cohesiveness, thereby enabling diverse collective behaviors. As the overlapping field grows, the cohesiveness gradually dissipates. Inconsistent visual lateralization among group members can reduce the cohesiveness of the group, and when there is a high degree of heterogeneity in visual lateralization, the group loses their cohesiveness. This study also examines the influence of visual lateralization heterogeneity on specific formations, and the results indicate that the directional migration formation is responsive to such heterogeneity. We propose an information network to portray the transmission of information within groups, which explains the cohesiveness of groups and the sensitivity of the directional migration formation.